Atom Optics Using an Optical Waveguide- Based Evanescent Field

ATOM OPTICS USING AN OPTICAL WAVEGUIDE- BASED EVANESCENT FIELD

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By Rajani Ayachitula Physics

The Ohio State University 2010

Dissertation Committee:

Professor Gregory P. Lafyatis, Advisor

Professor Richard Furnstahl

Professor Eric Herbst

Professor Linn VanWoerkem

Rajani Ayachitula

2010

ABSTRACT

The storage and manipulation of cold atoms near surfaces is of growing interest for applications like atom optics, the measurement of atom-surface interactions, and quantum information processing. In this work, we have constructed an apparatus to study cold atom physics above an optical waveguide. A two dimensional array of atoms trapped above our optical waveguide surface could serve as a quantum register, allowing for the individual addressing of single atoms from above or below using laser light. The first application of our system on the path to creating an addressable quantum register was to create a large area atom mirror.

To realize our atom mirror, we had two main tasks: creating the cold atom source to drop onto the surface and creating the atom mirror out of our waveguide. We designed our apparatus to move magnetically trapped cold atoms from the Rb source to the region above the optical waveguide to conduct the dropping experiment. Several cooling and trapping steps are necessary to create our cold atom sample that will be dropped on our waveguide surface. We show that we have successfully created a 3mK cold atom sample of 3 ! 108 atoms to drop onto our surface to realize an atom mirror. Our atom mirror consists of an optical waveguide with gratings evaporated on top, which we use to couple

ii light into the waveguide. By coupling light into a transverse electric mode of the optical waveguide, we create an evanescent wave above the waveguide surface. By coupling in tens of milliwatts of blue-detuned laser light, we create a sufficiently repulsive potential for a cold atom cloud. The strength of our repulsive potential is limited by scattering losses in our waveguide. Several processing steps that involve soaking the waveguide in a solution or heating the waveguide to high temperatures are required to manufacture our gratings on our waveguide surface. We show that we have created our optical waveguide with 20% coupling efficiency, while limiting our losses by maintaining a high quality waveguide surface.

Combining our optical waveguide and our cold atom sample in an ultra-high vacuum environment, we have a system to demonstrate our atom mirror. The bouncing is detected using a weak quasi-resonant probe beam that is monitored by a photodetector.

The atoms’ passage through the beam records the bouncing events. We have determined that our atoms must be at 10µK to properly resolve the bouncing. We have implemented the proper cooling mechanisms to cool our atoms in the ultra high vacuum environment to show this first bounce.

iii

For my mother, Nirmala and my father, Raj.

ACKNOWLEDGMENTS

First, I would like to thank my advisor, Professor Greg Lafyatis, for giving me novel ways to think about problems. When I was too lost in the trees to find the forest, he always helped me find my way to the back to the big picture. His insight has been valuable. I would also like to thank Professors Linn VanWoerkem, Eric Herbst and

Richard Furnstahl for serving on my dissertation committee, reading the various general exams, annual reviews and this thesis in the process, and asking questions that helped me push this work along.

When I first came into the lab, after finishing up coursework, I was greeted by an awesome group of people. Katharina Gillen was a great labmate and friend. I am sad I did not get to work with her longer, but regardless of where she is, she is an asset to physics. Andrei Modoran was always there to make a hilarious wisecrack or lift something really heavy, both of which I miss. James Keller, Rob Coridan, and Michael

Chmutov as undergraduates made valuable contributions to the lab and have no doubt become successful.

Without Justin McLaughlin, I may have not survived the times that the water lines broke, spraying water into our 500A power supply – I might owe him my life.

Furthermore, his aptitude with both electronics and music has been quite an asset to the

v lab. Jessica Roeder and Michael Eades are the newest additions to the lab and have already made useful contributions to the effort. Michael, with his extraordinary programming skills, has created LabView code we use regularly in the lab. And, he always kindly shares his donuts. Jessica is soon to take over the experiment and has really picked up things in a very short amount of time. I have no doubt that she will, in time, be leading a team of her own. I appreciate the effort that all three of these guys have put in the past year trying to get things up and running.

By the end, as the only graduate student working on laser cooling at Ohio State, I was lucky enough to be part of a network of great people to talk to about research. Of those individuals, Dr. Charles Sukenik , Dr. Jamil Abo-Shaeer, and Dr. Martin Zweirlein have been an important part of the end of this process for me. They deserve an award for patience for dealing with my discussions, texts, and emails.

I also must give a proper thesis shout out to “The Physics Boys.” Rakesh Tiwari,

Mike Fellinger, Rob Guidry, Jim Davis, and Kevin Driver have helped me in many ways, especially in the past year – for which I am grateful. For an only child, it is kind of nice to have so many little brothers in such close proximity.

I am lucky to have spent a good portion of my graduate school experience with astronomers, Juna Kollmeier, Rik Williams, and Amy Stutz. They shared my early- morning to late-night schedule, celebrated with me when I got the MOT and magnetic traps up and running, and were always up for 3 am visits to Kroger for various potato products – for which, I am quite thankful. Their current success is a testament to how great they are as people and scientists.

vi Another successful astronomer who deserves mention is Louis Strigari. We spent most of the first few years of graduate school fighting over problem sets and whose solution was “garbage” and whose solution was right. Although we were often frustrated with each other, I appreciate his passion for physics and the healthy debates we were somehow capable of having on no sleep at 4 am with teaching duties looming in a mere 3 hours.

I cannot forget to mention Maria Gonzalez-Sanchez, Lorena Galan-Platas, Maria-

Jose Roa-Garcia, and Agus Munoz-Garcia, who stayed wonderful friends despite my terrible Spanish vocabulary and inability to keep from becoming an abuela at 10pm.

Gracias a cada uno de vosotros por todo en esos anos. - la chica adentro de mi os da gracias tambien.

Other friends and colleagues without whom this thesis could not have been written and deserve thanks include: Aimee Bross, from whom I learned many of my processing skills and how to “take it out on the last hill” with running and with trying to finish this – which was so important; Jenn Holt, for having an amazing solution to any problem, big or small, as well as her appreciation for Bauhaus; Rita Rokhlin, who taught me to use the atomic force microscope and kept me in line; Tom Kelch, who always had a creative solution for how to build any part; The main machine shop guys, John

Spalding, John Shover, Pete Gosser and Josh Gueth, who would get my precision parts done quickly and perfectly and who were quick with a good “zipperhead” joke when I was injured, got staples and needed to lighten up; JD Wear, Brian Keller, Brian Dunlap, and Terry Bradley for dealing with all of my computer problems and questions; Kent

vii Ludwig for letting me borrow (on super-extended loan) several parts that I hope he sees again some day and for the constant reminders that there is a life outside of the lab; Dr.

Robert Davis, who was always willing to talk to me about noise problems; Mark Reed, who dealt promptly with any building issues I had; Harold Whitt and Chris Healy for making sure that my labs were always set up and for helping me get the demos together for my outreach presentations; Brenda Mellett, who answered any question I had regarding some obscure graduate school rule or regulation; Bob Wells and Mark Studer, who besides working on my surface mount electronics and packing all of my books, were quick with some hilariously inappropriate joke to get my day started.

John Spalding, Mark Reed, and John Shover deserve further mention for the actual moving of the evacuated apparatus to the new building (which was not easy).

They also skillfully brought down the heavy 500A power supply safely from above the evacuated apparatus so I could fix it, and then put it safely back up. The typed words do no justice to the care and skill with which they did either. They made a difficult process so seamless – for that, many thanks.

I also have to thank Katie Comer, Nicole Gibbs, Joelle Fenger, Glene Mynhardt,

Elizabeth Bentley, Joann Strunk, Alana Kumbier, Kristine Koehler, Jessica Kohlschmidt,

Carolyn Burke, Amanda Campbell, Judith Cusin, Siri Hoogan, and Richard Mitsak for helping me remember that I am not just the sum of my parts. Their support through the days when it felt like everything was broken, including myself, was invaluable. Zora

Neale Hurston begins one of my favorite novels with “Ships at a distance have every

viii man’s wish on board.” In that spirit, I await the news of your ships coming ashore with the tide.

When I was not in the lab, which was a rare event, I was lucky enough to be spending time with Michelle Pribe and Kim Reynolds. They tried to show me their world outside of the physics building. Just as I am finishing this work, I am happy to see them starting on their own journeys, Kim as the mother of Carter Andrew, and Michelle on her way to an MBA. I know they will do well in all of their endeavors and hope to give the same support I have received these many years. Carter deserves special mention for keeping me from becoming burned out in the lab. Some days, singing him to sleep with a few bars of “Baby Got Back” was just what I needed. Many years of dancing in the grocery store aisles and coming up with drunken witticisms awaits us, ladies. Aaron

Johnston, always quick-witted (and so modest), has helped me keep up my debating skills on many topics, especially with his inability to drop any subject. It is a shame we didn’t disagree about more. Chase Hurlow is also a great friend and musician - I can’t wait for more drum lessons! Jason Parry is always quick to make some reference to something completely insane to keep us all laughing into the night. I also have to thank these guys for helping me hone my all-important foosball skills.

Thanks to Michelle, Anne, and Sean of the St. James for always seeing to it that when evening mass was held, I was perfectly relaxed. While writing however, I was bound to the Po for a few weeks where Mark, Lorrie and Casey ensured that I was well fed and highly caffeinated.

ix Ian Mac deserves mention for reminding me that dancing is a cure for frustration and mental overload like no other. I know, regardless of where he is, he is curing someone of their ails. Surf’s up!

As “travelers in the wilderness of this world…the best we can find in our travels is an honest friend.” 1 While I have mentioned many of the amazing people I have met along the way, I have had a number of steady companions. Ashby Strassburger, whose support year after year never waned, has really helped me keep my eye on the prize. She is a gem and a rock, and I am lucky to have her in my life. Jim Soule is like a brother to me and has helped me countless times in the many years we have known each other

(including saving my life when I almost drowned at Rehoboth Beach) and especially in the past year, and for this I am indebted to him. Jerrah Edwards trudged through physics undergrad with me and has been a wonderful constant in my life ever since. I am pretty sure that the few times that we talk, the only silence is due to the fact that neither one of us can breathe because we are laughing so hard. This laughter has kept me sane. The only other people that I have laughed with as hard are Whitney Boon and Kristin

Pulkkinen. Whitney was always ready with an “awesome experience in med school” story to keep me in awe of humanity and laughing well into the night. Neither her wit nor her comedic timing can be surpassed. Kristin is well-read and always had a great book recommendation for whatever mood I was in - my favorite memory is our road trip to the Kentucky Derby while reading Hunter S. Thompson’s Shark Tales in the car – a perfect getaway to recharge. The value of the many years of laughter and support cannot

1 Robert Louis Stevenson

x be assessed. That being said, I cannot wait for free medical care and to finally meet

Matthew Modine! Emily Bond has also been a constant in my life for many years as well. Her quick wit and talent for the written word are impressive. I can finally tell her that I am done and ready to visit Spain! I also have to mention Pichai Raman and Anu

Dasika Raman. Anu and Pichai have been two of my best cheerleaders for the past few years and I am lucky to have them as family.

Last but not least, I want to thank my parents. Their continued sacrifice is what has allowed me to get as far as I have. My mother, although she knows very little of what this thesis is about, relates proudly that I “work with atoms” to anyone who will listen. This past year has been difficult for her but she has shown her strength in the face of it. The little of that that I can claim to have inherited has helped me finish this phase.

The end of this journey is dedicated to her and my father. Although my father did not see the completion of this thesis, he is a huge part of why it exists at all. He fostered my love of science and math early on by sharing his own love of it with me. He also taught me that if I really wanted something, I had to work at it. I really wanted this, I worked at it, and I hope he would have been proud.

VITA

December 11, 1977...... Guntur, India

June, 1995…………………………………………..Eleanor Roosevelt H.S. Greenbelt, MD

May, 2000…………………………………………..B.S., Physics University of Maryland, Baltimore County

November, 2004……………………………………M.S., Physics Ohio State University

May 2008…………………………………………..Hazel Brown Teaching Award AAPT Outstanding Teaching Asst Award

September, 2000 to Present………..………………Graduate Teaching and Research Assistant Ohio State University

Publications:

Bross, A, G. Lafyatis, R. Ayachitula, A. Morss, R. Hardman, J. Golden. Robust, Efficient Grating Couplers for Planar Optical Waveguides Using No- PAG SU-8 EBL. J. Vac. Sci. Technol. B. Vol 27 (6). November 2009. pp. 2602-2605.

Fields of Study

Major Field: Physics

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TABLE OF CONTENTS

ABSTRACT...... ii ACKNOWLEDGMENTS...... v VITA ...... xii TABLE OF CONTENTS ...... xiii LIST OF FIGURES...... xv LIST OF TABLES ...... xx INTRODUCTION...... 1 1.1 Atom-Light Interaction ...... 2 1.2 Optical Atom Mirror Work...... 3 1.2.1 Enhanced Evanescent Wave Mirrors ...... 9 1.2.1.1 Surface Plasmons ...... 10 1.2.1.2 Dielectric Layer Enhancement ...... 11 1.2.2 Gravito-Optical Surface Traps ...... 15 1.3 Optical Waveguide Atom Mirror ...... 18 1.4 Thesis Organization ...... 23 THEORY...... 24 2.1 Atoms in a Light Field ...... 24 2.2 Scattering Force: “Optical Molasses” and MOT Dynamics ...... 27 2.3 Atom Mirror Theory ...... 33 2.3.1 Properties of Evanescent Waves ...... 34 2.3.2 Slab Waveguide Introduction...... 37 2.2.3 The Dipole Force Introduction ...... 41 2.3.4 Dipole Potential Due to the Evanescent Wave...... 45 2.3.5 Van der Waal’s Potential...... 47 2.3.6 Diffuse Scattering...... 49 EXPERIMENTAL SETUP...... 52 3.1 Two-Chamber Vacuum System ...... 54 3.1.1 MOT-Loading Chamber ...... 54 3.1.2 Ultra High Vacuum (UHV) Experimental Chamber ...... 57 3.2 Lasers ...... 59 3.2.1 Free-running Laser Diodes ...... 60

xiii 3.2.2 External Cavity Feedback...... 62 3.2.3 Frequency Stabilization ...... 64 3.2.3.1 Temperature Control...... 65 3.2.3.2 Current Protection ...... 66 3.2.3.3 Grating and Current Feedback Controls ...... 68 3.2.3.4 Tapered Diode Amplifier...... 74 3.3 Atom Traps ...... 74 3.3.1 MOT Optical Setup...... 75 3.3.1.1 MOT Beam Intensity ...... 76 3.3.1.2 MOT Beam Polarization...... 80 3.3.1.3 MOT Magnetic Field ...... 81 3.3.1.4 MOT Characterization ...... 83 3.3.2 Transfer to the Magnetic Trap...... 86 3.3.2.1 Loading the Magnetic Trap ...... 87 3.3.2.2 Magnetic Trap Characterization...... 92 3.3.3 Transfer to the UHV Chamber ...... 94 3.4 Optical Waveguide ...... 95 3.4.1 Grating Fabrication ...... 97 3.4.1.1 Light Coupling Choice...... 97 3.4.1.2 Electron Beam Lithography ...... 100 3.4.1.3 Lithography Preparation ...... 103 3.4.1.4 Magnesium Fluoride Deposition...... 107 3.4.1.5 Lift-Off Procedure for MgF2 gratings...... 108 3.4.2 Waveguide Quality and Coupling...... 109 3.5 Elastic Bouncing of Atoms on a Waveguide ...... 113 RESULTS AND DISCUSSION ...... 115 CONCLUSIONS ...... 118 APPENDIX A: CIRCUIT DIAGRAMS...... 120 APPENDIX B: LABVIEW CODES...... 128 BIBLIOGRAPHY ...... 131

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LIST OF FIGURES

Figure 1.1 Electromagnetic mirror for matter waves. (Adapted from [21]) ...... 4

Figure 1.2 The first reflection of a thermal beam of sodium atoms. An evanescent wave is formed at the quartz-vacuum interface by total internal reflection of light in the quartz. The atoms are incident at a grazing angle, ϕ, with respect to the waveguide surface to limit the probability for spontaneous emission events. A probe beam measures the spatial separation of beams 1, 2, and 3. Beam 1 is the atom beam reflected by the atom mirror, Beam 2 is the part of the incident atom beam undeflected by the mirror and Beam 3 is a calibration beam to measure everything against...... 5

Figure 1.3 The first retro-reflection of cold atoms. Atoms are cooled to 25µK and dropped onto the mirror. To measure the reflected fraction, the magneto-optical trap was switched on upon the atoms’ return to the trapping region. To avoid collecting both slow moving and reflected atom populations, one of each pair of cooling beams is narrowed.. 7

Figure 1.4 Potentials seen by atoms as they approach the waveguide surface. a) Blue curve is the EW potential seen by the atom approaching the waveguide surface b) Red curve is the van der Waal’s potential seen by the atom approaching the waveguide surface due to the surface. c) Green curve is the total potential (due to both van der Waal’s and EW) seen by the atom as it approaches the waveguide surface...... 9

Figure 1.5 Total internal reflection in a prism with evanescent wave enhancement. The evanescent wave tunnels across the gap between the dielectric layer and the prism. The waveguide layer acts like an amplifying cavity, increasing the evanescent wave field strength in the vacuum region...... 12

Figure 1.6 a) Gravito-optic surface trap beam layout. The atoms can sit µms from the surface of the prism, with very little interaction with the laser radiation. b) Simplified energy diagram for Cesium. The excited hyperfine states are all very closely spaced. .. 15

Figure 1.7 The EW cooling scheme using a ladder of dressed states. The atom approaches the surface at 1 in the lower hyperfine state of Cs, shown here as 1,n . On

xv approaching the surface at 2, the atom scatters an EW photon and is pumped into the less repulsive dressed state 2,n ! 1 at 3. The weak repump laser completes the cycle, pumping the atom back into the lower hyperfine state shown in 4-6...... 17

Figure 1.8 Our optical waveguide mirror structure. We grating-couple our laser light into our optical waveguide such that it propagates 1cm. The gratings are 2.4mm! 1.6mm. . 19 The area of the evanescent wave mirror is about 2.0mm! 10mm. The enhancement of the evanescent wave field in the vacuum is due to the light repeatedly bouncing back and forth in the waveguide region...... 19

Figure 1.9 Atoms starting to fill a 2D array of atom traps. We want to create an “egg carton” evanescent field above the waveguide. To create a quantum register of atoms, we will fill each pit of the egg carton with a single atom...... 21

Figure 1.10 Nodal traps that lie at particular positions (y, z) (extending along the x- dimension) where the evanescent fields from the two TE modes cancel. These are our rod traps...... 22

Figure 1.11 Rod traps with transverse confinement by a hollow beam...... 23

Figure 2.1 Spatial dependence of the magnetic field during the magneto-optical trapping. The field gradient seen by the atoms is 7.8 G/cm ...... 28

