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Abstract Light Shift Measurements of Cold ABSTRACT LIGHT SHIFT MEASUREMENTS OF COLD RUBIDIUM ATOMS USING RAMAN PUMP-PROBE SPECTROSCOPY Nathan Jon Souther We have measured light shifts, also known as the A.C. Stark effect, in cold Rubidium atoms using pump-probe spectroscopy. The measurement was made both for atoms in a magneto optical trap (MOT) and for atoms that were in an optical molasses. We show that while the measured light shifts agree with theory for optical molasses there are additional Zeeman shifts in the MOT that the theory does not account for. To the best of our knowledge, this is the first time a careful systematic measurement has been performed in cold atoms of light shift as a function of intensity. LIGHT SHIFT MEASUREMENTS OF COLD RUBIDIUM ATOMS USING RAMAN PUMP-PROBE SPECTROSCOPY A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics by Nathan Jon Souther Miami University Oxford, Ohio 2009 Advisor Samir Bali Reader Bur¸cinBayram Reader James Clemens Reader Perry Rice TABLE OF CONTENTS List of Figures . iv Dedication . vi Acknowledgments . vii CHAPTER PAGE 1 Background and Motivation . 1 1.1 Organization of this Thesis . 3 2 Theory and Principles of Light Shift Measurement . 5 2.1 Magneto Optical Trap . 5 2.2 Doppler Cooling . 6 2.3 Trapping the Cooled Atoms in One Spot . 7 2.4 Sub-Doppler Cooling . 8 2.4.1 Motion Induced Atomic Orientation Cooling . 8 2.4.2 Sisyphus Cooling . 11 2.5 Light Shift for a Two Level Atom . 12 2.6 Simplified Light Shift Model for a Multi-Level Atom . 19 2.7 Expected Signal of Light Shift Measurement . 20 3 The Trapping and Repumper Systems . 26 3.1 The External Cavity Diode Laser . 26 3.2 Anamorphic Prism Pair . 28 3.3 Faraday Rotator . 29 3.4 Creating Six Trapping Beams . 33 3.5 Repumper Laser . 34 4 Locking the Lasers . 36 4.1 Saturated Absorption Set Up . 36 4.2 Lowering Threshold . 38 ii 4.3 Acousto Optical Modulator . 40 4.4 Locking the Trap Beam . 41 5 Frequency Scannable Probe . 47 5.1 Spectrum Analyzer . 52 6 The Vacuum System and Magnetic Field Considerations . 57 6.1 Vacuum System . 57 6.2 Canceling the Earth's Magnetic Field . 58 6.3 Applying Magnetic Gradient . 58 7 Experimental Procedure . 63 7.1 Preparation . 63 7.2 Data Collection, MOT . 64 7.3 Data Collection, Molasses . 66 8 Results and Discussion . 68 8.1 The Theoretical Prediction . 68 8.2 Molasses and MOT Data . 70 9 Conclusions and Future Outlook . 71 9.1 Conclusions . 71 9.2 Future Outlook . 71 9.2.1 Independent Pump-Probe . 72 9.3 Optical Fiber . 73 9.4 Independent Pump-Probe Measurements . 73 Bibliography . 78 iii LIST OF FIGURES FIGURE PAGE 2.1 Laser Cooling . 6 2.2 Atom Trapping . 8 2.3 Polarization Gradient for σ+ and σ− polarized Light . 9 2.4 Clebsch-Gordan Coefficients for J = 1 to J 0 = 2 Atomic System . 10 2.5 Motion Induced Population Imbalance . 11 2.6 Polarization Gradient and Energy Light Shift for π-polarized Light . 13 2.7 Clebsch-Gordan Coefficients for J=1/2 to J'=3/2 Atomic System . 14 2.8 Two Level Atom . 15 2.9 Ground State Light Shift . 18 2.10 Clebsch-Gordan Coefficients for the F=3 to F0= 4 Atomic System . 23 2.11 Light Shifts in the F=3 Ground State Atomic Levels . 24 2.12 Cause of Raman Peaks . 25 3.1 Trapping Beam Optical Layout . 27 3.2 Anamorphic Prism Pair Setup . 29 3.3 Anamorphic Prism Pair Angles . 30 3.4 Anamorphic Prism Pair Displacements . 31 4.1 Saturated Absorption Spectroscopy Setup . 37 4.2 Saturated Spectrum Hyperfine Ground State Pictures . 43 4.3 BNC Connections with Laser Locking Box . 44 4.4 Circuit for Creating Variable Fixed Offset for AOM . 45 iv 4.5 Locking Points for Different Detunings of Trap Laser . 46 5.1 Optical Layout for the Pump-Probe . 48 5.2 Circuit for Creating Variable Scanning Offset for AOM . 51 5.3 Double-pass AO Setup for Probe . 52 5.4 Single Pass Frequency Shift . 55 5.5 Double Pass Frequency Shift . 56 6.1 Getter Pin Diagram . 59 6.2 Magnetic Field Turn Off . 61 6.3 Magnetic Field Turn On . 62 7.1 Typical Light Shift Measurement . 65 7.2 Molasses Data Taking Timing . 67 8.1 MOT and Molasses Data . 69 9.1 Independent Pump Probe Setup . 72 9.2 Multi Mode vs. Single Mode Fibers . 74 9.3 Circuit Diagram for Pump Shutter Control . 75 9.4 Pump Shutter Opening . 76 9.5 Spectrum for Independent Pump-Probe . 77 9.6 Trap Shutter Closing . 