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Microwave Manipulation of Cold Atoms MICROWAVE MANIPULATION OF COLD ATOMS Thesis submitted in partial fulfillment of the requirement for the degree of master of science in the Faculty of Natural Sciences Submitted by: Ruti Agou Advisor: Prof. Ron Folman Department of Physics Faculty of Natural Sciences Ben-Gurion University of the Negev August 15, 2011 Abstract in hebrew 1 Abstract The coherent control of a two-state quantum system stands at the base of the field of quan- tum optics. In this work, I have utilized cold rubidium atoms as such a system, and developed a scheme for imaging multiple Rabi oscillations simultaneously. This may later be used for fundamental studies as well as metrology. For this purpose I designed and built, starting with a 'naked' optical table, a versa- tile laboratory system capable of trapping 109 87Rb atoms, cooling them to a temperature of 60 µK, and manipulating them by direct microwave radiation tuned to the ground-level hyperfine splitting. In this thesis I describe the experimental setup, including lasers, op- tics, electro-optics, vacuum, electronics and computers. Following the theoretical review, I present properties of the cooled atomic cloud, the atomic population oscillations (Rabi frequency of 10-20 kHz) induced by the microwave (MW) field, and the simultaneous ('one shot') observation of multiple spatial Rabi fringes, which "move" as a function of time as the populations in the two states evolve. I also present the dependence of the Rabi frequency, and thereby state populations, on the spatial position of the atoms. I conclude with a sum- mary and brief outlook. The work described in this thesis was done in parallel to the work of P. B¨ohi et al.1, who reported a technique that uses ultracold atomic clouds for mapping at a single shot, microwave near field distribution around a coplanar wave-guide integrated on an atom chip. The main novelty so far in my results is the ability to map at a single shot, microwave fields generated from an horn antenna at near and far fields. Since my setup is completely different and has no atomchip in it I had at my disposal more atoms, enabling the observation of more fringes. In addition, as I could move and rotate the source of microwave I could also observe a variety of dependencies of the fringe behavior on parameters such as time, field direction and polarization. 1App. Phys. Lett. 97, 051101 (2010) 2 Acknowledgements During my work on this thesis as part of the AtomChip Group, I had the honor of meeting and working with brilliant scientists which have made this work possible and to whom I owe my deepest gratitude. First of all, I would like to thank my supervisor, Professor Ron Folman, who has given me the opportunity to learn and apply the knowledge of the quantum atomic physics world. He guided me through my work with great patience and kindness. I am grateful to Dr. David Groswasser and Amir Waxman for spending long days, and even longer nights in the lab with me, offering me assistance whenever necessary and sharing their rich toolbox of knowledge. It was a great pleasure to work with you, and I thank you both extensively. I also want to thank Meny Givon for his professional assistance and his considerable experience in the Lab, which helped me progress in my studies. Your availability for con- versations about physics, politics and religion, during coffee breaks, forged an agreeable and colourful atmosphere enriching my experience. I would like to give specials thanks to Shimi Machluf and Ramon Szmuk, the BEC guys, for always being willing to help. Shimi: thank you for being my teacher, who was always ready to answer my trivial, and maybe even sometimes annoying, questions. Ramon: thank you for sharing your software knowledge (especially in 3D). Your love of physics in- spired me, and your true friendship means a lot to me. Many thanks is owed to the PhDs in our group: Yoni Japha, Tal David, Ran Salem, Julien Chab´e and Mark Keil for sharing their great knowledge with me. Also, I would to thank Jonathan and Asif from Weizmann institute, for lending me the MW amplifier and therefore allowing me to proceed with my research. 3 My lab work could not have been completed without the supportive, continual help of our electronics-wizard Zina, who built and fixed most of the electronic devices used in my work. None of this would have happened without the endless love, support and backing of my dear family: my parents, Daniel and Anne Marie Agou, to whom I owe so much, and my brothers Nathaniel and Jonathan, who were always there for me (Je vous aimee ´normement). Most important is the warm presence of my beloved husband Tomer: I thank you for understanding the endless hours I spent in the lab and the sudden moments of enthusiasm from physics which occasionally came over me. My appreciation can not be expressed by words, and for this I love you so much. And above all, thanks to the infinite kindness and awareness surrounding me, reminding me on each step of the way just how small I am... 4 Contents Contents . .6 List of figures . 