Figure 2.2 Simple diagram detailing MOT beam polarization and magnetic field. Note the left circularly polarized light is only resonant for one magnetic substate. The application of the light gives a net scattering force to the resonant substate. Hence the substates are pushed toward the center of the magneto-optical trap...... 30

Figure 2.3 Energy level diagram for Rubidium including fine and hyperfine structure. The transitions used for the trapping laser and repumping laser are included. The detuning of the trap laser Δ trap is shown with respect to the trapping transition...... 32

Figure 2.4 Three-medium slab waveguide. The bottom layer is the substrate layer (made of fused silica), the middle layer is the waveguide layer (made of Ta2O5) and the top layer is vacuum. The phenomenon of “guided waves” (shown above) requires that nwaveguide > nvacuum, nsubstrate...... 33

Figure 2.5 Total internal reflection at the vacuum-waveguide interface. The incident light comes from the waveguide side, where some of the light is reflected back into the waveguide side and some is refracted into the vacuum. As the angle of incidence (θinc) of the incoming light increases (away from the surface normal), there will be a critical angle (θcrit) where there is no longer a refracted beam and all of the light is reflected back into

xvi the waveguide. This is the minimum angle required for total internal reflection to occur...... 35

Figure 2.6 Transcendental equation solved for neff ,m . The effective refractive index for each TE mode, neff ,m , is related to the mode propagation constant by !m = neff ,mk0 . The solid red line is the left hand side of the transcendental equation in Section 2.3.2. The dashed blue line is the right hand side of the same equation. We show only two TE modes supported by our waveguide. The TE0(TE1) mode is described by neff ,0 = 1.934 ( neff ,1 = 1.528 ). Higher modes have lower characteristic neff ,m values...... 40

Figure 2.7 The TE0 and TE1 transverse electric waveguide modes in our waveguide layer. Below is the substrate and above is vacuum. The TE0 is the lowest symmetric mode of the guide and TE1 is the lowest anti-symmetric mode. Note that for each, the evanescent wave tail (that “leaks out” of the waveguide layer) falls off exponentially as it permeates the vacuum layer. The evanescent waves in the substrate and vacuum regions have different fall-off rates...... 42

Figure 2.8 The ray diagrams of light coupled into TE0 and TE1 waveguide modes. Each is characterized by a mode angle measured with respect to the surface normal. The higher order modes are coupled in at a smaller angle. Furthermore, the higher order modes hit the waveguide surface more times as they travel down the waveguide, sitting closer to the surface such that their evanescent tails are longer...... 51

Figure 3.1 Two chamber vacuum system. We use a long cylindrical chamber to create our cold atom source and transfer that cold atom cloud to the UHV cell to perform the science. The two chambers are separated by two 5mm pinholes to allow for a better vacuum in the UHV cell than in the MOT cell...... 53

Figure 3.2 The MOT loading cell. The SAES Rb dispensers, the magnetic coils, the cold spot (covered with a layer of ice), and one of the two 5mm pinholes separating the experiment cell and MOT loading cell are all labeled. Furthermore, you can see two of the cameras used to line up the MOT cloud with the center of the magnetic trap...... 55

Figure 3.3 Cold spot touching the MOT cell. The cold spot ensures that Rb does not coat the inside of the MOT glass cell, which would block the incoming cooling laser beams.56

Figure 3.4 The UHV cell containing the waveguide ...... 57

Figure 3.5 Remote loading system with straight-through valve shown. The copper finger to which the waveguide arm is attached is shown as well as the three-axis manipulator that adjusts the position of the waveguide...... 58

xvii Figure 3.6 Tapered diode amplifier TA100. The seed beam comes in and is adjusted into the amplifier chip using the two mirrors located in the lower half of the above image. .. 60

Figure 3.7 Gain curves. a) Medium gain curve (Green). This is dependent only on the band gap of the semiconductor material used. The broad peak position changes with temperature. b) Laser diode junction cavity modes (Blue). This cavity has a normal mode structure like a Fabry-Perot etalon and gives a frequency dependent gain function that shifts with changes in diode temperature and injection current. Using grating feedback, we choose one of the blue peaked modes of the normal mode structure. By altering the angle of the grating, we choose different peaks. c) With the long external cavity, we get closely spaced modes that shift by changing the grating position...... 61

Figure 3.8 External cavity diode laser in Littrow configuration...... 62

Figure 3.9 Photo of external cavity diode laser...... 64

Figure 3.10. Beam layout for the DAVLL locking setup...... 68

Figure 3.11. Beam layout for saturated absorption setup...... 72

Figure 3.12 The saturated absorption (red) and DAVLL error signal (blue). The trap transition is shown in a) and the pump transition is shown in b). The thin dotted line shows our zero crossings in both cases...... 73

Figure 3.13 Beam layout on Optics Table. Beams leading to regions b, c, d, e, and f are located on the following figures: b) See Figure 3.10 c) See Figure 3.11 d) See Figures 3.14, 3.15 e) See Figure 3.29...... 76

Figure 3.14 The MOT trapping beam layout. This view is from the top looking down. Side views are located in Figure: 3.15...... 78

Figure 3.15 Side views of the beam layout. The pump beam is coupled to the trap beam path through the polarizing beam splitter...... 79

Figure 3.16 Coil assembly on the servo track ...... 82

Figure 3.17 Camera placement for MOT alignment...... 86

Figure 3.18 Homebuilt shutters. Our shutters are made from disassembled hard drives. The circuit diagram for the shutter drivers is included in Circuit Diagram A6 in Appendix A. Digital output TTL pulses drive the shutter drivers...... 90

Figure 3.19 a) CCD image of the magnetic trap. (False color added). The center of mass of the magnetically trapped atoms is 4mm above the waveguide. The waveguide surface

xviii is shown. b) The widths of the magnetically trapped cloud are shown. The top plot shows the width along the z-dimension parallel to the waveguide surface and the bottom plot shows the width along the y-dimension perpendicular to the waveguide surface. The full width half max (FWHM) of the cloud along z is 2.0mm and the FWHM of the cloud along y is 1.0mm...... 93

Figure 3.20. Grating pattern on the waveguide...... 96

Figure 3.21 Different light coupling techniques. a) End-butt coupling b) End-fire coupling c) Prism coupling d) Grating Coupling...... 98

Figure 3.22 Electron beam lithography machine cross-section...... 101

Figure 3.23 Inverted bilayer photoresist structure...... 102

Figure 3.24 Sample holder we designed for the ebeam...... 105

Figure 3.25 Mask to protect the waveguide during MgF2 thermal evaporation...... 107

Figure 3.26 a) Atomic force microscope images of the MgF2 gratings b) The height profile of the MgF2 gratings showing a grating profile height of 45-50nm...... 109

Figure 3.27. The waveguide cut on each side placed in the waveguide holder which extends into the UHV chamber. Note the visible center grating pair...... 110

Figure 3.28 The beam path for the waveguide coupled beam. By adjusting the calcite prism orientation, we adjust which type of mode we send in: TE or TM...... 111

Figure 3.29 Beam layout for probe beam into experiment cell...... 113

Figure 4.1 Typical photodiode scans of the atom cloud passing through the probe beam in time for three different runs. In the red scan, we observed the atoms were sitting closer to the probe beam light, causing the peak in the absorption prior to 40ms...... 115

Figure 4.2 Expected signal in the photodetector as a function of time after the atom cloud is released. As the cloud temperature is increased, the number of atoms initially passing through the probe decreases and the cloud temperature should be a less than 25µK to be able to see a bounce. The dotted red line shows the signal we can expect to see with our measured temperature...... 116

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LIST OF TABLES

Table 3.1 Magnetic trap loading sequence. This sequence (with our current alignment) gets us roughly 3 ! 108 atoms. To see an image of the magnetically trapped cloud, refer to Figure 3.21...... 92

Table 3.2 Photoresist processing information...... 103

Table 3.3. Properties of two lowest TE modes of our slab waveguide...... 112

CHAPTER 1

INTRODUCTION

It has been known for many years that laser light can be used to manipulate a neutral atom’s motion and intrinsic properties. The atom-laser interaction has allowed for the laser cooling of atoms to ultracold temperatures. It has become routine for atomic labs to be able to cool atoms to microKelvin temperatures. Neutral atoms have also been cooled down to sub-nK temperatures where they form novel forms of matter like Bose-

Einstein condensates [1,2] or degenerate Fermi gases [3]. As cold atoms provide a sensitive probe for measurement, the ability to cool down atoms to low temperatures opened the door to many discoveries. Precise measurements of the earth’s gravitational field [4,5] have been made possible by the use of cold atoms. The most precise clocks in the world are formed from cold atoms [6,7]. Ultracold atoms also allow the investigation of purely quantum mechanical phenomena such as entanglement. Many groups hope to manipulate such quantum effects exhibited by cold neutral atoms to create quantum computers or registers, (where the cold atom’s internal states would serve as qubits)

[8,9,10,11]. To perform quantum information processing, often it is important to maintain coherence, such that the atom does not pick up any unwanted phases (leading to information loss). An atom chip, on which cold atoms could be coherently manipulated

1 optically or magnetically, would provide a compact location to do quantum information processing [12,13,14]. The desire to make an integrated atom chip to coherently manipulate cold atoms brings us to the field of atom optics. Much of the chip-based atom optics work done to date uses the magnetic manipulation of atoms.

The permanent magnetic dipole moment of a paramagnetic atom interacts with a magnetic field via the Zeeman interaction. Using the Zeeman interaction, chip-based atom mirrors for cold [15,16,17] and Bose-condensed atoms [18,19] and chip-based atom lenses [20] have been realized. While much of the previous work on atom chips has used magnetic fields, there are distinct advantages to creating the chip-based atom optics devices all-optically. A larger variety of atoms can be controlled optically than magnetically. Additionally, with light, we can manipulate atoms in multiple magnetic substates at the same time and we are not limited just to paramagnetic atoms. To discuss the all-optical realizations, let us consider the characteristics of atom-light interaction.

1.1 Atom-Light Interaction

An atom in an inhomogeneous light field will feel two different forces. Details of these forces are given in Chapter 2. An atom’s absorption and subsequent spontaneous emission of light is responsible for the dissipative scattering force. The atom also feels a conservative dipole force as a consequence of the atom’s coherent absorption and subsequent stimulated emission of light. The dipole force may be understood as follows.

Due to the atom’s intrinsic polarizability, the light induces an electric dipole moment in the atom. This induced dipole moment in turn interacts with the field that created it. If

2 the frequency of the light field is tuned above (below) an atomic resonance, the atom will be repelled from (attracted to) the high intensity regions of the light. Another way to think about this is that in the presence of the light, the atom’s energy levels shift (as detailed in Chapter 2). The dipole force, which is the gradient of this energy shift, is important in creating atom optics devices. We will specifically discuss the atom mirror, which reflects a de Broglie matter wave like an optical mirror reflects a light wave

For atom mirror work, I will distinguish among reflection, specular reflection, and diffuse reflection. Reflection of an atom from the surface is characterized by the angle of reflection (measured from the surface normal) of the atom being equal to the angle of incidence of the atom. If the atomic motion does not abide by this law of reflection, the reflection is diffuse. Specular reflection requires a stronger condition than reflection in that the phase of the incident matter wave must be preserved upon reflection. This becomes important when creating an atom interferometer or performing certain quantum computational activities.

1.2 Optical Atom Mirror Work

First proposed by Cook and Hill in 1982 [21], the atom mirror is created by totally internally reflecting light at a vacuum-dielectric interface as shown in Figure 1.1. The light is tuned to the blue of the atomic resonance and is completely reflected back into the

Figure 1.1 Electromagnetic mirror for matter waves. (Adapted from [21])

dielectric medium. In obeying boundary conditions, some amount of the field leaks across the surface. The wave that “leaks through” the boundary is wave is called an evanescent wave. This evanescent wave (EW) field propagates parallel to the dielectric surface and falls off exponentially perpendicular to the surface. The EW potential depth increases with increased intensity and decreases with increased detuning from the atomic resonance.

Cook theorized [21] that there were two primary conditions for reflection of an atom off of the EW. First, the atom’s kinetic energy perpendicular to the surface must be less than the maximum of the EW potential at the surface. Second, the ratio, R, of impulse on the atom parallel to the surface to the impulse on it perpendicular to the surface must be small. The maximum angle of incidence allowed for reflection is a

function of this ratio given by !inc =ArcTan(R). 4

Balykin, in 1987 [22,23] first experimentally realized the reflection of alkali atoms off of an EW atomic mirror. They created their EW mirror potential by totally internally reflecting laser light in a quartz plate held in vacuum. The laser light was

23 tuned to the blue of the 3S1/2 → 3P1/2 transition of Na by 2GHz. In keeping with

Cook’s constraints for reflection, they kept the perpendicular velocity low by sending their thermal sodium beam in at grazing incidence with respect to the surface. Refer to

Figure 1.2 for the experimental setup. Roughly perpendicular to the mirror they directed a weak resonant probe beam to detect the reflected atoms. Sending their thermal atoms at

the mirror at a grazing incidence angle less than !inc (shown above), they saw nearly

5 100% reflection. As this angle was increased towards the surface normal to !inc , the reflection of the atoms decreased to 10%. More atoms either hit the surface or were scattered diffusively. In restricting the velocity perpendicular to the surface, they kept their atoms from penetrating as deeply into the EW. If the atoms are exposed to the radiation for a short time, they do not scatter enough photons to cause them to reflect diffusively [21].

Kasevich and Chu [24] were the first to realize an atomic mirror for normally incident cold atoms. The slower atomic velocities of their cooled atoms allowed them to drop the cold atoms directly onto the surface and observe retro-reflection. These laser cooled cesium atoms of ~25µK were dropped onto an EW mirror located 2 cm below.

See Figure 1.3. To create the EW, they coupled a Gaussian beam into a Dove prism. By coupling in 1W of 589nm-laser light tuned below atomic resonance by 400MHz they created an EW potential created with light of intensity1 4.3W/cm2 at the prism surface.

The atoms were detected by using a retro-reflected resonant probe beam kept above the atom mirror directed perpendicular to the motion of the atoms. Upon dropping 107 atoms onto the surface, they saw two bounces, retaining only 0.3% of their atoms each time.

The reflected atom fraction was limited in large part by the area of the mirror. Most of the atoms were lost because they did not interact with the reflective potential. Due to the transverse Gaussian EW intensity profile, the mirror potential was also slightly convex even if the surface itself was flat.

1 The intensity of an electromagnetic field is however normally described by the magnitude of the Poynting vector. However, the Poynting vector for the evanescent wave is zero perpendicular to the surface. Therefore, use the term intensity to mean the amplitude squared of the EW electric field magnitude. 6

It was realized that in replacing the flat EW mirror with a concave EW mirror, the confinement time of the atoms could be increased. To create a concave parabolic evanescent wave mirror, Aminoff et al. and Wallis et al. [25,26] carved out a spherical parabolic cavity in the surface of a prism. They created the EW mirror by totally internally reflecting 800mW of laser light in the parabolic cavity region, creating a 1mm2 mirror. The light was blue-detuned from the 6S1/2|F=4> → 6P3/2|F=5> transition in cesium. Upon dropping 107 cesium atoms cooled to 4µK, they noted 8 bounces, retaining

73% of their atoms after each bounce. Because of the extra transverse confinement, they retained more atoms. The atom loss was predominantly due to the stray light from the mirror beam, collisions with the background gas, and possible misalignment of the mirror

7 with the vertical axis such that the atoms were not dropped over the center of the mirror.

Losses were not due to spontaneous emission during reflection.

When an atom approaches the repulsive EW potential, it can also come close enough to the surface to feel the van der Waal’s (vdW) force. Depending on the intensity of the EW, the turning point can be within 100 nm of the mirror. Within this region, the vdW force considerably lowers the total potential close to the prism surface. See Figure

1.4. Classically, as the atom approaches the surface, the light induces an electric dipole in the atom, causing it to be attracted to its own image dipole in the surface. If there were no atom-surface interaction, one would expect that as you lower the total potential below the incident kinetic energy of the atoms, the reflection would cease. To test this threshold,

Aspect et al. [27] conducted an experiment dropping cold rubidium atoms on a far blue- detuned EW mirror. They measured the reflection intensity threshold as a function of the kinetic energy of the incident atoms. In varying the height of the total potential by varying the strength of the EW potential, they measured the barrier height required to see reflection. While they expected to see reflection at a barrier height equal to the kinetic energy of the atoms, they observed a reflection threshold of three times what they expected. The atom-surface potential was too important to ignore. One way to avoid surface interactions is by increasing the EW intensity. Increasing the intensity pushes the turning point further away from the surface such that the vdW potential has a minimal effect on the incident atoms.

U(y) !!

Umax !!

y(nm)

1.2.1 Enhanced Evanescent Wave Mirrors

Beyond the simple dielectric-vacuum interface, atom mirrors based on two distinct surface treatments had a stronger EW fields in the vacuum. Esslinger et al. [28] coated their prism with a silver layer. The evanescent wave supported by the prism excites charge density waves that propagate along the metallic surface and induce a large evanescent enhancement in the vacuum [28,29]. Kaiser et al. [30] added thin dielectric layers to the prism supporting their EW light to create an amplifying cavity to enhance their EW field into the atom-mirror interaction region [30,31]. 9

1.2.1.1 Surface Plasmons

A surface plasmon is a coherent electron oscillation that exists at an interface between metal and a dielectric. Light waves of the correct polarization2 and frequency can excite surface plasmons. One can couple in a light beam into the dielectric such that it undergoes total internal reflection at the dielectric-metal interface. The propagation

2!nprism sin"inc vector of the EM wave inside the dielectric is k = where !0 is the free- #0

space wavelength of the light, nprism is the index of refraction of the prism, and !inc is the incident angle of the light. Inside the metal layer, the complex plasmon propagation

2! $ # ' vector is given by 1 where ' '' is the relative permittivity of kplasmon = & ) !1 = !1 + i!1 "0 % #1 + 1( the metal. Most of the energy (~95%) from light coupled in at the optimal incidence

angle, !inc , which can be found such that k = kplasmon , will be transferred to the plasmon wave. The resulting EW field on the vacuum side of the metal film can be two orders of magnitude higher than seen with the bare prism [30]. The large enhancement allows useful atom mirrors to be created by low laser powers, of a few milliwatts [28, 29]. The plasmon enhancement was first demonstrated by Esslinger et al. [29] in reflecting thermal

2 The electric field vector of the incident laser light must be parallel to the plane of incidence giving a Transverse Magnetic (TM) wave. TM waves are briefly mentioned in Chapter 2. 10 rubidium atoms using only 6mW of power and an evanescent field enhanced by a factor of 60.