77 v To Drea vi ACKNOWLEDGMENTS I would first like to thank my advisor Samir along with undergraduates Peter Harnish and Richard Wagner for all their work along side of me, including those 30 hour days in the lab. I would not have been able to accomplish what I have without their help. I am also indebted to Michael Eldridge and Mark Fisher. If it was not for Mike's helpfulness, expertise, and availability work in the lab would have been a lot slower. He was always able to make or help me make the pieces that I needed in the lab. Mark's helpfulness and ability to have random electronic components stored away on his shelves has proved invaluable and saved us a lot of time. I'm thankful for all the department faculty and staff that taught me and helped me in numerous ways, along with my fellow graduate students who provided me with entertainment, and especially those who provided used of their vehicles. Finally, I would like to thank my family for all the support they have given me over the years and Andrea for putting up with me being 700 miles away for two years. vii CHAPTER 1 BACKGROUND AND MOTIVATION A magneto optical trap (MOT) has become a standard tool in recent years, allowing for cold atomic samples in the micro Kelvin temperature range. Doppler broadening and collision rates in the MOT are greatly reduced. These properties make cold atoms an attractive environment to conduct fundamental experiments in atomic and optical physics. Since this setting has become so popular it is important to fully understand it. The use of pump-probe spectroscopy allows for diagnostic measurements of the MOT while still in operation. Due to the low powers used in the probe, the measure- ments are nondestructive allowing for continuous measurement of the behavior of the atom in the trap and the parameters of the trap. Pump-probe spectroscopy can also be used right after the atoms are released from the trap as is the case with optical molasses which are formed by turning off the magnetic field gradient in the MOT. Through a careful study of the MOT or molasseses new information is gained about the dynamics of the cold atoms. One particular area of interest is the exploration of Raman transitions that occur between the light shifted Zeeman sublevels of the trapped atoms. By exploring the correlation between the light shift and radiation pressure among the trapped atoms one group [1] has suggested using negative pressures to induce an optical implosion of trapped atoms. Grison et al. [2] was the first group to experimentally show, using a probe beam, the existence of population differences in 1 Zeeman ground state atomic sublevels. Another group [3] has studied the polarization dependence of the probe when performing spectroscopy of a MOT. The differences they found are signatures of optical anisotropy in the cold atoms. Our own motivation to study Raman spectroscopy of the light shifted Zeeman sublevels of the cold trapped atoms is threefold. First, since there are many schools with working MOTs, there is clearly a peda- gogical interest to demonstrate spectroscopy on a sub-MHz scale. Almost all MOT setups use saturated absorption techniques to lock the trapping lasers. Saturated Absorption offers a great introduction to atomic spectroscopy at the few MHz level to the advance undergraduate and graduate student. We show here that with the addition of a weak probe beam that can be scanned in frequency, a $30 photo diode detector, and a standard oscilloscope one can easily perform atomic spectroscopy with 0.01-0.1 MHz resolution. Second, upon scouring the literature we have found, to our surprise, no evidence of a systematic measurement of light shifts in cold atoms as a function of laser intensity. Several interesting questions arise: Many atomic groups use the MOT as a target for a variety of spectroscopic mea- surements [4], without feeling a need to instead use molasses (obtained by turning off the magnetic field gradient in the MOT). Molasses are colder and denser than the MOT, however the disadvantage is that molasses are transient, with the atoms diffusing away in a few hundred milliseconds. Hence, the question arises: While the MOT is a more convenient test-bed than molasses, is it possible at all to reliably measure light shifts in the MOT? How badly are these measurements affected by the presence of the magnetic field gradient? The traditional theoretical treatment of the light shift is based on a completely coherent light-atom interaction where spontaneous emission can be taken to be ab- sent. How well does this coherent theory compare with measurements performed on cold atoms trapped by near-resonant light? 2 Third, our immediate goal is to build an optical lattice for the purpose of studying anomalous atomic transport that has been predicted in near-resonant lattices.
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