11 1 Introduction 12 1.1 Background . 12 1.2 Thesis content . 14 2 Theory of Rabi Oscillations in a Two-state Atom 15 2.1 Bloch sphere representation . 15 2.2 The Schr¨odingerequation for a two-state atom . 16 2.3 Rabi oscillations induced by microwave radiation . 18 3 Theory of Laser Cooling 21 3.1 The 87Rb alkali metal . 21 3.2 Theory of light-matter interaction . 23 3.2.1 Light force on a two-level atom . 23 3.2.2 Doppler cooling . 23 3.2.3 Doppler and sub-Doppler limit . 24 3.3 Magneto-Optical Trap (MOT) . 25 4 Experimental Apparatus 29 4.1 Ultra-high vacuum setup . 29 4.2 Atom source . 31 4.3 Lasers and optics system . 32 5 4.3.1 Laser lock and spectroscopy . 32 4.3.2 Optical layout . 36 4.3.3 Science chamber . 40 4.4 Static and AC fields . 40 4.5 Optical pumping . 42 4.6 Imaging . 45 4.6.1 Temperature and gravitation measurements . 48 4.7 Experimental control . 50 5 Rabi Oscillations in Cold Atoms 53 5.1 Experimental Sequence . 53 5.2 Results . 55 5.2.1 Inducing Rabi oscillations simultaneously over space . 55 5.2.2 Inducing Rabi oscillations over time . 57 5.2.3 The Rabi frequency's dependence on the position in the cloud in the far field . 60 5.2.4 The fringe pattern dependence on the position of the MW antenna . 61 6 Summary and Outlook 63 Bibliography 66 6 List of Figures 2.1 The Bloch Sphere .................................. 16 2.2 Rubidium 87 D1 and D2 transition hyperfine structure. ................ 20 3.1 Illustration of a MOT in 1D. The detuning δ is for atoms at rest at the trap's center. Due to the Zeeman shift of magnetic sublevels, and the arrangement of laser polarizations, atoms are driven to the trap's center. Spatial confinement and cooling are obtained simultaneously [Met99]. ....................................... 26 3.2 MOT pictures from the experiment. (left) Image of the 87Rb cloud as it appears in the vacuum chamber. (right) Fluorescent image of the MOT using a CCD. The cloud size is 8 87 13 mm (2σz) and contains 9 · 10 Rb atoms, in both images. ............. 27 3.3 Photograph of optical molasses taken by fluorescent imaging using a CCD. Three orthogonal MOT beams cross in the center where atoms which are further cooled, glow brightly. .. 28 4.1 Image of the vacuum system and science chamber. ................... 30 4.2 Laser Box. (top) Three home-made lasers: The Cooler and Repumper utilized for the cooling cycle (the Cooler is also used for imaging and optical pumping). The Tapered Amplifier (T.A.) amplifies the injected Cooler beam (drawn in red) up to 1.3 W. (bottom) Polarization spectroscopy scheme. A 3 mW beam is split off from the main laser beam, and used for spectroscopy. The Rb vapor cell is covered with two layers of µ-metal shielding. Two photo-diodes are used to produce the error signal. The remaining 30 mW in the main beam is mode-matched by a telescope to allow for the best injection into the T.A. Then, the amplified beam exits on the right side of the box, passing through a cylindrical lens to fix the dispersion of the horizontal axis of the beam with respect to the vertical axis. ... 34 7 4.3 Two 87Rb spectroscopy images used for the laser frequency stabilization: Cooler spec- troscopy (left), Repumper spectroscopy (right). An absorption spectroscopy signal (top) is compared to a polarization spectroscopy signal (bottom). ................ 35 4.4 Mechanical and thermal housing for the tapered amplifier. (left) Exploded diagram. The blocks are made of copper (the centring rods are of steel). From [Nym06]. (right) Photo- graph of our assembled system. ............................ 35 4.5 The frequencies of the four laser beams used for the experimental cycle are superimposed on 87 the level scheme of the Rb D2 transition hyperfine structure. The ground state levels are denoted by F, and the excited state levels by F0. Dashed lines correspond to the cross-over peaks (1x2, 1x3), to which our lasers are locked. Arrows indicate these lock points, as well as the frequency of each laser component after passing its AOM. ............ 37 4.6 Optics behind the laser box. (top) Image of the setup. The Cooler beam is divided into three paths through three different AOMs, Cooler (blue), Imaging (yellow), Optical Pumping (red).
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