The metallic surface treatment has its drawbacks. As a plasmon travels along the surface, it loses energy to the metal due to absorption and decays with the square of the electric field such that after propagating a distance z with kz, the plasmon has decayed by a factor of e!2kz z . The plasmon can also lose energy due to surface irregularities [32].

Furthermore, the decay length of the evanescent wave is determined purely by the material properties and cannot be altered to create a steeper potential. Therefore, the probability for spontaneous emission for a given intensity (which is decreased for steeper potentials) at a reflection is set. Finally, the films become damaged over time [29, 31,

32] due to the heat dissipation (from the laser field) in the metal layer. Since the heat dissipation is an issue and over 95% of the light coupled in is transferred to the surface plasmon mode, it is beneficial to use lower intensity light to avoid damage to the metallic films. The enhancement due to the plasmon degrades accordingly. Esslinger et al. found that the films could only be used reliably for a few days.

1.2.1.2 Dielectric Layer Enhancement

Another surface treatment to enhance the EW field was realized by Aspect et al.

[31]. Starting with their bare (n=1.894) prism, previously used to create a flat un- enhanced EW mirror, they added a gap layer of SiO2 (n=1.49) followed by a cavity layer of TiO2 (n=2.387). When light is totally internally reflected in the prism, the incident beam couples to the waveguide mode by tunneling across the SiO2 gap layer to the cavity 11 layer. See Figure 1.5. To get the coupling into the cavity mode, the component of the propagation vector along the interface is matched to the propagation vector of a transverse mode of the cavity. In this way, the electric field in the cavity as well as of the evanescent wave is resonantly enhanced. The enhancement in the cavity layer can be understood as the buildup in a two-mirror cavity with one low transmission input mirror

(the cavity-gap interface) and a 100% reflection output mirror (the cavity-vacuum interface). Because of the buildup of the field in the cavity layer, modest incident power can result in a large enhancement of the EW field.

12 Aspect et al. dropped a cloud of 2 ! 108 atoms at 20µK onto the waveguide surface from

14mm above the surface. A weak retro-reflected4 quasi-resonant probe beam was placed between the surface and the dropping point to study successive passages of the atom cloud. They found for a fixed laser power that their atoms could be reflected with a detuning as large 140GHz, where their spontaneous emission probability upon reflection

I was <1%. The height of the potential barrier goes as . By measuring the largest ! detuning of laser light (of a given intensity) that would reflect atoms of a given kinetic energy, they could get a measure for the enhancement due to the dielectric layer. They expected an enhancement by a factor of ~2600. They measured an enhancement 5 times smaller. This large discrepancy is explained by the van der Waal’s interaction lowering the potential barrier at the surface.

Because preserving coherence is a requirement from some applications of atom mirrors, they also tested the coherence of the de Broglie wave upon reflection. A true test of coherence would be to interfere bounced atoms with unbounced atoms and look for interference fringes. However, incoherent reflection would not be the only reason for low visibility fringes. Instead, they decided to check for the necessary but not sufficient condition that a collimated beam of atoms obey the law of reflection. Their reasoning lie in the fact that a process like spontaneous emission that would destroy the spatial reflection of a collimated beam would also destroy the phase coherence of the de Broglie wave.

4 The probe beam is retro-reflected to cancel the radiation pressure that will act to heat the atoms and interfere with their downward trajectory. 13 In dropping an atom cloud with a velocity distribution of full width

87 !v = 2vr where vr is the single photon recoil velocity of the Rb atom. They monitored the longitudinal widths of the atom cloud before and after reflection to get a measure of how the velocity spreads changed both parallel and perpendicular to the mirror surface.

They found reflection for the velocity components perpendicular to the surface and diffuse reflection for the velocity components parallel to the surface. The diffusion of

full width 9vr corresponds to 40 spontaneous emission events during a single bounce, which is inconsistent with the detuning and intensity in their experiment. With their experimental parameters, they expected a spontaneous emission probability of <1%.

The diffuse reflection initiated an investigation of how the surface roughness of the mirror contributes to the diffuse reflection of the atoms. They measured the diffuse reflection of atoms off of bare prisms of rms surface roughness varying from 0.9Å to

2.3Å. The vertical width of the atom cloud in each case was consistent with a specular bounce. However for the transverse cloud width, they found that only the prism with the smallest 0.9Å rms roughness produced non-diffused and assumed specular reflection. To ensure that the diffuse reflection was not due to spontaneous emission for the rougher mirrors, they varied the detuning for a given laser power. The transverse width of the atom cloud after bouncing was the same for all detuning values. This experiment showed how important surface roughness is in creating a coherent atom mirror.

14 1.2.2 Gravito-Optical Surface Traps

In another direction, some groups decided to trap atoms using the EW potential.

Gravito-optical surface traps may be used to efficiently remove energy from atoms and produce a BEC. [34,35,36]. As in Figure 1.6a, traps were created using a far detuned hollow beam superimposed on a parabolic EW mirror such that confinement was achieved horizontally and vertically. The goal was not to bounce the atoms elastically anymore but to cool them down such that they rested close to the surface of the parabolic mirror.

Gravito-optic surface traps (GOSTs) allow a different way to cool atoms. The principle of cooling in a GOST is as follows. The ground state of cesium or any alkali is

15 split into two hyperfine sublevels, one energetically higher than the other. The cesium atom is modeled as a three-level system with one excited state (P3/2|F’>) and two ground states (S1/2|F=3> and S1/2|F=4>), which are separated by 9.2GHz in the case of cesium.

For the energy diagram see Figure 1.6b. The EW is blue-detuned from the

S1/2|F=3>→P3/2|F’> resonance by Δ and blue detuned from the S1/2|F=4>→|P3/2> by (Δ +

9.2GHz). An inelastic reflection takes place when the atom enters an EW potential in the lower hyperfine ground state (F=3) and, by scattering an EW photon during the inelastic reflection, is pumped into the less repulsive upper hyperfine ground state (F=4). The cooling cycle is finished when the atom gets pumped back into the lower hyperfine state with a weak pump laser. In the process, the atom has lost energy

2 !!I0 $ 1 1 ' KElost = & # ) 3 8I % " + 9.2GHz "( sat There is also some energy lost in the spontaneous emission to end the cooling cycle if the pumping beam is directed downward onto the EW mirror surface [26]. Figure 1.7 shows the dressed ladder picture of the cooling process. As the atom scatters photons from the

Figure 1.7 The EW cooling scheme using a ladder of dressed states. The atom approaches the surface at 1 in the lower hyperfine state of Cs, shown here as 1,n . On approaching the surface at 2, the atom scatters an EW photon and is pumped into the less repulsive dressed state 2,n ! 1 at 3. The weak repump laser completes the cycle, pumping the atom back into the lower hyperfine state shown in 4-6.

EW while in the more repulsive lower hyperfine state, relaxes to the less repulsive upper hyperfine state, and is optically pumped back to the lower hyperfine state again, the atom climbs down the dressed state ladder.

In one experiment, Ovchinnikov et al. [36] cooled and trapped an ensemble of

~105 cesium atoms to 3µK such that the trap sat about 20µm from the prism surface.

GOST traps are particularly attractive for the purpose of making dense ultracold samples.

Since the atoms are not exposed to light for very long, they stay predominantly in the lower hyperfine ground state, where spin-exchange collisions are suppressed and densities of 1013atoms/cm3 could be reached. Rychtarik et al. [40] in 2004 reached such a density regime and thereby created the first BEC of cesium atoms in a GOST.

1.3 Optical Waveguide Atom Mirror

The research presented in this thesis concentrates on creating a large area atom mirror with a strong EW potential by using a modest input power (8mW/mm of width) and 6.8GHz detuning. This is the first atom mirror created by coupling light directly into an optical waveguide. Coupling the light directly into the waveguide requires less input power to create a strong EW potential than conventional prism-based atom mirrors.

To perform our atom mirror experiment, we create a repulsive evanescent mirror field by coupling laser light into our optical waveguide. Our cold Rb source sits above the waveguide in a magnetic field. A near-resonant probe “light sheet” sits below the atom cloud and is monitored by a photodiode to detect the motion of the atoms. Once the magnetic field is turned off, the atoms fall through the probe light, absorbing on their way. In this way, we detect the atoms falling, hitting the EW, and bouncing back up.

To create our repulsive EW potential, we couple light into the optical waveguide

(See Figure 1.8) using a grating. We have evaporated three pairs of MgF gratings onto the waveguide film surface. Figure 3.20 shows the grating pattern. The light is coupled into one grating (of the center pair) and coupled out of the opposing grating situated

10mm from the input grating. The polarization of the input light is adjusted such that we couple into a transverse electric mode of the waveguide that is characterized by an electric field polarized only along the x-direction. The evanescent field that leaks out of the waveguide surface is enhanced by the multiple bounces in the guiding layer much like light amplified in a cavity.

Mode angle x z

Figure 1.8 Our optical waveguide mirror structure. We grating-couple our laser light into our optical waveguide such that it propagates 1cm. The gratings are 2.4mm ! 1.6mm. The area of the evanescent wave mirror is about 2.0mm! 10mm. The enhancement of the evanescent wave field in the vacuum is due to the light repeatedly bouncing back and forth in the waveguide region. A major consideration for previous atom mirror work stood with reducing the scattering force experienced by an absorbing atom while still maintaining the strength of the dipole force. In previous experiments, the strength of the EW potential is limited by the fact that it is created by a single bounce in a prism. To ensure a strong potential in this case,

Watts of input power are required. With a large intensity beam creating the EW, to decrease the possibility for spontaneous emission, the laser detuning was made high on the order of 100GHz. At large detunings for a given light intensity, the dipole potential strength is reduced. For a given detuning, it is advantageous to enhance the EW field without increasing the intensity of the light. Kaiser et al. [31] enhanced the EW potential due to the bare prism by adding a cavity layer to act as a buildup cavity.

We couple laser light directly into the waveguide using grating couplers. As a result of the multiple reflections of the light as it is guided down the optical waveguide, 19 the EW field in the vacuum region is enhanced. As a result of this enhancement, we only have to couple in milliwatts of power at a much lower detuning than previous experiments. Decreases in the reflecting potential are limited only by losses in the waveguide. Furthermore, the size of the mirror along the propagation distance is the distance between the input and output gratings, 10mm. The width of the grating limits the size of the mirror in the transverse dimension. In this way, we make a large-area EW mirror by sending in modest intensities of light detuned by 6.8GHz from the 5S1/2|F=2>

87 → 5P3/2|F=3> transition in Rb .

Using several cooling and trapping steps, we have prepared our cold atom sample containing 3 ! 108 87Rb atoms that we dropped onto the surface. We determined that our atoms are at 3.4mK. We need to get the atom cloud cooled to 10µK to resolve the first bounce. Upon cooling, we will monitor the first bounce of the atom cloud off the waveguide. After recording this first bounce, we will use the EW itself to cool the atoms.

Using the EW, we can cool the atoms in a fashion similar to that used in making

GOST traps. We have a hollow beam that will be employed to constrain the atoms in the transverse dimension. Once the atoms are cooled, they will settle in the potential minima of the EW. This is the first step in the overall goal of this project of creating a 2D-array of single atom traps that are easily addressable by laser light from above and below for use in creating a quantum register. See Figure 1.9.

On the path to creating this quantum register, we will create an array of rod-like traps in the evanescent waves above the waveguide. To do this, we will interfere two different transverse electric modes of the waveguide, creating a standing wave with alternating potential minima and maxima in the EW above the waveguide surface. This is described theoretically in [52]. The evanescent wave from each transverse electric mode of the waveguide is characterized by a different decay rate and a different mode angle as shown in Figure 1.8. The higher modes have smaller mode angles and penetrate more deeply into the vacuum region. If we couple light with the appropriate polarization into the two modes of the guide, we will see the interference of the two modes. Above the waveguide, there will be a single point y above the waveguide at certain points z along the guide length where the fields from the two modes will cancel. As shown in 21 Figure 1.10, we can trap atoms at these nodal lines that lie at particular (y, z) locations.

These extend along the x-dimension.

Figure 1.10 Nodal traps that lie at particular positions (y, z) (extending along the x- dimension) where the evanescent fields from the two TE modes cancel. These are our rod traps.

We also need confinement on the edges of the rods such that the atoms do not spill out of the edges of these potential minima. For this, we will superimpose a thin- walled hollow beam onto the surface as shown in Figure 1.11 to constrain the atoms.

22 x

z y

Figure 1.11 Rod traps with transverse confinement by a hollow beam.

1.4 Thesis Organization

Chapter 2 provides a mathematical description of the tools needed to create an atom mirror. I discuss the forces involved close to a surface, as well as how those forces impact the atom reflection. Chapter 3 describes the features of our experimental system.

Chapter 3 also details the manufacture of the waveguide gratings, the creation of the cold

Rb atoms, and specifics of the bouncing experiment. Chapter 4 gives a discussion of the results of the atom mirror experiment. Chapter 5 contains our conclusions and future work that is planned.

CHAPTER 2

THEORY

2.1 Atoms in a Light Field

A two-level atom in a light field will experience two forces, the scattering force and the dipole force. The light field will act to polarize the atom. This polarization will have an in-phase component giving the dipole force and an out-of-phase component giving the scattering force. These forces due to the light will affect the relative populations in the two levels as well as the energy levels. In the presence of laser radiation, the atomic energy levels will shift. This is known as the A.C. Stark Shift. To understand this level shift, we first consider a two-level atom, with a polarizability, ! , in !" an electric field, E , due to the laser light. We will treat this atom in the light using the semi classical approximation. The ground (excited) state of the two-level atom is given by g ( e ). The sum of the atomic Hamiltonian and the laser –atom interaction is given by

ˆ ˆ ˆ Htot = H 0 + H int

24 where Hˆ is the field-free Hamiltonian with eigenvalues, E and E = E + !! , the 0 g e g 0 lower and upper energy states respectively with resonant frequency ! 0 as the frequency

ˆ separation between the two states. The interaction Hamiltonian is given by H int . The !" ! ! laser electric field E induces a dipole moment in the atom given by d = er . The dipole moment in turn interacts with the field that created it resulting in an interaction energy given by ! "! Hˆ d E . int = ! • The interaction Hamiltonian allows for dipole transitions between the ground and excited states such that the total Hamiltonian operator is given by

! "! " H !d • E % Hˆ = $ 0 ' . total ! "! * $ !(d • E) H 0 ' # & !" " # ! Given a laser electric field, E E (r) cos( t) with the unit polarization vector and = 0 ! "laser ! laser frequency,!laser , we can characterize the strength of the atom-light interaction. We introduce the Rabi frequency ! , given by

eE !(r) = 0 e r g ! such that the total Hamiltonian matrix elements with Eg=0 can be expressed as

$ ' !! 0 "!#(r)cos!lasert H = & ) total & * ) % "!# (r)cos!lasert 0 ( where the Rabi frequency is the coupling between the upper and lower energy states

and!laser is the laser tuning. By solving the Schrödinger time-dependent wave equation

25 with the total Hamiltonian of our atom using the rotating wave approximation, we get the following solutions:

2 2 !! 0 ! "(r) + (!laser # ! 0 ) E± = ± , 2 2 where E+(E-) is the excited state (ground state) energy eigenvalue of the atom in the presence of the radiation. Note that the effective Rabi frequency is given by

2 2 !eff = !(r) + ("laser # " 0 ) .

We can solve the time-dependent Schrödinger equation with the above total

Hamiltonian using the rotating wave approximation ! " ! ! ! + ! supposing ( laser 0 laser 0 ) that the atom is in its ground state. We would find that the probability of the atom being

2 " !(r) % " !eff (r)t % in the excited state 2 . The atom oscillates sinusoidally Pexcited = $ ' sin $ ' # !eff (r)& # 2 & between the ground and excited states at the effective Rabi frequency.

This treatment of the two-level atom will produce level shifts and population time evolution that does not include spontaneous emission term, so it must be added manually.

In the far-detuning limit however, the atom does not scatter many photons. The damping term is much more important with the laser tuned close to resonance, when we laser cool for instance. In this case, spontaneous emission adds a damping term to the time evolution of the atomic states. When we include spontaneous emission, an atom in a light field no longer evolves in a purely oscillatory fashion. We find the steady-state

!2 4 probability for an atom to be in the excited state is Pexcited = . 2 !2 #2 " + 2 + 4

26 2.2 Scattering Force: “Optical Molasses” and MOT Dynamics

The absorption and spontaneous emission of photons is a dissipative process and allows for the cooling of neutral atoms to µK temperatures. The force associated with this is the aforementioned scattering force. The magnitude of the scattering force is

F = (!k) ! R scattering scattering where !k is the magnitude of the momentum of the incoming photons and Rscattering is the frequency of spontaneous emission by an atom, which is proportional to the excited state population. The scattering force is then shown to be

$ "2 ' 4 Fscattering = !k!& 2 2 ) & # 2 + " + ! ) % 2 4 ( where the light is detuned from an atomic ground-excited state transition frequency by δ and Ω is the Rabi frequency.

In cooling the atoms, we use three orthogonal laser beams, intersecting in a region with Rb atoms. With the incident laser tuned near resonance, the atom scatters incoming photons, absorbing and subsequently spontaneously emitting a photon in a random direction. Cooling is achieved by making the photon scattering rate velocity-dependent.

By tuning the laser to the red of resonance, the atom selectively absorbs photons that they see Doppler-shifted into resonance.

If an atom is moving towards the laser beam, the frequency the atom sees is shifted higher than its rest-frame resonance frequency. Conversely, if the atom is moving away from the laser, the atom sees a downshifted frequency. If we tune the frequency of the laser such that it is below the resonance frequency, the atom will scatter photons at a 27 higher rate if it is moving toward the laser beam than if it is moving away from it. With the three pairs of counter-propagating laser beams in all three dimensions, we are left with the velocity dependent force described above and can perform cooling by adjusting the laser frequency appropriately. Because of the viscous nature of this force, this configuration is known as an “optical molasses.” If there is no spatial dependence to the optical force, the atoms will simply immediately diffuse out of the molasses region.

A magneto-optical trap (MOT) uses a position dependent magnetic field to bring about a spatial dependence to the frequency dependence of the optical forces responsible for cooling the atoms. The principle of the MOT is as follows. The field has a linear spatial dependence as shown in Figure 2.1. The spatially dependent Zeeman shift of the

Figure 2.1 Spatial dependence of the magnetic field during the magneto-optical trapping. The field gradient seen by the atoms is 7.8 G/cm

28 atomic energy levels regulates the scattering rate of an atom at a particular distance from the trap center. The net effect of this is that the atoms are pushed toward the center of the trap, increasing the trap density and localizing the atoms in space.

While the total angular momentum states of Rb are J=1/2 and J=3/2, we will consider a simplified model to understand the dynamic of a MOT in one dimension.

Consider a two-level atom in a magnetic field has a characteristic magnetic dipole ! moment given by . In our simplified model, we assume the atom’s ground (excited) µ state has a total angular momentum given by Jg=0 (Je=1). Refer to Figure 2.2. The atom interacts with the field via the Zeeman effect. The interaction energy of the atom in a ! magnetic field which points along the z-axis, B = B , is given by z

Emagnetic = !µz Bz = gJ µBmJ Bz dipole

where µz is the magnetic dipole moment component along the quantization axis z, gJ is the Lande g-factor, µB is the Bohr magneton, and mJ is the magnetic substate of the atom

or the projection of J along z. The interaction energy for a given state J,mJ of an atom is either positive, negative or zero.

Along the z-axis, the excited level will split into three magnetic substates given by mJ = 0,±1 as a result of the magnetic field, B. The energies of the substates are position-

dependent and shifted by an amount given by Emagnetic above. dipole

We use this spatially dependent energy shift to cool and trap our atoms near the quadrupole trap center. We shine two equally intense circularly polarized counter- propagating laser beams on the atom sample. Both beams are red-detuned from the unshifted atomic resonance and propagate along the z-axis. The σ- (σ+) beam propagating 30 from the right (left) is capable of exciting only the mJ =-1 (mJ= +1) transitions. As in

Figure 2.2, the B field decreases negatively for z<0, is zero at z=0, and increases positively for z>0. For atoms in the region z<0, moving left, the σ+ light is closer to resonance than the σ- light. Since the σ+ light is closer to resonance, the atom scatters more photons from this beam than from the σ- beam. Thus, the net force on the atoms from the photons is towards the center where Bz=0. For atoms in the region z>0, the opposite occurs. They are more likely to scatter photons from the σ- light, since it is closer to resonance. Again, the net force on the atoms moving to the right is towards

- Bz=0. This can experimentally be expanded to three dimensions by configuring three σ -

σ+ counter-propagating beam pairs in the x-, y- and z- dimensions. With these three pairs of beams, the atoms will be pushed toward the center of the quadrupole trap. As we cool the atom, the atoms are trapped near Bz=0.

Real Rb atoms that would be cooled in a MOT have a much more complicated level structure than that shown in Figure 2.2. The complex hyperfine structure of 87Rb is shown in Figure 2.3. The trapping laser (of the appropriate polarization as described

2 2 above) is the cycling transition 5 S1/2|F=2> →5 P3/2|F’=3>.

Figure 2.3 Energy level diagram for Rubidium including fine and hyperfine structure. The transitions used for the trapping laser and repumping laser are included. The detuning of the trap laser Δtrap is shown with respect to the trapping transition.

For typical conditions in our apparatus, 1 out of 1000 scattered photons will excite an

2 2 atom to the 5 P3/2|F=2> state. Upon spontaneous decay to the 5 S1/2|F=1> state the atom no longer scatters photons from the trapping laser. To get the atom back into resonance with the trapping laser, we employ a pumping laser that can excite an atom from the

2 2 2 5 S1/2|F=1> to the 5 P3/2|F’=2> state. From the 5 P3/2|F’=2> state, it decays back down to 32 2 5 S1/2|F=2> state, where it may be excited and decay repeatedly until it is able to scatter photons from the trapping laser again. This process is referred to as “optical pumping”.

2.3 Atom Mirror Theory

In 1982, Cook and Hill [7] first suggested that slow atoms could be reflected from evanescent waves. We create our evanescent waves by coupling light into a planar slab waveguide structure as shown in Figure 2.4. The evanescent waves exist in the vacuum near the vacuum-waveguide region boundary. Our guiding region is only capable of supporting total internal reflection (like that described in the introduction) for certain angles of reflection or waveguide modes. Each mode will have a particular evanescent

33 wave with slightly differing characteristics. For laser light detuned to the blue of atomic resonance, the evanescent wave field exerts a force on incident atoms such that they are repelled when they enter the field.

We will drop a cooled sample of atoms onto the waveguide surface. Upon hitting the repulsive evanescent wave, the atoms will be reflected back up; thus, the evanescent wave acts like a mirror for atoms. “Reflection” requires that the atom be reflected at the same angle (with respect to the perpendicular or normal to the surface) at which it came in, preserving the transverse velocity and reversing the vertical velocity. “Specular reflection” requires that the atom not pick up any unwanted phase from a dissipative event. The following sections will set up the theory behind ensuring that an atom can be reflected.

2.3.1 Properties of Evanescent Waves

Our optical waveguide is made up of three layers. Figure 2.4 shows a schematic of our guide. Each medium in the guide is described by a characteristic refractive index, n. The top layer in our structure is vacuum with a refractive index of 1.00. The second layer, the waveguide layer, has a large refractive index nwaveguide. Let us presume the light is totally internally reflected in this layer. The third layer is the substrate layer with refractive index nsusbtrate. In this structure, the goal is to create an evanescent wave field above the waveguide region in the vacuum region.

To mathematically describe the evanescent wave, consider the surface between the vacuum and the waveguide layers shown in Figure 2.5. For a λ=780nm light wave

34 ! 2!nwaveguide propagating with kinc = at an angle θinc with respect to the normal to the "

! 2! surface, the transmitted beam exits with ktrans = that is bent toward the surface "

! 2!nwaveguide normal. The reflected beam propagates with k refl = and is reflected at an " angle that is equivalent to the incident angle. As θinc is increased, there will be some

surface normal

point where there will no longer be a transmitted wave and all of the incident light is reflected back into the incident medium. This critical angle, θcrit occurs at the value

35 " nvacuum % !crit = ArcSin$ ' . For incident angles larger than this angle, all incident light will # nwaveguide & be reflected.

As a result of the total internal reflection and because the electric field must be continuous across the boundary, some amount of the field “leaks out” into the vacuum region. The field that leaks out is referred to as the evanescent wave. The field strength of the evanescent wave is largest at the surface and falls off exponentially as it penetrates the vacuum. This evanescent field, which carries no energy with it across the border, is characterized by the equation

E E e!ay ei(ktrans z!"t !#) evanescent = 0 ( ) where a is the decay constant, ktrans is the propagation constant in the vacuum, and ω is the characteristic frequency of the 780nm wave, and ϕ is an arbitrary phase. Since the amplitude of the evanescent wave, which oscillates in place along z with frequency ω, decreases exponentially as it permeates the vacuum region, it exhibits a large field gradient on the vacuum side. This field gradient is responsible for reflecting atoms.

The optical waveguide structure in Figure 2.4 supports waveguide radiation modes and guided modes. Radiation modes are waveguide solutions that imply plane wave radiation incident on the waveguide layer from either the substrate side or the vacuum side. Guided modes are solutions of the wave equation that describe electromagnetic field distributions localized in the waveguide region. In this thesis, we will consider only the guided wave solutions since those are what we use to create our evanescent wave. A good discussion of the radiation modes can be found in [41].

36 2.3.2 Slab Waveguide Introduction

Considering the planar slab waveguide shown in 2.4, Maxwell’s equations can be written for each layer of index of refraction n as ! ! ! $H ! " E = # µ t $ ! ! ! $E ! " H = # n2% $t ! ! ! • E = 0 ! ! ! • H = 0 where µ and ε are the permeability and permittivity respectively of the layers. Assuming a time harmonic field of the form e!i"t , we can derive from Maxwell’s equations, the three-dimensional vector wave equation for a uniform dielectric with refractive index n, !" " !" " 2 E(r) k 2n2 E(r) 0 ! + 0 = where k0 is the free-space wavelength of the light. We can simplify this equation by assuming that the structure is uniform and extends to infinity in the x-dimension (Figure

2.4). Furthermore, assuming the field can be described by a plane wave of the form

e!i"z in the z-dimension, we find the reduced scalar equation

2 d Ex (y) 2 2 2 + k n ! " E (y) = 0 dy2 ( 0 ) x where k0 is the vacuum propagation length, n is the index of refraction in each layer, and

β is the propagation constant for the guided mode.

There are two types of solutions to this wave equation: the transverse electric

(TE) modes and the transverse magnetic (TM) modes. TE modes are characterized by single electric field component, Ex and magnetic field components, Hy and Hz (parallel to 37 the waveguide surface). A single magnetic field component, Hx and electric field components, Ey and Ez, characterize TM modes. This thesis uses a TE mode to create an atomic mirror, so we will concentrate on the TE mode description.

Each mode m in the guiding layer is described by an effective refractive index

nm,eff such that nm,eff satisfies nsubstrate < nm,eff < nwaveguide and !m = nm,eff k0 is the propagation constant for the mth TE mode. For now, we will consider a general solution with the propagation vector ! . The solutions for the electric and magnetic fields for a TE mode take the form:

!i"z Ex (y,z) = Ex (y)e " H (y) = ! E (y) y #µ x i $E (y) H (y) = ! x z #µ $y where Ex is the electric field amplitude, which is dependent on the laser intensity, β is the propagation constant, and µ as the permeability of the medium.

We can write trial solutions for the guided modes for each layer of the optical waveguide as

$Ae!ay (y " 0) & Ex (y) = %Bcos(by)+ C sin(by) (!h # y # 0) . & c(y+h) 'De (y # !h)

By substituting our trial solutions in the scalar electric field wave equation, we get

2 2 2 2 2 2 a = ! " k0 , b = (nwaveguidek0 ) ! " , c = ! " (nsubstratek0 ) (since nvacuum=1.00)

2! and k = for the vacuum-laser wavelength λ. The constants A, B, and D are 0 "

38 determined by matching the boundary conditions requiring Ex (y) and

!1 #E (y) H = x (with µ as the permeability in the medium) to be continuous at the layer z "µ #y boundaries. In matching the fields and field gradients at y=-h (with h as the layer thickness) and y=0, we derive the solutions for the fields in each region as

$ &C 'e!ay ( y " 0) & E ( y)= C '[cos(by) ! a sin(by)] (!h # y # 0) x % b & ( ) &C '[cos(bh) + c sin(bh)]ec( y+ h) ( y # !h) '& ( b )

1 # & 2 ' !µ where C = 2b% ( . The magnetic field Hz, in the three % 1 1 2 2 ( $ " (h + a + c)(b + a )' regions is found to be

) !ay + C 'ae (y # 0) !i + H (y) = C 'b !bsin(by) ! a cos(by) (!h $ y $ 0) z * ( ( b) ) "µ + +C 'c %sin(bh) + c cos(bh)'ec(y+h) (y $ !h) , & ( b) (

By ensuring the field components Ex and Hz are continuous at the boundaries, we find the transcendental equation

(a + c) tan(bh) = . b 1! ac ( b2 )

This equation can be solved graphically by plotting the right and left hand sides as a function of β. The result is a set of discrete values of β corresponding to modes. The transcendental equation for our system is shown in Figure 2.6. 39

LHS and RHS of transcendental function neff ,1

neff ,0

neff

These discrete values can also be determined using the ray picture shown in

Figure 2.4. As described above, the propagation vector of mode m is given by

!m = nm,eff k0 where nm,eff = nwaveguide sin!m , where!m is the characteristic mode angle (of the ray picture) shown in Figure 2.8. Ensuring that the round trip phase accumulated in the light bouncing up and down between the walls must is an integer multiple of 2π, we obtain the following resonance condition for allowed modes

a c bh ! tan!1 ! tan!1 = 2m" b b

40 where a, b, and c are all functions of β. As the mode number m increases, the effective

refractive index nm,eff decreases. As the waveguide layer gets thicker, it can support more

TEm modes. In solving for the allowed propagation constants, we solve for the allowed mode angles possible for each of the m modes for a given thickness h.

The evanescent wave field we are concerned with lies just outside the waveguide layer in the vacuum region. Here, the field is (according to the above calculations)

!am y !i"m z E(y,z) = E0e e .

th The decay constant am of the m mode as it permeates the vacuum layer is

2 am = k0 nm,!eff 1 . The TE0 and TE1 modes are graphically shown in Figures 2.7 and their decay constants are detailed in Table 3.3. We use the TE1 mode to create an EW mirror.

2.2.3 The Dipole Force Introduction

To get an atom to reflect off of a surface specularly like light off of a mirror, we must create a potential (for the atom to interact with) at the surface. The reflection of an atom at the surface of the waveguide (where there is an evanescent wave field) is based on the “dipole force.” In the presence of the light field, the energy levels of the atom are shifted. Because the field is due to the evanescent wave, which is falling off quickly away from the waveguide surface, there is a spatial gradient to this light field. Since there is a spatial gradient to the light field, there is a spatial gradient to the light shifts seen in the atom, as it gets closer to the surface. The dipole force is a result of this spatial gradient of the light shifts of the energy levels of the atom in the presence of light field. 41

To mathematically understand the dipole force, let us return to the two-level atom discussed at the beginning of this section. We showed that the unperturbed energy levels of the atom shift due to the presence of the light. Light shifts are more important in the regions of large frequency detuning. Here, the effect of absorption is negligible. In the large detuning limit where ! ",# , the eigenvalues for the perturbed Hamiltonian are !

2 !! 0 !" E± = ± . 2 4# The unperturbed energy levels are shifted in the presence of the light by an amount

!"2 !Eint = , 4# such that the excited state is shifted up by !Eint and the ground state down by the same amount. This energy shift due to the atom interacting with the field is known as the a.c.

42 Stark shift. Since Fdipole = !"Udipole , the dipole force is the negative of the spatial derivative of this light shift,

" % "#2 (y)( F (y) ! ! . dipole y ' 4 * " & $ ) There are good treatments of the derivation of this force [41,42,43].

A ground state atom moving in this force field sees a scalar potential given by the light shift of its energy levels:

"!2 (y) Udipole (y) ! . 4"

The Rabi flopping rate, Ω is the rate at which the atom switches between ground and excited states in the light intensity. With this in mind, we can express the dipole potential in terms of the intensity of the incoming radiation, I(y). To do this, we define the saturation intensity, Isat as the incoming intensity that will result in ¼ of the atomic population in the excited state. This saturation intensity is 1.67mW/cm2 for Rb. The

"2 I(y) Rabi frequency associated with unsaturated intensity light is given by !2 (y) = . 2 Isat

In terms of the incoming radiation I(r), our dipole potential is given by

"!2 I(y) U (y) ! dipole 8" I sat The scalar dipole potential above has a maximum where the intensity is highest, when the detuning, δ, is positive (or to the blue of the resonant transition). When the laser is blue-detuned, the atom is repelled from regions of high intensity. Conversely, when the detuning is negative (or to the red of the resonant transition), the atom is

43 attracted to the regions of highest intensity. So, by adjusting the detuning of the laser light with respect to the atom’s resonance we can cause the atom to be repelled by the light.

The dipole potential given above is for the case of a single available excited state.

However, in Rb, we have two important excited transitions termed the D1 and D2 lines

[43]. An atom in the S1/2 state can be excited either into the P1/2 state (D1 transition) or the P3/2 state (D2 transition). See Figure 2.3 for the energy level diagram. The dipole potential will vary slightly depending on which transition your laser is tuned to. For equal laser intensities and detunings, the strength of the potential for the D2 transition

(which is what we use) is twice that of the D1 line. The dipole potential seen by the atom in a light field tuned to the D2 (|5S1/2> → |5P3/2>) resonance of Rb is given by

!!2 # 2 + Pg m & I(y) U (y) = F F dipole 8 $% 3" '( I 2.F ' sat where !2,F is the detuning from the D2 resonance and P is the light polarization. The constant P=0, +1, and -1 for linearly, right circularly, and left circularly polarized light respectively. The magnetic vector term of the potential depends on the magnetic sublevel of the atom and the light polarization. For linearly polarized light, we use P=0. For a discussion of this, refer to [43, 44]. Given this, we can define our dipole potential as

2 # "!2 & # I(y)& U (y) ! . dipole 3 $% 8" '( $% I '( sat with δ being the detuning from the D2 resonance.

44 2.3.4 Dipole Potential Due to the Evanescent Wave

In section 2.3.1, we showed that the electric field of the evanescent wave is given

!am y !i"m z by E(y,z) = E0e e . The intensity of the evanescent wave is given by

!2am y I(y) = I0e where I0 is the intensity of the field leaking through the surface into the vacuum and

# 2! & 2 th am = % ( nm,eff ) 1 is the decay constant for the m mode of the waveguide. $ " ' ( )

Referring to the ray optics image of the light in the waveguide in Figure 2.6, different TE modes will be guided at different mode angles. The TE0 mode is guided at a much larger angle to the surface normal than the TE1 mode. Higher modes are guided with smaller mode angles and hit the waveguide surface more (in a ray optics picture). Each TE mode also has a different decay constant, am, which is dependent on the effective refractive index of the mode. As a result, the evanescent wave amplitude for the TE0 mode falls off much faster than for the TE1 mode. The higher modes decay slower than the lower modes and therefore penetrate further into the vacuum region. The field amplitudes will

1 reach 1/e of their maximum values when they have penetrated a distance ~ into the am vacuum region.

Since the evanescent wave decays exponentially, the dipole potential also decays exponentially. Suppose we couple light into the TE1 mode of the waveguide. If the light sent into the waveguide is blue-detuned with respect to the D2 line, the resulting evanescent wave potential is repulsive and given by 45 2 # "!2 & # I e)2a1y & U (y) ! 0 . EW 3 $% 8" '( $% I '( sat Depending on the parameters of a given evanescent wave, when the atom is far from the waveguide surface, the light force dominates. Very close to the surface, the interactions between the atom and the surface dominate. As detailed in [45,46], depending on how far the atom is from the surface, it will see different potentials. If the atom-surface distance y >> 100 nm, the atom will feel an attractive force that falls off as

1 called the Casimir-Polder force. The Casimir-Polder force can be seen as due to the y5 interaction of the electric dipole moment with the fluctuations in the vacuum (or virtual photons in the vacuum). For y << 100nm, the atom will feel an attractive force that

1 diminishes as called the van der Waal’s (vdW) force. The vdW force can be seen as y4 due to the interaction of the atom’s electric dipole moment with its image in the dielectric material. The force that exists in the intermediate region has been calculated using quantum electrodynamics [45] and shows a smooth transition to fit the asymptotic behavior for large and small distances. We will only be concerned with the forces close to the surface since the dipole force due to the evanescent wave falls off very quickly just outside of the surface. We also neglect the gravitational force, as it is orders of magnitude smaller than the dipole and vdW forces on the length scale of the evanescent wave tail.

At these distances, the atom sees the repulsive potential of the dipole potential as well as the waveguide surface itself. When the atom comes towards the surface, it interacts with the evanescent wave (EW) field, which induces a transient dipole moment

46 in the atom. The dipole moment, now close to the dielectric surface, sees an image of itself in the surface and is attracted to it. This is the vdW force.

2.3.5 Van der Waal’s Potential

When our ground-state atom comes within ~100nm of the surface [45], it will feel attracted to the surface due to the van der Waal’s force. We can get the interaction energy of the atom and the surface by looking at how the electric dipole moment of the atom interacts with its own induced image charge in the surface.

The van der Waal’s interaction energy between an atom and a nearby dielectric ! surface (with surface normal pointing along + ) is given by y

2 2 2 " nwaveguide ! 1 % " d + 2d % 1 ( ) ( ! ( ) UvdW (y) = ! $ 2 ' $ ' 3 $ nwaveguide + 1 ' $ 64)*0 ' y #( )& # & where n is the refractive index of the waveguide layer, d 2 and d 2 are the rms waveguide ! ! squares of the transition dipole moments parallel and perpendicular to the surface normal,

ε0 is the vacuum permittivity (a measure of how the vacuum responds in the presence of an electric field) and y is the distance from the surface of the waveguide. ! ! ! ! The transition dipole moment is given by where q is the charge d = q(x + y + z) associated with the moment. The dipole moments d and d in the equation above are ! ! defined such that d! = qx,qz and d! = qy . The 5S1/2 ground state of the rubidium atom

(which has a valence electron shell similar to that of hydrogen) is characterized by a wavefunction that is spherically symmetric. This symmetry suggests that d and d have ! ! 47 the same magnitude that we will call d. As a result of this spherical symmetry, we can reduce the van der Waal’s potential to

2 2 " nwaveguide ! 1 % " d % 1 U (y) ( ) . vdW = ! $ 2 ' $ ' 3 n 1 48() y #$( waveguide + )&' # 0 &

By taking the natural radiative linewidth, Γ for a transition of strength d such that

2 k0d ! = , an atom is a distance y from the surface of index of refraction of nwaveguide, 3"# 0! sees a vdW potential given by

" 2 % " 3 % (nwaveguide ! 1) !( U (y) = ! $ ' . vdW $16 ' 2 3 # & $ nwaveguide + 1 ' (k0 y) #( )& where k0 is the free-space wavelength and y is the distance between the atom and surface.

To find the total interaction energy caused by the van der Waal’s force, we must sum over all possible allowed dipole transitions states. The polarizability of Rb is dominated by the D1 and D2 transitions mentioned in Section 2.2.3 and shown in Figure 2.3, making the van der Waal’s potential

" 2 % " 3 % (nwaveguide ! 1) ! * 1 2 - U (y) = ! $ ' ( + ( . vdW $16 ' 2 3 +, 3 5S1/2 )5P1/2 3 5S1/2 )5P3/2 ./ # & $ nwaveguide + 1 ' (k0 y) #( )& 1 This potential gives rise to an attractive force that goes as away from the surface. The y4 presence of the vdW force close to the surface reduces the maximum total potential due to the evanescent wave. If the kinetic energy of the atoms perpendicular to the surface is high enough, the atoms will hit the surface and stick to it. Given the kinetic energy of the incident atoms should be lower than the maximum potential at the surface, there will be

48 some classical turning point, where the atom will bounce back up. The turning point is given by the comparison of the incident atom’s kinetic energy to the total dipole potential. For a given detuning of the evanescent wave, we can calculate the minimum intensity required to reflect atoms of a given temperature. See Figure 1.4 for a graph of the potential (due to both van der Waal’s and dipole forces) that an atom sees near the waveguide surface.

2.3.6 Diffuse Scattering

A cold atom is one that moves slowly. In atom optics, we use temperature and speed analogously. To find the speed of an atom, one can equate the kinetic energy to the temperature of the atomic sample as in

1 1 mv2 = k T . 2 2 B

An atom can also be described as a matter wave, having a de Broglie wavelength given

h by ! = . Colder atoms have longer de Broglie wavelengths. deBroglie mv

“Specular reflection” takes place coherently. For the reflection to preserve the coherence of the incident matter wave, there can be no spontaneous photon scattering.

Such scattering events destroy the particles spatial coherence since the scattered photon is an avenue to spatially localizing the particle.

As mentioned above, there are two components to the force on an atom in a light field: the dipole force and the scattering force. The dipole force is a conservative force but the scattering force is dissipative. This latter force causes an atom to absorb a photon

49 and re-emit spontaneously in a random direction. As a result, the atom will get a kick in a random direction. Such an event could drastically alter the atom’s trajectory upon reflection or could alter the trajectory of the incoming atoms. The probability for a spontaneous event to occur is calculated by integrating the scattering rate over the

m ! trajectory [44] to be pspont = v# , where v! is the velocity component of the atom !a " perpendicular to the surface, a is the decay constant for the evanescent wave, m is the atomic mass, δ is the detuning of the laser from resonance, and Γ is the transition natural linewidth. Having a minimal vertical component to the atomic velocity and using far- detuned laser light reduces the probability for such a nonspecular or incoherent event due to spontaneous emission. As discussed in Chapter 1, if the reflection is not diffuse, the atom cloud’s transverse velocity distribution should remain unchanged. The vertical velocity should be reversed and there should be no change in the horizontal velocity.

Another cause for incoherent reflection is the light scattering losses from the waveguide. There are two types of scattering seen in waveguides: bulk scattering and surface scattering. Bulk scattering is caused predominantly by voids, defects or contaminant atoms in the bulk of the waveguide film. Light will scatter or be absorbed at these imperfections. The bulk loss per unit length is proportional to the number of imperfections along the propagation length and depends on the relative size of the imperfections with respect to the guided light wavelength.

For thin film waveguides, the losses are predominantly from surface imperfections. Tien derived an expression for the scattering losses due to surface

50 scattering based on the Rayleigh criterion where the loss in db/cm is L = 4.3! s where

! s is the given by

4" 1 & cos3 % ) & 1 ) 2 2 2 m ! s = 2 ($ ws + $ vw ) ( + ( + # ' 2sin%m * ' h + (1 / a) + (1 / c)*

where λ is the wavelength of the evanescent wave light, σws and σvs are the roughness of the waveguide-substrate layer and waveguide-vacuum layer respectively, and θm is the mode angle characterizing the particular waveguide mode (as shown in Figure 2.8), and a and c are the decay constants of the evanescent waves in the vacuum region and substrate region respectively. The measured roughness on the surface translates to a rough potential at the surface [48] and has been shown to cause diffuse events. Even the smoothest waveguides [27] of 0.9Å rms roughness can cause an added transverse velocity of 11.8 mm/s.

CHAPTER 3

EXPERIMENTAL SETUP

To realize the waveguide atom mirror experiment, we need to cool and trap a large number of cold 87Rb atoms and drop them on the waveguide surface to observe the coherent bounces. We first magneto-optically cool 87Rb atoms in a high vacuum chamber. Upon collecting our cold atoms, we transfer them to a purely magnetic trap such that they are held just in a magnetic field. Once the atoms are magnetically trapped, the atoms can be lost through collisions with hot background 87Rb gas. To retain the atoms we have trapped, we move the sample to an area where we limit the collisions with the 87Rb background gas. To be able to collect a large number of atoms, but retain them for the experiment, we employ a two-chamber design similar to that found in [47] and shown in Figure 3.1. In creating the transportable cold atom source, we follow several experimental procedures to ensure appropriate cooling and subsequent transfer to the magnetic trap. We manage to cool and trap 3 ! 109 atoms in the MOT and transfer 10% of those atoms to the magnetic trap. Subsequently, we transport the atoms to the UHV

experiment cell, where we can drop them onto the waveguide where we hope to observe the atoms bouncing on the waveguide.

This chapter gives a detailed explanation of the experimental system, including the design of the two-chamber system, the lasers and associated laser feedback electronics to cool the atoms as well as create the evanescent wave, the design and setup of the cooling, trapping, and transport of the atoms, and fabrication of the optical waveguide.

53 3.1 Two-Chamber Vacuum System

To capture a large number of atoms in our cold atom sample we use a separate magneto-optical trap-loading chamber and science chamber. In the magneto-optical trap

(MOT) loading chamber, we cool and magnetically trap our 87Rb. The ambient pressure in the MOT chamber is high enough however, that collisions with background Rb gas can knock atoms out of our trap. Before we can carry out the experiment, we would like to be in a region where the Rb background pressure is much less.

3.1.1 MOT-Loading Chamber

As seen in Figure 3.2, the Rb loading chamber is a long 2’’ diameter cylindrical glass tube with 1-1/3’’ comflat flanges on each end. The Rb source for the experiment is two SAES Rb dispensers, which are spot-welded to an electrical vacuum feed-through located on one end of the cylinder. The dispensers are small metal containers (12mm

2 ! 1mm ), which contain a mixture of Rb2CrO4 and a reducing agent consisting of 84%Zr and 16%Al. When current is run through a dispenser, the joule heat raises the temperature of the container such that it releases Rb. We only run current through a single dispenser at a given time, but have included two individually accessible in the event that one dispenser runs out. This allows us to avoid breaking vacuum to replenish the Rb source. To remove any contaminants built up on the getter as well as reduce any

54 thermal shock on the getter, a slow turn-on process is employed at every Rb loading. The current through the dispenser is ramped up slowly, starting at 2A for 1min, increasing the

Rb for a day’s experiments. A cold spot consisting of a water-cooled copper block with two thermo-electric coolers in series is placed just under the glass cylinder at the end nearest the getters. See Figure 3.3. We use the cold spot simply so that Rb, which tends to stick to the walls of the glass, will accumulate at the cold area instead of the areas of the glass walls where the MOT beams gain optical access to the atoms. After running the loading sequence, the cylindrical glass cell contains Rb with a vapor pressure ~10-7 Torr.

55 To pump out background species, which is anything that is not Rb, in the MOT-loading cell, we attach an 8liter/s ion pump to the end of the cell closest to the dispensers.

Figure 3.3 Cold spot touching the MOT cell. The cold spot ensures that Rb does not coat the inside of the MOT glass cell, which would block the incoming cooling laser beams.

In addition, to reduce the pumping of released Rb, a 5mm pinhole is placed between the flanges connecting the ion pump and the MOT-loading chamber.

The effused Rb is used to load the MOT. Once loaded, a series of techniques allow us to load our MOT cooled atoms into a trap consisting of just a magnetic field.

Details of this are contained in Section 3.4.4. Once in the magnetic trap, we can no longer add atoms to our sample, but we can lose them. To avoid losing atoms from our sample,

56 we must transport the cold atom sample out of the MOT-loading region to the ultra high vacuum experiment cell. See Figure 3.4.

3.1.2 Ultra High Vacuum (UHV) Experimental Chamber

The UHV science chamber is a 2’’ (in height) glass cylinder of 3’’diameter with

1’’diameter tubes connected to the curved surface. (See Figures 3.1 and 3.4.)

Connecting the UHV cell and the MOT-loading cell is a 3’’ long bellows of 1-

1/3’’diameter that acts to limit the stress on the glass and the glass to metal seals. Also,

Figure 3.4 The UHV cell containing the waveguide

to ensure that the pressure in the UHV cell is several orders of magnitude lower than the

MOT-loading cell, copper blanks with 5mm pinholes were placed on either end of the 57 bellows, reducing the conductance of Rb gas into the UHV cell. We also attach a Ti- sublimation pump to the UHV chamber on one end. The Ti-sublimation pump coats the stainless vacuum parts in a layer of Ti on which background gas will adsorb. The Ti-sub pump has a much higher pumping speed than the ion pumps. This differential pumping ensures the good vacuum in the UHV cell. On the other end of the UHV cell is the remote loading setup to allow us to load our waveguide sample. This allows us to load a sample without breaking vacuum and be able to swap out waveguides if necessary. The remote loading setup is connected to the UHV chamber via a commercial straight- through vacuum valve.

58 The waveguide sample is located at the end of an aluminum rod, which is mounted to a copper bracket, which can be screwed into a copper finger, located at the top of the vacuum chamber (See Figure 3.5). The copper finger’s position and angle is manipulated using a large optical tilt mount.

3.2 Lasers

Lasers are essential for creating a cold atom source and the evanescent wave in the waveguide. Two lasers are required to create magneto-optically cooled atoms and one laser is coupled into the waveguide to create the evanescent wave. To get a large trapped atom cloud, we ensure that the laser frequency is stable and that the laser linewidth is narrow enough to perform efficient cooling. We use Sharp 120mW

GH0781JA2C 780nm diodes. We alter the temperature and injection current of the bare diode and use optical feedback from a grating to set the laser frequency to the 87Rb

5S1/2→5P3/2 (D2) transition. We use electronic feedback to our lasers to ensure their stability there. This information is explained in Section 3.2.1 and 3.2.2, and 3.2.3. In addition to these diode lasers, we use a tapered diode optical amplifier (Toptica TA100 -

See Figure 3.6) to amplify light from one of the trapping lasers to get enough power to trap a large number of atoms.

Figure 3.6 Tapered diode amplifier TA100. The seed beam comes in and is adjusted into the amplifier chip using the two mirrors located in the lower half of the above image.

3.2.1 Free-running Laser Diodes

Through the adjustment of the injection current and temperature of the laser diode, we control the lasing wavelength. As shown in Figure 3.7, the free-running laser diode has a medium gain, which is very broad-peaked and depends on the material of the laser diode. The bare diode is also characterized by internal cavity modes, which are broad-peaked (~GHz widths). As we increase the temperature, the medium gain shifts with respect to the internal cavity mode structure, such that we adjust which cavity mode has the highest gain. This is the frequency at which the laser will lase. As we increase the injection current, we go to higher wavelengths. Using the temperature and current

60 lasing characteristics of the bare diode, we can coarsely tune our lasing frequency.

However, our free running diode lasers in single mode typically have linewidths around

25MHz, which is too wide to do efficient atom-cooling. We, therefore, use optical feedback to reduce the linewidth and do any meaningful science.

61 3.2.2 External Cavity Feedback

We employ the use of external cavity grating feedback to provide optical feedback to reduce the linewidth of the free-running diode. As in Figure 3.8, the extended cavity is the diode laser and a diffraction grating. The diffraction grating is also the frequency selector. The diffraction grating equation is given by

d(sin!i + sin!m ) = m" where d is the grating spacing, θi is the angle of incidence, θd is the angle of diffraction, m is the diffraction mode, and λ is the wavelength of light being diffracted.

Figure 3.8 External cavity diode laser in Littrow configuration.

We mount our grating in Littrow configuration such that the m=1 diffracted beam is coupled back into the laser diode. This corresponds to θi = θd. With this condition satisfied, the grating equation becomes:

2d sin!i = " 62 This allows us to tune the wavelength coupled into the laser diode by tuning the angle of the grating. In this way, we control the nominal lasing frequency of the laser. As the grating angle is changed however, the output beam of the laser diode will move. To minimize this, we mount a dielectric mirror at a right angle to the grating, bringing the output beam in the same direction as the first order beam off of the grating into the laser.

This mirror will effectively shift the light beam output from the diode by 180 degrees.

This allows the beam to always point in the same direction even if the beam position is shifted slightly in the plane of incidence as the grating angle is changed.

The external cavity modes are more closely spaced than the laser diode internal cavity modes as in Figure 3.7. By adjusting the angle of the grating using a piezoelectric device, we can tune the frequency and narrow the natural linewidth of the laser. As the temperature of the diode is increased, the gain curve associated with the laser shifts to longer wavelengths more rapidly than the cavity modes. Therefore, there is a relative shift of the cavity mode comb (modulated by the internal cavity mode comb) and the laser medium gain. As we scan through the temperature, the mode closest to the peak of the gain curve lases until the gain curve is shifted such that the gain associated with that mode is insufficient to cause lasing. The lasing wavelength then jumps to the next mode of longer wavelength, which is now closest to the peak of the gain curve. We stay on one of these modes associated with the D2 transition of Rb and ensure that we are nowhere near a mode hop for stability. Furthermore, with our external cavity, we see a linewidth reduction from 25MHz to 450kHz.

63 3.2.3 Frequency Stabilization

Once we tune the laser to the appropriate frequency, we must ensure that it stays at that frequency. To do this, we employ temperature controls and grating and current feedback controls.

The external cavity diode lasers used in this experiment are similar in design to that found in [48]. See Figure 3.9. Because our lasers at room temperature tend to

Figure 3.9 Photo of external cavity diode laser.

64 lase at higher wavelengths than we need, we cool our lasers using two TEC coolers. To get fine control of our temperature we attach a resistor that heats the laser through joule heating. By adjusting the voltage across this resistor, we control the outfitted with two

TEC coolers that cycle heat in and out of the diode.

We also use optical feedback to ensure the laser stays locked to the appropriate frequency. To tune the laser wavelength, we employ a piezoelectric transducer (PZT) affixed behind the grating on the flex-hinge. An adjustment screw sits on the other side of the PZT to allow for manual adjustment of the azimuthal grating angle. To adjust the grating vertically, an adjustment screw alters the vertical tilt of the plate holding the external cavity arm and thermistor. Feedback electronics ensure that both the temperature and grating setting ensure a stable frequency.

3.2.3.1 Temperature Control

The temperature of the laser strongly affects its frequency. Therefore, it is important to have good control of the laser temperature. A thermistor (10kΩ at 25°C) is located below the laser head is used to measure the temperature of the laser diode. To maintain temperature stability, we monitor this thermistor voltage and compare it to a fixed control voltage using a home-built power supply. This power supply consists of a feedback circuit that adjusts the temperature by changing the voltage across the heating resistor (50Ω, ¼ W) that is fixed to the aluminum plate under the laser base plate. Two thermoelectric coolers (TEC, Melcor PT2-12-30) configured in series are mounted side-

65 by-side just underneath the heater plate and continuously cool the laser. The hot side of the TEC is placed against the liquid-cooled heatsink and the cool side is placed against the heater plate. The voltage supplied to the TECs is adjusted such that the laser is kept near the “setpoint temperature”, dialed on the power supply. The “setpoint temperature” is the desired voltage across the heating resistor. This heater supplies the fine adjustment knob of the temperature. If the voltage measured by the thermistor is low, the electronic feedback circuitry will signal the voltage across the heating resistor to increase. To ensure good thermal conductivity, all junctions between the aluminum parts are layered with a thin layer of heatsink thermal compound. Circuit diagrams A1-A4 of the power supply and temperature feedback are included in Appendix A.

Air currents in the room can affect the temperature of the laser. To prevent ambient temperature changes from affecting the laser, we mount the laser in a hermetically sealed Plexiglas box with airtight water and electrical feedthroughs. See

Figure 3.9. We also added a Brewster’s angle window such that we get little reflection through the hermetically sealed box back into the laser. This has minimal effect on the output beam power. We see <5% losses from the window.

3.2.3.2 Current Protection

The diode laser is highly sensitive to static charge. As such, when installing a new diode or even storing a diode, we tie the two pins of the laser diode together.

Similarly, when the diode is installed, whether in use or not, we must protect it from

66 static charge or current spikes. To prevent reverse biasing or over-biasing the laser diode, we feed through the current supply wires through a shorting box that has two sets of protection diodes. Circuit Diagram A5 for this circuit is included in Appendix A. In addition, to avoid damage to the diode due to current spikes, we put a 10mH inductor in series with the diode and a 1000µF capacitor is placed in parallel with the diode. In this configuration, high frequency signals will bypass the laser diode. To ensure that the laser is not damaged when it is not being used, we tie the inputs together using a 10kΩ potentiometer.

67 3.2.3.3 Grating and Current Feedback Controls

To keep our lasers tuned to the appropriate frequencies, we employ the technique

of dichroic-atom-vapor-laser lock (DAVLL) originally described in [49] and shown in

Figure 3.10. The principle of the DAVLL locking is as follows. In the presence of a

Figure 3.10. Beam layout for the DAVLL locking setup.

weak magnetic field, the Doppler broadened absorption signal is split into the absorptions of the associated Zeeman components. By subtracting the absorptions of the Zeeman components, we get an error signal that has a zero crossing and is relatively insensitive to changes in intensity.

This setup of the DAVLL locking system is as follows. The laser beam is first sent through a calcite crystal to isolate a single linear polarization. The linearly polarized light travels through a Rb vapor cell centered inside a magnetic solenoid. The beam

68 continues through a quarter wave plate and is split into two orthogonal polarizations by the polarizing beam splitter (PBS). Two photodetectors are placed in each beam path to collect the power in each beam. With the quarter wave plate properly aligned and no magnetic field in the solenoid, the quarter wave plate circularly polarizes the incident linearly polarized light and the PBS emits beams of equal intensity, which are detected by the photodiodes. The photodiodes are followed by an operational amplifier circuit that will turn 1 µA of photodiode current into a 10mV signal.

With no magnetic field in the solenoid, as the laser is scanned in frequency, the photodetectors observe identical Doppler-broadened absorption lines. However, when the field is turned on, the resulting longitudinal magnetic field produces a Zeeman- splitting of the Rb hyperfine states. The incident linear polarization is a linear superposition of σ+ and σ- polarizations. The σ+ light drives ΔmF=+1 transitions. The lower mF energy levels are shifted down by the magnetic field such that the energy difference between the |F=1, mF =-1> and the |F=1, mF =0> states is larger. Therefore, the transition now occurs at a higher frequency than in the zero field case. The σ- transition conversely is shifted to lower energies or frequencies. The quarter wave plate changes the two circularly polarized beams into orthogonal linearly polarized beams, which are separated by the PBS and detected by the individual photodetectors. With the nonzero field the two signals measured by the photodetectors are shifted relative to one another and can be subtracted electronically to give an error signal. Through this subtraction process, we will get a zero voltage crossing to which we can lock. By adjusting the gains of the photodiodes relative to each other or by applying a dc offset, we can change where this zero crossing occurs. Once we have locked to the zero 69 crossing, the error signal is fed back to the PZT. If the frequency drifts, a nonzero voltage appears in the error signal, the voltage applied to the PZT will adjust the grating angle such that the frequency is again brought back to its lock point and a consequent nonzero voltage. See Circuit Diagrams that allow for this in Diagrams A1-A4 in

Appendix A.

The grating feedback adjusts for unwanted shifts in frequency over a longer period of time. To compensate for faster fluctuations, we feed the error signal back to the laser diode current. This is electronic in contrast to the mechanical nature of the grating feedback and can adjust for fluctuations on a much shorter time scale. The current supply lines are in series with a 10mH inductor to ensure protection from current spikes. To provide high-speed frequency control with the current feedback, the feedback circuit bypasses this inductor.

We can lock to a particular frequency using the zero crossing of the error signal but we must know the locking frequency to ~ 1 MHz. To do this, we use Doppler-free saturated absorption spectroscopy to resolve the hyperfine transition structure of the

5S1/2(F)→5P3/2(F’) transitions in Rb. Because this hyperfine structure is not resolvable when we look at the absorption through the Rb cell due to Doppler broadening, we use.

See Figure 3.11. In saturated spectroscopy, two laser beams from the same laser (of the same frequency) counter-propagate in a Rb cell. The probe beam in our setup is weaker by a factor of 100 than the pump beam. When on transition, the more powerful pump beam will excite all the atoms and the weaker probe beam will pass unabsorbed. Since the linewidth of the laser (~450kHz) is much less than the Doppler width, when near the transition, the pump laser will excite only the atoms moving at the velocity such that they 70 see the Doppler-shifted frequency as resonant. The probe laser, which is counter- propagating, will be resonant with atoms moving with the same speed, but traveling in the opposite direction. So, off of exact resonance, the atoms absorb the probe beam, because the pump and probe beams affect two different atom populations (atoms of the same speed but traveling in opposite directions). Right on resonance, however, the two lasers will affect the same population of atoms (atoms that move perpendicular to both beams). Here, the pump beam will “saturate” the transition, putting all of the atoms in the excited state. As a result, the probe beam will pass unabsorbed and be detected by a photodiode. The probe beam absorption signal is much smaller than the total intensity of the probe beam, resulting in a very small absorption signal that is hard to measure in a noisy environment. To detect the weak absorption signal of the probe beam, we use lock- in detection.

To ensure that we have locked the lasers to the appropriate frequency, the saturated absorption signal is compared to a frequency reference that is provided by a

Fabry-Perót etalon with a free spectral range of 300MHz. When a single longitudinal mode is sent into the etalon, the output peaks are 300MHz apart. When we compare these peaks to the saturated absorption signal, we can identify the correct transitions (by frequency).

Figure 3.11. Beam layout for saturated absorption setup.

To set the lock point of the laser to the appropriate frequency, we use the zero crossing of the error signal. As we scan the frequency by applying a computer voltage ramp to the PZT and thus tilting the grating, we plot simultaneous scans of the error signal and the Doppler-free absorption. See Figure 3.12. Using both of these scans simultaneously, we adjust the error signal until the zero crossing is at the correct frequency. Our electronics allow us two ways to adjust the zero point of the error signal.

The photodetectors have individual gains associated with them that can be individually changed such that the zero crossing can be changed with respect to the saturated absorption signal. We also have the ability to put a DC offset on top of the error signal.

However, changing the gains of the photodetectors has the advantage of leaving the locking point insensitive to changes in the laser intensity, as both photodetectors will

72 change equally with a change in the overall laser intensity. Adjusting the zero crossing by using the DC offset makes the locking sensitive to changes in laser intensity.

73 3.2.3.4 Tapered Diode Amplifier

To get enough power to the trapping beams, we amplify our master trap ECDL into a Toptica TA100 tapered diode amplifier (See Figure 3.6). A tapered diode amplifier is a tapered cavity used to amplify a relatively low power seed beam (~30mW) to Watts of the power in a single spatial mode. We outfitted the setup with a 1W 780nm amplifier chip from Eagleyard Photonics. The maximum operating current for the amplifier is

1600mA. With a seed beam of 38mW, we obtain an amplified power of 650mW at

780nm. To trap large numbers of atoms, we want to have large cooling beams. Our power drops to 350mW after the beam shaping optics used to make the beams the appropriate size.

3.3 Atom Traps

To create the cold Rb sample with which to perform the bouncing experiment, we must perform a specific sequence of experimental steps. The cooling and trapping sequence begins with the cooling and localizing the atoms at the center a magneto-optical trap (MOT) formed by six cooling beams (of two laser frequencies) and a magnetic field.

We then compress the atom cloud in the MOT, allowing us to efficiently transfer it to a purely magnetic trap, where the atoms are trapped by their magnetic dipole moment at the center of a quadrupole field. The magnetic trap is then moved about 1m in about 1/3s to the experimental chamber. We will present an overview of how magneto-optical traps 74 and magnetic traps function and how we implement those traps in our experiment. We will also characterize our magneto-optical and magnetic trap and discuss the translation of the magnetic trap to the experimental chamber.

3.3.1 MOT Optical Setup

In our MOT setup, we chose to use six individual trapping beams co-propagating with pumping beams. Frequently, groups choose to retro-reflect their MOT beams. We do not retro-reflect our beams because we expect a large optical density in our MOT. As such, we expect a considerable number of photons from the incident beam is scattered by the atoms leaving the retro-reflected beam with less intensity such that the intensities of the counter-propagating beams would be unequal. Our six-beam MOT scheme is detailed in Figures 3.13, 3.14, and 3.15. The trap and pump lasers used to create our

MOT are both external cavity diode lasers described earlier. The trap laser is tuned (as in

2 2 87 Figure 2.3) 18 MHz to the red of the 5 S1/2|F=2> → 5 P3/2|F’=3> Rb transition. The

2 2 87 pump laser is tuned to the 5 S1/2|F=1> → 5 P3/2|F’=2> Rb transition to repump any

2 atoms that fall into the 5 S1/2|F=1> state back into the trappable state.

We want large beams in our MOT to capture a large number of atoms. After enlarging the beam that comes out of the tapered amplifier (Toptica TA100), we get approximately 350mW of power for our experiment. All diagnostic beams to lock the laser to the appropriate frequency (See Figure 3.13) are located at table level. The trap center is elevated by about 12’’ above the optical table. 75

3.3.1.1 MOT Beam Intensity

To trap large number of atoms in the MOT, we decided to use 3cm diameter beams. We will now describe the optics that we used to create these. The laser incident into the trapping optics is ~1cm diameter. We split this beam into six beams with a series of polarizing beam cubes. In our beam paths, there are four half-wave plates before the polarizing beam cubes that control the relative intensities in each of the three pairs of

76 opposing beams. The beam size helps to ensure that we capture the most number of atoms, so we expand each of the six 1cm-diameter beams using telescopes mounted about

25cm from the MOT center. The telescopes to expand the transverse beams are formed from a 1’’ lens of focal length f1=-50mm lens fixed 50mm behind a 3’’ lens of focal length f2=100mm lens. This expands the diffracted beam to 3cm. The vertical beams are split off before the transverse beams and have a shorter beam path to the trap so the telescopes for those beams are different. The vertical beam telescopes consist of a 1’’ lens of focal length f1=-25mm fixed 50mm behind a 3’’ lens of focal length f2=75mm.

We take the 1cm beam and expand it to 3cm by this 3:1 telescope. Typically, we get

15mW/cm2 in each beam. The intensity of all six beams entering the MOT cell must also be the same. Since the intensity is not uniform across the beam as described in 3.2.3.4, it is important that we align the most intense parts of all six beams. We send the brightest part of the beam through the iris and line up the beam using a set of two targets: the first target is used to adjust the position of the beam before entering the MOT cell and the second target is used to align the angle of the beam going through the MOT cell. To align one of the six beams, the first target is placed after the gold mirror sending the beam into the telescope and the second target is placed in front of the telescope expanding the counter-propagating beam. We do this for all six MOT beams and ensure that the brightest part of the beams is lined up. In the event an optic prior to Iris 1 (See Figure

3.14) is misaligned, we have placed Iris 2 after Iris 1 in the beam path such that realigning the beam through Iris 1 and Iris 2 will again ensure the six beams are well aligned again. As in Figure 3.18, we need to use circular polarization to create the MOT.

To obtain the correct polarizations, we place quarter-wave plates before each telescope.

77 Each quarter-wave plate and telescope setup is mounted on individual tracks that limit the translation and tilt of the elements.

Figure 3.14 The MOT trapping beam layout. This view is from the top looking down. Side views are located in Figure: 3.15.

Figure 3.15 Side views of the beam layout. The pump beam is coupled to the trap beam path through the polarizing beam splitter.

79 3.3.1.2 MOT Beam Polarization

It is easy to align the quarter-wave plate such that the beams are circularly polarized but it is harder to know whether the beams are σ-- or σ+-polarized. If the fast axis is marked, it is simple to align the system correctly. However, the fast or slow axis is not always marked on the quarter-wave plates. To ensure that our quarter-wave plate is set such that we have the correct polarization in each beam, we mock up a setup similar to that in our DAVLL setup. The laser beam first passes through a polarizing beam cube in the orientation it would in the MOT. A half-wave plate placed before the beam cube adjusts the laser polarization to maximize the transmitted beam. The quarter-wave plate is placed after the beam cube and is oriented to give nearly circular polarization. The beam then passes through a Rb cell centered in a solenoid. The solenoid field is set to be what it should be for each beam in the MOT. The absorption of the beam is measured by a photodiode. We record both the Doppler-broadened absorption and the saturated absorption signal on a single plot for the field and no field cases. We can detect which direction the absorption has shifted with respect to the saturated absorption signal. If the absorption is red-shifted, the light is σ--polarized. If it is blue-shifted with the field on, the light is σ+-polarized. We want to have the light σ--polarized with respect to the local magnetic field as explained in the previous section. With the axes marked appropriately now, we make the light perfectly circular by sending the beam through a polarizing beam cube, then the quarter-wave plate, and retro-reflecting it back through the quarter-wave plate and the polarizing beam cube with a well-aligned mirror. The retro-reflected light

80 should be linearly polarized opposite the incident linear polarization if the quarter-wave plate is at the angle to create perfect circular polarization. As we fine-adjust the quarter- wave plate, the retro-reflected beam will be reflected instead of transmitted by the polarizing beam cube. We measure the maximum of the reflected beam using a photodiode. We could potentially more accurately measure the transmitted beam minimum using a photodiode by putting in a beam splitter after the beam cube. After placing the appropriately adjusted quarter-wave plates back into the MOT optics, all six beams are σ--polarized with respect to the local magnetic field in the MOT.

3.3.1.3 MOT Magnetic Field

The magnetic field is supplied by a set of magnetic coils wound on a Teflon spool and covered with Plexiglas walls to contain the coils. The coils were wound from 3/16’’

OD refrigerator tubing, which is water-cooled. To electrically insulate the tubing, it is covered with a layer of heat shrink tubing. To prevent the tubing from higher layers from slipping into the lower layers, each layer is separated by a 1/16’’-sheet of Teflon. Two identical coils were wound and mounted onto a Plexiglas mount such that they oppose one another. See Figure 3.16. The center-to-center coil distance is 10cm and the coil radius is 3.75cm inner coil diameter and 7cm outer coil diameter. The coils are connected in series electrically. We send about 365A (The maximum current we can get using our 19.7V power supply) through the coils. We do not leave this high field on for longer than a couple of seconds, because we do not want the dissipatively heat the coils

81 too much. We water-cool the coils using building chilled water cycled through the tubing such that at the above current the coils are only warm to the touch after a few seconds.

Figure 3.16 Coil assembly on the servo track

82 This is sufficient for us to be able to conduct our experiment. The magnetic field gradient along the axial dimension of the coils is 0.6G/cm for each Amp of current through the coils. To collect atoms in our MOT, we use a current of 13A. We experimentally found that this current gave us the most atoms. The MOT magnetic field gradient at this current is 7.8G/cm. The number of atoms in the MOT cloud is insensitive to changes of the field gradient within a couple of G/cm. Once the MOT beams and the field are optimized we can characterize our MOT through the fluorescence of the Rb atoms.

3.3.1.4 MOT Characterization

The two main properties that determine the quality of the MOT are the number of atoms that are trapped in the MOT and the MOT fill-time. The number of MOT-cooled atoms is determined through the fluorescence signal detected by a photodetector assembly with a plano-convex 1’’ diameter lens with a 2’’ focal length.

An atom in a light field will scatter photons at a rate that depends on the intensity of the incident light as well as the detuning of that light from resonance. The scattering rate in photons scattered per second is given by

" I0 % " ! % $ ' $ ' # Isat & # 2 & ! scattered = 2 " I0 % " ( % 1+ $ ' + 4$ ' # Isat & # ! & where I0 is the intensity in all six trapping beams, Isat is the saturation intensity for Rb, Γ is the natural linewidth of 87Rb, and δ is the detuning of the laser from resonance. When

83 the atom fluoresces, the spontaneously emitted light is given off over all angles. Only some of that light will hit the photodetector. So, the detected rate will be determined by the solid angle subtended by the collecting lens in front of the photodetector.

Furthermore, there is a 4% loss of photons at the reflection of the detected light for each of the n non-AR coated glass surfaces. The detected rate is now reduced (from the photon rate incident on the photodetector) to

2 # "rlens & n ! measured = ! scattered % ( (0.96) $ 4"ltrap ' where rlens is the collecting lens radius, ltrap is the distance from the lens to the trap, and n is the number of non-AR coated glass surfaces between the photodiode and the MOT.

With our laser red-detuned from resonance by 18MHz, an atom will scatter about 2 ! 106 photons per second. The rate that can be detected at the photodiode due to the limited solid angle and the losses at the non-AR coated surfaces is down to 1000 photons per second. To get a meaningful value for the number of atoms fluorescing, we use the

Ithaco 564 current pre-amplifier to turn the photodiode current to a voltage. The pre- amplifier has adjustable gain as well as low-noise and high-speed settings. We calculate the photodiode current by dividing the voltage measured by the trans-impedance of the pre-amplifier. With the photodiode current and the responsivity of the photodiode, R

I (0.55A/W), we get an incident power on the photodiode of P = PD . Based on this incident R incident power and the scattering rate of one Rb atom as measured by the detector, we can calculate an atom number as

84 (4!Pincident ) N = # hc& % ( () measured ) $ " ' where Γmeasured is the scattering rate as measured by the detector, Pincident is the power

hc incident on the photodetector, and is the energy of a single photon of wavelength λ. !

The photodiode will invariably detect some background light from the background Rb vapor in the cell. To ensure that we get a voltage corresponding to the atoms alone, we turn the magnetic field off to get a background measurement. All six

2 incident beams have intensity I0 = 50mW/cm . The energy of a 780nm photon is

2.53 ! 10"19 J. Typically, we get a photodiode signal of 0.200V (on 106-gain setting) after the background subtraction, resulting in about 3 ! 109 atoms in the MOT.

We also measure the fill time of the MOT. If the beams are well aligned and the vacuum in the MOT chamber is sufficiently good, the fill time of the MOT will be long at

~10s. Short fill times are a sign of a bad vacuum or misaligned beams. The fill time is estimated at ~12s, which shows that our vacuum in the MOT cell is sufficiently low.

Furthermore, a good test of the beam alignment is the dissipation of the optical molasses when the magnetic field is turned off. The longer it takes for the atoms to dissipate, the better the alignment of the six beams. We were only able to perform a qualitative measurement on this and noted that the molasses would last about 1s when the field was shut off. Once we have the atoms trapped into the MOT, we must trap them in a purely magnetic trap to shuttle them to the UHV experiment region.

85 3.3.2 Transfer to the Magnetic Trap

After capturing atoms in the MOT, we much transfer them to a region with a better vacuum to perform the science. To do this, we trap our atoms in a magnetic bottle.

To transfer the MOT atoms to the purely magnetic trap efficiently, the MOT cloud center must overlap with the magnetic trap center, located at the zero of the quadrupole field.

The MOT cloud center is affected by the relative intensities of opposing MOT beams.

We control the balance of these intensities by adjusting the half-wave plates located in front of the polarizing beam cubes.

To ensure that the cloud center is on top of the field center, first, we must locate the field center. To do this in three dimensions, we place IR security cameras along the two transverse dimensions and a Watec-902B CCD camera to look at the vertical trap position. See Figure 3.17. To prevent the cameras from blocking the beams, the two IR

Figure 3.17 Camera placement for MOT alignment.

86 cameras are placed at an angle looking up at that trap (instead of head-on).

As we increase the magnetic field gradient, the MOT cloud will decrease in size until it is about a pixel on the monitor. We achieve a maximum axial magnetic field gradient of 105 G/cm (which occurs at a coil current of 175A) before we are unable to see the trap anymore. We mark the point on the screen corresponding to this magnetic field center. The point is marked on all three screens corresponding to the three cameras.

The current through the coils is now reduced to the usual MOT current. We now ensure that the center of the MOT cloud on the three screens overlaps the field center points that were marked at high field gradient. We do this by changing the relative intensities in the three counter-propagating pairs of beams. The intensities can be adjusted using each of the three half-wave plates located before the polarizing beam splitters for each MOT branch. We have arranged the beam paths such that one half-wave plate adjusts the motion in one dimension of the MOT. We generally check the MOT position every day and typically, we only have to adjust the half-wave plates once a week.

3.3.2.1 Loading the Magnetic Trap

In a purely magnetic trap, the atoms are held by their magnetic dipole moments.

The Zeeman energy of holding an atoms magnetic moment in a magnetic field B is given !" !" by Emagnetic = !µ • B . This sign of this energy will indicate whether the atoms are dipole attracted to low magnetic fields (weak-field seeking) or high magnetic fields (strong-field seeking). The magnetic field directly at the center of the trap is zero and as we move

87 away from the center, the field increases linearly. Low-field seeking atoms are localized at the center of the quadrupole trap.

Our procedure for transferring atoms to the quadrupole magnetic trap is similar to that of Lewandowski et al. [49]. Rapidly turning on the magnetic trap gives the cloud potential energy. The more energy we add to the cloud, the more we raise the cloud temperature. To minimize the energy gained from the Zeeman energy at points away from the zero of the field, it’s advantageous to load a smaller cloud into the quadrupole trap. To reduce the size of the cloud, we reduce the radiation pressure from the re- radiated photons that are not part of the MOT cooling process. Detuning both the trap and pump lasers reduces the amount of spontaneously emitted re-radiation. Detuning the pump laser from resonance causes the atoms to spend more time in the lower hyperfine

2 state 5S 1/2|F=1>, where they are unaffected the trap laser. Detuning the trap laser decreases the number of photons scattered from the trap laser and reduces the absorption of any re-radiated photons. The detunings cause the trap to become round and compressed. This step is referred to as the compressed MOT (cMOT) step. We red-

2 2 detune the trap laser from the 5S 1/2|F=2> → 5P 3/2|F’=3> transition. We detune the

2 2 pump laser 50MHz to the red of the 5S 1/2|F=1> → 5P 3/2|F’=2> transition. This step lasts for 20ms, which is long enough to get the compression but short enough to not lose atoms to rethermalization and reduced cooling power. The detuning is applied by adding a computer-controlled DC offset to the locking signal as described in Section 3.2.3.2. We use two individual analog output channels on our National Instruments PCI-6520 data acquisition board to control the offsets applied to the lasers. The offset voltage that must be sent to the laser locking electronics is determined beforehand by determining the slope 88 of the error signal as the error signal passes through zero. This locking slope is calculated in volts per MHz such that applying a certain number of volts will detune the laser by an intended frequency. We detune the lasers for a period of 20ms. Varying this time between 5ms and 2s, we noticed the least loss of atoms with the 20ms detuning stage. The cMOT compresses almost all of the atoms that were originally in the MOT in a smaller volume. Using the fluorescence of the atoms, we see less than 10% loss in our atom number, however the 4mm cloud is decreased to 2mm along the transverse dimension.

After the cMOT step, we turn the trap laser off, allowing atoms to be kept in the

2 upper hyperfine 5S 1/2|F=2> ground state. Assuming that the magnetic substates are all equally populated, we can trap about 2/5 of the MOT population. This is because only

2 the mF=+1 and mF =+2 states of the 5S 1/2|F=2> manifold are weak-field seekers and may be trapped. To ensure that the atoms are in the upper hyperfine manifold of the ground state, we leave on the pump laser for 2ms longer than the trap laser. The pump and trap laser beams are then shut off using both the acousto-optic modulators (AOMs) and the home-built shutters (See Figure 3.18). The AOMs are controlled by analog output channels that have sub-ms timing required for the operation and the shutters are controlled using digital outputs that do not sub-ms timing. Before loading the magnetic trap, we shut off the trap laser, leaving the pump laser on.

To load the magnetic trap, we shut off the pump laser after 2ms and increase the magnetic field gradient from 8G/cm to 60G/cm. This initial step is done quickly to avoid losing atoms that would fall out of the trap due to gravity. The magnetic field gradient is then increased to 210G/cm over 500ms. To check how many atoms are trapped, we image the fluorescence of the atoms upon shutting the field off quickly and pulsing the pump and trap lasers for 50µs-500µs. We use the same detunings as are used for the

MOT to image the fluorescence. The fluorescence is imaged onto a CCD and the trap approximate depth is determined. By varying the time we leave the magnetic trap running before we image the fluorescence, we can also get a trap lifetime for the magnetic trap. In the MOT loading chamber, this is limited by the Rb vapor pressure

90 (~10-7 Torr). We note a lifetime of about 2 seconds in the MOT chamber. In the UHV experiment chamber, we see ~7 second lifetime.

To be able to efficiently load the magnetic trap, we need to be able to change the magnetic field gradient quickly. Later, we will also need to be able to shut the field off quickly. We use a Gauss meter to measure the field as we turn it off and note that the field is extinguished in 500µs. To achieve our magnetic field, we connect a TCR20T500 power supply, which is capable of supplying 20V and 500A to our magnetic coils. The circuit is shown in Appendix Circuit Diagram A5. In series with the power supply and the coils, we have two Toshiba MG300J1US51 power insulated gate bipolar transistors

(wired in parallel to each other). The power transistors are affixed to water-cooled heat sinks, such that they will be capable of running intermediate currents for seconds. The transistor gates are controlled by an analog output signal from the computer that allows

13A through the circuit during the MOT creation. To transfer the atoms to the magnetic trap, the gate voltage is switched such that we run 100A through the coils. Finally, we ramp the gate voltage such that the current through the circuit goes from 100A to 350A in

500ms. See Figure 3.19 for false color images of the magnetic trap. The trap is now

1mm in the axial dimension and 1.5mm in the transverse dimension. Currently, we are only capable of efficiently transferring about 10% of the atoms (about 3 ! 108 atoms) into our magnetic trap. The magnetic trap current control circuit is shown in Appendix

B. The Labview code that controls the MOT and magnetic trap loading sequences is shown in Appendix C. The loading sequence is summarized in Table 3.1.

91 Magnetic Trap Loading Sequence Laser Field Time Detuning AOM Shutters Step Gradient (MHz) (G/cm) Trap Pump Trap Pump Trap Pump

MOT 10s 7.8 -18 0 On On Open Open

Compressed 20ms 7.8 -40 -50 On On Open Open MOT Pump to F=2 2ms 7.8 -40 0 Off On Shut Open hyperfine state

Catch Step 2ms 60 -40 0 Off Off Shut Shut

Adiabatic 500ms 60→210 -40 0 Off Off Shut Shut Ramp of Field

Table 3.1 Magnetic trap loading sequence. This sequence (with our current alignment) gets us roughly 3 ! 108 atoms. To see an image of the magnetically trapped cloud, refer to Figure 3.21.

3.3.2.2 Magnetic Trap Characterization

An atom in a magnetic trap is characterized by an interaction energy given by !" !" Emagnetic = !µ • B where µ is the magnetic dipole moment of the atom and B is the field

magnetic field vector. Once we have efficiently loaded the magnetic trap, the atoms that

are contained within the atom trap have the maximum energy Emagnetic . Note that the field

Figure 3.19 shows a magnetically trapped atom cloud that is smaller axially than in the

transverse dimension. The quadrupole magnetic field is twice as strong axially than in

the transverse dimension. Using our magnetic trap images, the known field gradient and 92

Figure 3.19 a) CCD image of the magnetic trap. (False color added). The center of mass of the magnetically trapped atoms is 4mm above the waveguide. The waveguide surface is shown. b) The widths of the magnetically trapped cloud are shown. The top plot shows the width along the z-dimension parallel to the waveguide surface and the bottom plot shows the width along the y-dimension perpendicular to the waveguide surface. The full width half max (FWHM) of the cloud along z is 2.0mm and the FWHM of the cloud along y is 1.0mm.

the interaction energy of the atom and the field, we can approximate the cloud temperature. The temperature can be related to the energy due to the magnetic field at the outer edge (half-width half-max) of the imaged magnetic trap such that

1 k T ! µ B (z = 0.1cm) . 2 B B z

93 We know the maximum field gradient is 210G/cm. According to our images, the cloud is

1mm in the axial dimension and 2mm in the transverse dimension. Based on this, we estimate an initial cloud temperature of 3.4mK.

3.3.3 Transfer to the UHV Chamber

To perform the experiment, we must transfer these 3.4mK atoms to the UHV chamber using our servo-track. The number of cold atoms in the cloud of magnetically trapped atoms can be reduced by collisions with background gas. For this reason, we must transfer the cold atom cloud to a better vacuum. To transfer the atoms to the UHV chamber efficiently, we run the coil assembly on the servotrack from the MOT chamber to the UHV chamber. The servotrack is a linear stepper motor by Compumotor, controlled by an SX driver that receives commands from the computer through the serial port. To ensure that the atoms clear the pinholes, we must align the centers of the MOT chamber and experiment chamber with the centers of the two 5mm pinholes that allow for the differential pumping between the two chambers. The center of the magnetic trap is assumed to be at the center of the magnetic coils in the axial and transverse dimensions. As such, we align the 1.33’’ OD flanges containing the 5mm pinholes to the servotrack itself using a sub millimeter-precision jig. With the aid of an IR bullet camera, a height gauge, and a horizontal jig adjusted to within 0.5mm to the nominal trap center from the track, we align the pinholes to within 0.5mm. The adjustment of the first pinhole requires delicate movement as we risk damaging the MOT cell glass or the glass to metal seals. For this reason, we adjusted the track (instead of the vacuum chamber) to

94 get the horizontal dimension correct. Once the track was placed, we used the height gauge to adjust the vertical position of the flange. Once the first flange was positioned, we more easily adjusted the second flange. The second flange is a little easier to adjust as the glass and seals are less likely to break closer to the UHV cell.

Once the pinholes are adjusted, we can run the atoms down to the UHV cell, where the pressure is ~10-11 Torr which we need to do science. To check the pressure, we perform a test similar to what we do in the MOT loading chamber. We hold the atoms in the magnetic trap and release them, imaging the fluorescence in a CCD camera. By increasing the time that we hold the atoms in the magnetic trap, we will reach a time when the fluorescence is no longer visible. We noted that our atoms last in the experiment chamber for ~10s. To retain and improve our vacuum in the UHV chamber, we run the Ti-sublimation pump once a week. When we do not run the pump once a week, we notice our vacuum worsens and the atoms are trapped for ~2s.

Our cold atom source is now ready to be dropped onto our waveguide surface.

The following sections detail the manufacture and implementation of the waveguide.

3.4 Optical Waveguide

For details on the structure of our optical waveguide, let us refer back to the three- layer guide shown in Figure 2.4. For us, the top layer is a vacuum layer with index of

refraction nv=1, the second layer is the 370nm Ta2O5 layer of nw= 2.07 (at λ=780nm) and the bottom layer is the fused silica substrate of ns=1.42. To create guided modes, we

95 satisfy the requirement that the waveguide layer must have the largest index of refraction of the three. This influenced our choice on our material.

We chose Ta2O5 as our waveguide material for several reasons. First, we wanted a material that has a high refractive index and low attenuation. The dielectric Ta2O5 is used for low loss biosensors as well as highly reflective mirrors [6,7,8] As described in Section

2.2.6, scattering losses are the main mode of loss for waveguides. This requires the waveguide surface quality to be extremely good. As a result we purchased ultra-smooth

Figure 3.20. Grating pattern on the waveguide.

96 waveguides from Research Electro-Optics (REO). They deposit a thin layer (~370nm)

Ta2O5 on a super-polished fused silica substrate. They quote a surface roughness of <1Å rms. Using an atomic force microscope on the Ta2O5 surface, we measured the rms roughness varied between 0.7Å and 2Å.

3.4.1 Grating Fabrication

We decided to use gratings made of thermally evaporated Magnesium Fluoride

(MgF) to couple light into our waveguide. We pattern three pairs of opposing gratings on our Ta2O5 surface. See Figure 3.20. To get these gratings on our waveguide, we had to coat our waveguides in a variety of materials as well as soak them in a variety of liquids.

This has the potential to destroy the surface quality, something we were concerned with.

We however found that even after the gratings were finally placed, the rms roughness of the waveguide material was still between 2-5 Å. The following sections detail why we chose grating coupling as well as the process we used to fabricate the gratings. We end with measurements of coupling efficiencies of the TE0 and TE1 modes.

3.4.1.1 Light Coupling Choice

There are four main mechanisms for coupling light into and out of a waveguide: end-fire coupling, end-butt coupling, prism coupling, and grating coupling. The simplest coupling mechanism is referred to as end-fire coupling, where laser light is directly

97 coupled into the cross-section of the waveguide. See Figure 3.21. To successfully end- fire couple light into the mth mode, one must match the beam field to the mth waveguide mode field. Therefore, precise alignment is a requirement for having even efficiencies of

60%. [9]. In end-butt coupling, one directly couples the light-emitting layer of a semiconductor laser to the waveguide layer. Two parameters are critical in being able to couple efficiently into the mth mode: the waveguide thickness as compared to the light-

a) b)

Figure 3.21 Different light coupling techniques. a) End-butt coupling b) End-fire coupling c) Prism coupling d) Grating Coupling. emitting layer thickness and the specific mode into which you wish to couple. For each mode, there is a different optimal thickness, as the coupling efficiency will vary with this thickness ratio [9]. The TE0 waveguide mode has the highest coupling efficiency for this coupling technique at 30%. When coupling from the cross-section of the waveguide is

98 not possible, one can use prism coupling or grating coupling. In prism coupling, a prism is affixed to the surface of the waveguide structure. When light is sent into the prism, a standing wave mode is set up in the prism. As in Figure 3.21c the tail of the standing wave mode extends into the top layer of the guiding structure (which for us is vacuum).

The concern with this type of coupling is that the tail of the mode in the prism must match the evanescent wave tail of the mode into which you are coupling. For us to successfully do this, the prism must be placed within 150nm of the surface of the waveguide layer. Different modes can by accessed by sending in the incident beam at different angles. To mode match appropriately to get efficient coupling the prism needs to pressed either mechanically or via a phase-matching epoxy specialized for UHV systems. Large forces are applied to press the prism to the surface of the guide such that the gap size between the prism and the guide maximizes the coupling for a particular mode. Upon baking out the chamber, we risk thermal effects changing the gap layer and the mode coupling. All three of these techniques would have been experimentally difficult with our experiment design. Because the vacuum chamber was designed before the waveguide setup, we had constraints due to the chamber geometry and the bake-out required after inserting our waveguide in vacuum.

For this reason, we chose the grating-coupling scheme. We coat our gratings directly onto the waveguide surface. The following sections will detail the process for obtaining MgF2 gratings on our guides while ensuring a good surface quality. We use electron beam lithography to write our gratings in a photoresist. Upon developing the photoresist, we obtain alternating lines with no photoresist and stacks of photoresist. We then thermally evaporate MgF2 onto the photoresist stacks such that it coats both the

99 stacks and inside the lines. We finally remove the excess photoresist stacks, leaving only the lines of MgF2. This process is referred to as lift-off. We begin with a discussion of electron beam lithography, lead into our choice for photoresist, and end with a discussion of our MgF2 deposition and final cleaning procedures.

3.4.1.2 Electron Beam Lithography

Electron beam lithography or e-beam lithography is the process of scanning a beam of electrons across a film sensitive to scattered electrons and selectively removing either the exposed or unexposed part of the film. The purpose is to make small features in the film that can be transferred by evaporation or etching to the substrate on which the film is deposited. One of the major attractive features of ebeam lithography is the fact that it can create finer features than photolithography. This is a limitation of optical lithography. The diffraction limit of electrons is the deBroglie wavelength. We intend to make 200nm features, much larger than the smallest features possible with a commercial e-beam (~10nm).

100

Figure 3.22 Electron beam lithography machine cross-section.

A typical e-beam system consists of the following parts: 1) an electron gun; 2) an electron column that “shapes” and focuses the beam of electrons; 3) a mechanical stage that translates the wafer being written on in three dimensions; 4) a wafer system that feeds wafers into the system and unloads them after processing; and 5) a computer system that controls the aforementioned equipment. See Figure 3.22.

101 With e-beam lithography, one must write into a material that is sensitive to the electron beam. This material is referred to as the resist. Resists are classified as either positive or negative. Positive resists are films in which the portion exposed to the electron beam is removed and negative resists are films in which the portion unexposed to the resist is removed. There are specific resists that are sensitive to the e-beam. Two positive photoresists are Poly(methyl methacrylate) or PMMA and Copolymer (MMA

(8.5) MAA) from MicroChem. The resolution is highly dependent on the photoresist used as well as the thickness of the photoresist layer. Copolymer is highly reactive to scattered electrons exhibiting coarser features, while PMMA exhibits finer features. Because of this and the fact that we wanted nice vertical walls for our gratings, we chose to use a configuration called the “inverted bilayer”. In an inverted bilayer, we first coat our waveguide with a Copolymer layer and then a PMMA layer. The effect is that the Copolymer features are wider underneath a thinner PMMA feature. Figure 3.23 shows an inverted bi-layer on top of our waveguide structure. Copolymer and PMMA are dissolved in 2% Anisole.

Figure 3.23 Inverted bilayer photoresist structure.

102 3.4.1.3 Lithography Preparation

Once we have decided on a configuration for our photoresist stacks, we can

perform the processing. All of our processing is done in a Class 100/1000 clean room.

The photolithography area of the clean room is appropriate lighted to ensure that it does

not affect any of the photosensitive materials we use. Before doing anything with our

waveguide, we must do a pre-bake step to ensure that any water vapor on the waveguide

surface from being in the clean room environment will be drawn out. As such, we As

such, we attached a thermocouple to a heat sink made from a 1’’ ! 2’’ ! 2’’ block of aluminum. We placed the heatsink in an oven at 180º C for 4 hours to get the heat sink thermally stable. We then placed the waveguide of ¼’’ thickness on the heat sink. This

stayed in the oven for fifteen minutes. One can place thinner materials on a hotplate and

achieve the same effect. Note that if this dehydration bake is not done, the photoresist

that is layered on the surface will not adhere well and will lift when you try to develop it

by soaking it in the developer solution. After removing the waveguide from the oven you

can allow it to cool in a dessicator such that there is minimal water vapor exposure. Once

it is cooled, we are ready to coat the waveguide in photoresist. We place the waveguide

Film Spin Spin Oven Heat Thickness Photoresist Speed Acceleration Temp Time (nm) (rpm) (rpm2) (°C) (minutes)

Copolymer 1500 3000 180 30 700

PMMA (2% 1500 3000 180 30 200 in Anisole)

Table 3.2 Photoresist processing information.

103 on the spinner with the settings in Table 3.2. While spinning, we cleaned the waveguide with a few sprays of acetone followed by a few sprays of methanol. Before coating the resist, we must ensure that it is filtered. We use syringes affixed with 0.2µm screw mount nylon filters. If the photoresist is unflitered, large (>5µm) stringy material appears in the photoresist layer. We must also filter slowly to avoid bubbles in the resist. We start the coater spinning and when it is at the desired spinning speed, we slowly lay a few drops photoresist in the center of the spinning waveguide. First, we coat the Copolymer. We set the coater to spin for 90s with an acceleration of 3000rpm2 and a velocity of 1500rpm. The Copolymer is rather viscous so, spinning for 90s ensures that we get a uniform thickness of photoresist. We must now heat the photoresist-coated waveguide on the aluminum heatsink in the oven at 180º C for thirty minutes. This allows the photoresist to set. After removing the guide from the oven, we place it in a dessicator to cool. We should now have a ~700nm thick layer of Copolymer. Once cool, the guide is ready for the second coating. After the first coating, we coat the second photoresist, PMMA. We use the same spin settings for the PMMA as listed in Table 3.2. Again, we repeat the setting and cooling procedure for the PMMA layer. From this setting, we obtain a ~200nm layer of PMMA. Once the photoresists are set, cooled and ready for e-beam writing, we must perform one more step. To ensure that the electrons are drawn towards the surface we must coat the photoresist stack with a 50nm layer of aluminum. This allows a conductive surface. To coat the aluminum, we use a CHA electron beam evaporator. The CHA heats a tungsten boat containing aluminum by sending high-energy electrons at it. As the boat heats, the aluminum heats and eventually evaporates, coating the sample mounted above the boat. We pump down the evaporation chamber using a roughing-pump backed cryogenic pump to a base pressure of 3 ! 10-7 Torr before heating up the aluminum. Once the aluminum boat is heated, the pressure has increased to 1.8 ! 10-6 Torr. This is our 104 deposition pressure. We now deposit our aluminum on our surface at ~2Å/s for 4- 5minutes to coat 500Å of aluminum on our surface. The wafer is cooled, removed from the chamber, and is now ready for writing. To write the sample, we must mount the sample onto the ebeam stage. Our sample is ¼’’ thick, which is thicker than the ebeam stage is typically made to hold. As a result, we had to design a special holder that could accommodate mounting our thicker sample to the translating stage. Our holder is an aluminum piece with a 1’’-diameter, ¼’’-thick hole to allow for our full waveguide samples. The sample is held in with two thin shims each of which is held down by a 4-40 screw. To allow the holder to be adequately conductive to ensure the lack of charge buildup on the surface and potential beam deflection and distortion, we coated our holder in a 50nm of gold. The sample holder in the ebeam holder is in Figure 3.24.

Figure 3.24 Sample holder we designed for the ebeam.

105 We are now ready to write the sample. The program used by the ebeam to create a pattern is L-Edit. We created an L-Edit program to create a rectangular pattern of 225nm lines separated by 225nm to create our 450nm pitch grating. To get the optimal electron dose for our writing, we spent many months creating dose arrays. Our dose arrays were

800nm! 800nm patterns of various doses (50µC/cm - 275µC/cm) at different electron accelerating voltages (20keV, 50keV and 100keV). Upon performing the dose arrays, we discovered that we wanted to use 225µC/cm dose at an accelerating voltage of 50keV to create our gratings.

We designed gratings that were roughly 3.0mm ! 1.5mm. The beam-deflection optics are only capable of deflecting the beam so far at the different accelerating voltages

For the 50keV electron gun voltage, the beam can deflect to create a 0.8mm ! 0.8mm pattern. As such, we had to translate the stage to create a two by three array of 0.8mm patterns. The pattern we created on the waveguide is located in Figure 3.20. Once the pattern is loaded into the computer controlling the ebeam setup, we stabilize the ebeam gun at 50keV. We load our sample by placing the disc in the sample holder placed in the ebeam holder (See Figure 3.24.). Upon loading the ebeam holder, we pump down the ebeam system to ~10-6 Torr using a diaphragm pump-backed Turbo pump. Once the ebeam is pumped down and the L-edit program loaded and processed by the ebeam, the ebeam can start writing. The writing process (for our settings) takes about 2 hours. The writing is done by automatic deflection of the beam optics. The height meters located on the ebeam holder keep track of the beam location. Once the writing is done, we are ready to process the waveguide to expose the gratings. We first remove the aluminum by soaking the waveguide sample in Microposit MF CD-26 developer, an aluminum etch. After a three-minute soak, we rinse the sample well with deionized water. The aluminum should be completely removed. We are then ready to develop our photoresists. We create the developer by mixing a 3:1 (by volume) Isopropyl 106 alcohol: Methyl Isobutyl Ketone solution. After placing the sample in the developer for one minute, we saw gratings and promptly rinsed the sample with Isopropyl alcohol. These gratings are in photoresist (as in Figure 3.23’s inverted bilayer) sitting on top of the Ta2O5 waveguide material.

3.4.1.4 Magnesium Fluoride Deposition

Our sample is now Ta2O5 material coated with a photoresist mask of alternating lines and gaps. We are now ready to deposit our magnesium fluoride (MgF2) in the gaps in the photoresist to create our final gratings. We use a thermal evaporator affixed with a tungsten boat containing MgF2 crystals. Amps of current flow through the tungsten boat, heating the boat. A crystal whose resonant frequency changes as more and more material is added to it monitors the thickness of the evaporated material. We must ensure that MgF does not evaporate over any of the waveguide surface that does not have a grating.

Depositing MgF2 on the part of the sample where light is being guided will affect whether the light will be guided. So, we created a mask to leave only the gratings exposed, protecting the Ta2O5 surface. An image of the mask is located in Figure 3.25.

Figure 3.25 Mask to protect the waveguide during MgF2 thermal evaporation.

107

We mount our sample to the thermal evaporator base, covering it with the mask to expose only the gratings. We then pump down our chamber to 8 ! 10-7 Torr using a turbo pump backed by an oil-based roughing pump. After pumping down our chamber we deposit 100nm of MgF2 at roughly 10Å/s. Once the material is deposited, we let the sample cool for a couple of hours, remove the sample, and prepare to perform the final lift-off step to remove the photoresist mask to leave just the MgF2 gratings. As we heat the boat using Joule heating, we melt the crystals. The MgF2 evaporates onto our surface mounted above.

3.4.1.5 Lift-Off Procedure for MgF2 gratings

Our sample now is a Ta2O5 material coated with a photoresist mask over which we have now evaporated MgF2. The MgF2 gets into the grooves of the photoresist mask and

adheres directly to the Ta2O5 material. Where there is still photoresist, the MgF2 just sits on top. To expose the purely MgF2 gratings, we must remove the residual photoresist. To do this, we heat 500mL of acetone in a beaker to 55º C. The acetone will bubble, such that the friction from the bubbles removes the residual acetone. Extreme care was taken, performing the heating in a chemical hood away from any other chemicals or materials, as the flashpoint of acetone is -20º C. Heating the acetone carries the risk of auto-igniting the acetone. Tapping the glass beaker reduces the instability in the boiling acetone. After a ten-minute soak in boiling acetone, the boiling solvent removes all of the residual photoresist, leaving only the MgF2 gratings. We transfer the sample directly from

108 the boiling acetone to a room temperature beaker of isopropyl alcohol. With the sample face-up, we swirl it in the isopropyl alcohol for 2 minutes. We finally pull out the sample and blow off any alcohol with clean, dry nitrogen. We can now look at the grating and sample quality. One concern is that the many steps of soaking the sample and evaporating material on the sample have the potential to destroy the impeccable surface quality that we started with. We determine the new surface quality and grating quality using atomic force microscopy (AFM). Images of the MgF2 gratings are shown in Figure 3.26.

a) b)

Figure 3.26 a) Atomic force microscope images of the MgF2 gratings b) The height profile of the MgF2 gratings showing a grating profile height of 45-50nm.

3.4.2 Waveguide Quality and Coupling

Upon first observation of the waveguide sample, we noticed that some of the gratings were incomplete. We deposited three sets of gratings to ensure that one pair would be usable. The center pair (pair 2 in Figure 3.20) is mostly complete. We performed atomic force microscope (AFM) scans of the gratings as well as the surface between the gratings. A typical grating profile scan can be found in Figure 3.26. The gratings themselves appear to have sharp peaks and valleys. We believe the tips that we are using are

109 unable to get down into the groove to image the grove spacing with higher precision. The grating spacing measured from peak to valley, however, is 440-460nm. Furthermore, the surface quality scans taken using the atomic force microscope between the center grating pair showed an rms surface roughness between 2-5Å. Once we have processed the waveguide, we cut the sides using a home-built diamond saw such that the waveguide fits in the holder we have designed. The waveguide is a ¼’’ thick sample of 1’’ diameter. We cut two of the sides to allow it to fit in the waveguide mount we designed. This was challenging, as we had to cool the sample to cut it but keep the surface solvent-free in order to maintain good surface quality. We built a holder that would cover the waveguide center while exposing the two edges that we wanted to cut off. We sealed the waveguide center on all sides with a thin layer of indium that kept out the methanol solvent we used to cool the sample while cutting. See Figure 3.27 for an image of the cut waveguide in the aluminum holder.

Grating Pair

0.5’’ 1’’

Figure 3.27. The waveguide cut on each side placed in the waveguide holder which extends into the UHV chamber. Note the visible center grating pair.

110 When the light is totally internally reflected in our thin guiding material, the main mechanism for loss is through surface scattering. As discussed in Section 2.2.6, the loss

2 # 4! & goes as 2 2 where is the wavelength of the guided light within the guiding % ( () vw+ ) ws) λw $ "w '

layer, σvw is the rms surface roughness of the vacuum waveguide layer and σws is the rms surface roughness of the waveguide-substrate layer. In our thin film waveguides, we expect

<5db/cm scattering loss for both our TE0 and TE1 modes. The scattering losses increase for higher modes. To measure our coupling and get an idea for our losses, we performed coupling experiments by sending a laser beam focused to <1mm on our waveguide grating.

Figure 3.28 The beam path for the waveguide coupled beam. By adjusting the calcite prism orientation, we adjust which type of mode we send in: TE or TM.

111

We send in a 2mm –wide “top hat”-shaped beam into the waveguide. The beam is created using an injection locked laser tuned to the pump laser frequency. The beam path for the injection locked laser is shown in Figure 3.28. To recap, a planar waveguide mode is excited by the polarization component of the incoming laser light that has the largest overlap with the polarization of the guided beam. TE waveguide modes are excited by s-polarized light where the polarization is parallel to the plane of incidence. TM modes are excited by p-polarized light where the polarization is perpendicular to the plane of incidence. By sending our incident beam through a calcite prism before coupling into the guide, we can select which type of mode we excite in the waveguide. By adjusting the incoupling angle, we adjust which of the TE or TM modes that we send in. Table 3.3 displays information used for coupling the first two modes of each type. We couple the light into one grating, it propagates down the one-centimeter gap between the gratings, and the coupled light exits the opposing grating. We measure our coupling efficiency into the guide as

P % = output _ grating ! 100 Poutput _ grating + Pthru _ beam where Poutput_grating is the power coupled out of the output grating and Pthru_beam is the uncoupled power that passes through the incoupling grating. As indicated in Table 3.3, we see that we have coupled in ~20 percent for both the TE0 and TE1 modes.

1 (nm) Predicted Coupling TE Mode neff ,m !m (°) am Loss (db/cm) Efficiency (%)

TE0 1.934 69.1 37 0.62 18%

TE1 1.530 47.7 54 3.82 15%

Table 3.3. Properties of two lowest TE modes of our slab waveguide.

112 3.5 Elastic Bouncing of Atoms on a Waveguide

Once we have light coupled into the waveguide and a cold atom source to interact with the evanescent wave that results from the field leaking out of the waveguide, we have all the tools to perform the bouncing experiment. To observe the bouncing of the atoms on the waveguide, we observe the passing of atoms through a resonant probe beam

Figure 3.29 Beam layout for probe beam into experiment cell. similar to work done in [31,32,48]. As shown in figure 3.29, the probe beam is the -1st order of the probe AOM. It is tuned 5MHz to the red of resonance. The actual probe beam that is sent into the UHV cell to detect the atoms is sent through a vertical slit and subsequently picked off by a 4% beam splitter. The beam that is picked off is 1mm wide in the vertical dimension and 1cm long. This “sheet” of light sits 1mm below the atom

113 cloud. The sheet of light must be retro-reflected after it is sent into the cell to keep from pushing the atoms out of their downward trajectory. The retro-reflected beam absorption is measured using a photodetector. The weak probe beam power is about 3.6µW. The atoms are allowed to free-fall upon turning off the magnetic trap. The number of atoms crossing the probe beam and the time of their passage through the beam are obtained by monitoring the probe beam with a photodiode. To avoid perturbing the trajectory of the atoms, the probe beam is retro-reflected and turned on just before dropping the atoms.

114

CHAPTER 4

RESULTS AND DISCUSSION

We monitor the atoms bouncing using a weak probe beam that is detuned 5MHz from resonance. As the atoms pass through the beam, some of the light will be absorbed.

Typical absorption scans in time is shown in Figure 4.1.

115 We found that the field begins to shut off 30ms into the scan. It takes about 500µs for the magnetic field to shut off. The absorption prior to this 30ms in Figure 4.1 can be explained as the atom cloud extending into the beam and absorbing probe light prior to dropping. There is also a 30Hz noise component that we have isolated to a vibration in one of the mirrors.

4mm 3mm

Probability

3mK 50µK 100µK 400µK 10µK 1mK 15µK

25µK

Time (ms) Figure 4.2 Expected signal in the photodetector as a function of time after the atom cloud is released. As the cloud temperature is increased, the number of atoms initially passing through the probe decreases and the cloud temperature should be a less than 25µK to be able to see a bounce. The dotted red line shows the signal we can expect to see with our measured temperature.

116 We have theoretically determined the signal we expect to see as a function of the temperature of the atom cloud. The theoretical curves can be found in Figure 4.2. Figure

4.2 shows the probability of seeing a signal at a particular time in milliseconds if the atom cloud (of a particular temperature) is released above the waveguide from the magnetic trap at t=0. The first peak in time represents the atoms first passing through the probe beam before they hit the EW. The second peak is the relative signal after the atoms have bounced off of the EW. To well resolve the first bounce, the atoms must be at 10

µK. For temperatures higher than 25µK, we do not resolve the bounced atoms. As the temperature is increased from 25µK, the atoms are hot, spreading quickly, limiting the number of atoms that pass through the probe beam and hit the EW stripe above the waveguide. As a result, the first peak decreases in size and is pushed closer to the release point in time. We also fail to see a second peak. Our atoms are at 3.4mK (shown by the dotted red line in Figure 4.2). Therefore, we do not see any bounced atoms.

The temperature 10µK can be achieved using three pairs of cooling beams at the

UHV cell. While we have not had a chance to use them, we have implemented them and will be able to produce the colder cloud.

117

CHAPTER 5

CONCLUSIONS

We have presented the results of our work in creating a large area atom mirror using an optical waveguide. An evanescent wave field leaking out of the waveguide surface provides the repulsive dipole force required to have the atoms bounce. To create

2 the evanescent field, we couple laser light (blue-detuned from the 5 S1/2|F=1> →

2 87 5 P3/2|F’=2> Rb transition) into the TE1 transverse electric mode of the waveguide.

Using a modest 10mW of laser power, we create a strong repulsive potential. This strong field is due to the enhancement of the EW resulting from the multiple bounces of the light in the optical waveguide layer as the light travels down the guide. Similar systems have been investigated however a major drawback of these systems is the amount of input power required, which is on the order of Watts. We have found that to see our low- power large area atom mirror, we require an atom cloud with a temperature as cold as

10µK to well resolve the atoms bouncing.

To couple light into our optical waveguide, we use gratings. We have successfully created our MgF2 gratings on our Ta2O5 waveguide sample. We must keep the surface roughness of our waveguide layer low to ensure low scattering losses. The 118 strength of our EW potential is limited by these losses. We have manufactured our

450nm pitch MgF2 gratings on our waveguides using electron beam lithography followed by thermal evaporation, while maintaining a good surface roughness of 2-5Å rms.

We have successfully collected 3 ! 109 cold 87Rb atoms in our MOT, transferred

10% to the purely magnetic trap, and dropped the 3 ! 108 atoms onto our waveguide surface. Upon dropping the atoms on the surface, we find that our atom sample is too warm to resolve the first bounce of the atoms off of the guide. However, we are equipped to cool the atoms adequately by having already implemented three pairs of orthogonal cooling beams in the UHV region.

The goal of this project was originally to create a system to realize an all-optical atom chip for use as a quantum register. See Figure 1.8. Upon cooling the atoms to

10µK using the cooling beams at the UHV cell, we will observe the first bounce of the atoms. After observing this, we will add a thin hollow beam to constrain the atoms in the transverse dimension. Using the EW, we can cool the atoms near the surface (as with

GOSTs described in Section 1.2.2) and confine them in rods above the waveguide surface using the both the EW and the hollow beam. These rod traps can be created as described in [52], by interfering two transverse electric modes of the waveguide, which our system can readily do. By interfering the TE0 and TE1 waveguide modes, we create a standing wave with alternating potential minima and maxima in the evanescent wave field above the waveguide. Upon cooling the atoms using the evanescent wave at the waveguide surface, the atoms will settle into the potential minima created by the interfered waves.

This is imaged in Figure 1.9. These rods are the first step in creating a two dimensional array of potential minima above the waveguide. 119

APPENDIX A: CIRCUIT DIAGRAMS

120

Circuit Diagram A1. Temperature feedback circuit. 121

Circuit Diagram A2. Laser locking circuit 122

Circuit Diagram A3. Laser locking circuit ct’d 123

Circuit Diagram A4 Laser locking circuit ct’d 124

Circuit Diagram A5 Laser shorting box circuit diagram.

125

Circuit Diagram A6 Shutter driver box. The box contains four of these circuits to control four shutters.

126

Circuit Diagram A7 Magnet current supply switch box circuit.

127

APPENDIX B: LABVIEW CODES

128

Code B1 The ramp program to tune our lasers to the appropriate frequency

129

Code B2 LabView code to control the creation of the cold atoms and the dropping experiment 130

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