Ion trap cavity quantum electrodynamics

ION TRAP CAVITY QUANTUM ELECTRODYNAMICS CHUAH BOON LENG B.Sc. (Hons.), NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2013 Declaration of Authorship I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Signed: Date: 4th December 2013 i Acknowledgements The completion of my project would be impossible without the support from my family. I have to thank my parents for their unconditional loves and supports, which give me peace of mind and keep me going all the way. I also have to thank my sister, who has been taking good care of my parents all these years. I am very grateful to my wife, Mei Fei; my life would definitely be a mess without her spiritual supports and guidances. Of course I have to thank my supervisor, Murray, who welcomed me in his group and taught me everything from aligning optics to writing manuscripts. A special thank to Meng Khoon, for giving me his invaluable advices all these years. If I were to build all the experimental setup by myself, the project would never come to a completion. For this, I owe 50% of my achievements to Nick, who has been my project mate all along. A big thank you to Markus, for his significant contribution to my first publication and the useful discussions we had when I was struggling hard with writing manuscripts or solving theoretical problems. Equally important are Kyle and Radu, their constructive comments and advices on various aspects are deeply appreciated. Thanks to Joven and Andrew, for providing technical supports from machining to technical drawing. I am also very thankful for the joy and laughter brought by Arpan, which comforted me and others even when things went really wrong in the lab. To my other friends, thanks for supporting me during the bad times and celebrating with me during the good. It has been a great experience for me to work on this project. Although the journey has never been easy, in the end I realize that every obstacle I came across was actually a stepping stone towards success. Therefore, I am proud and grateful for being part of my team: Microtrap group. ii Contents Declaration of Authorship i Acknowledgements ii Abstract vii List of Publications viii List of Tables ix List of Figures x Abbreviations xii Introduction Theoretical Considerations 2.1 Linear Paul Trap . . . . . . . . . . . . . . . . . . . . . . . 2.2 Doppler Cooling . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Coherent State Manipulation of Trapped Ions . . . . . . . 2.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Raman Transitions . . . . . . . . . . . . . . . . . . 2.3.2.1 Phase Fluctuations . . . . . . . . . . . . . 2.3.2.2 Motional Coupling . . . . . . . . . . . . . 2.3.3 Raman Sideband Cooling . . . . . . . . . . . . . . 2.4 Cavity QED: A Brief Theoretical Overview . . . . . . . . . 2.5 Thermal Effect on Ion-cavity Coupling . . . . . . . . . . . 2.6 Cavity Cooling in the Presence of Recoil Heating and Cavity Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 10 10 11 14 15 17 18 24 . 27 Apparatus 30 3.1 The Ion Trap . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 The Experimental Cavity . . . . . . . . . . . . . . . . . . . . 34 iii Contents 3.3 3.4 3.5 3.6 3.7 3.2.1 The Cavity Design . . . . . . . . . . . . . . . . . . 3.2.2 Detection of the Cavity Emission . . . . . . . . . . The Imaging System . . . . . . . . . . . . . . . . . . . . . The General Considerations of the Laser System . . . . . . 3.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 The Transfer-Cavity-Lock . . . . . . . . . . . . . . 3.4.3 The Self-heterodyne Locking System . . . . . . . . 3.4.3.1 Theory . . . . . . . . . . . . . . . . . . . 3.4.3.2 Implementation . . . . . . . . . . . . . . . The Doppler Cooling Lasers . . . . . . . . . . . . . . . . . 3.5.1 The 493 nm Laser System . . . . . . . . . . . . . . 3.5.1.1 The 986 nm laser . . . . . . . . . . . . . . 3.5.1.2 The doubling cavity . . . . . . . . . . . . 3.5.1.3 The EOM and AOM setup . . . . . . . . 3.5.2 The 650 nm Laser System . . . . . . . . . . . . . . 3.5.2.1 The laser frequency stabilization . . . . . 3.5.2.2 The repumping system for 137 Ba+ . . . . . The Raman Lasers . . . . . . . . . . . . . . . . . . . . . . 3.6.1 The Red Cavity . . . . . . . . . . . . . . . . . . . . 3.6.2 The 493 nm Raman Laser . . . . . . . . . . . . . . 3.6.3 The 650 nm Laser . . . . . . . . . . . . . . . . . . . The Synchronization Between the Experimental Cavity and the Cavity Probing Laser . . . . . . . . . . . . . . . . . . . 3.7.1 The Blue Cavity . . . . . . . . . . . . . . . . . . . 3.7.2 The Compensation for the Fast Jitter in the Experimental Cavity . . . . . . . . . . . . . . . . . Experimental Methods 4.1 Ion Loading . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Barium Oven . . . . . . . . . . . . . . . . . . . . 4.1.2 Photo-ionization . . . . . . . . . . . . . . . . . . 4.2 Temperature Measurement of 138 Ba+ . . . . . . . . . . . 4.3 Two-color Raman Cooling of 138 Ba+ . . . . . . . . . . . 4.4 General Methods in Cavity QED Experiments . . . . . . 4.4.1 Cavity Linewidth Measurements . . . . . . . . . . 4.4.2 Alignment of the Cavity Field to a Single Ion . . 4.4.3 Ion-Cavity Emission Profiles . . . . . . . . . . . . 4.4.3.1 Birefringence induced phase retardation 4.4.4 The Single Atom Cooperativity . . . . . . . . . . 4.5 The Cavity-Enhanced Single Ion Spectroscopy . . . . . . 4.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 35 36 38 38 40 43 43 44 47 47 48 49 50 50 50 52 54 54 56 56 . 58 . 59 . 61 . . . . . . . . . . . . . 63 64 64 65 66 70 75 75 76 77 79 81 83 83 Contents 4.5.2 4.5.3 4.5.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 84 Measurements . . . . . . . . . . . . . . . . . . . . . . 86 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 87 State Detection Using Coherent Raman Repumping and Two-color Raman Transfer 89 5.1 The Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.1 State Preparation . . . . . . . . . . . . . . . . . . . . 93 5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3.3 The Limiting Factors . . . . . . . . . . . . . . . . . . 95 5.4 Two-color Raman Transfer . . . . . . . . . . . . . . . . . . . 99 5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . 101 Detection of Ion Micromotion in a Linear a High Finesse Cavity 6.1 Introduction . . . . . . . . . . . . . . . . . 6.2 The Model . . . . . . . . . . . . . . . . . . 6.3 The Experiment . . . . . . . . . . . . . . . 6.4 Results . . . . . . . . . . . . . . . . . . . . 6.5 Limiting Factors . . . . . . . . . . . . . . 6.6 Concluding Remarks . . . . . . . . . . . . Sub-Doppler Cavity Cooling Regime 7.1 Cavity Cooling . . . . . . . . 7.2 Setup . . . . . . . . . . . . . . 7.3 Experiments . . . . . . . . . . 7.4 Concluding Remarks . . . . . Paul Trap with 102 . . . . . . . . . . 102 . . . . . . . . . . 104 . . . . . . . . . . 108 . . . . . . . . . . 111 . . . . . . . . . . 114 . . . . . . . . . . 115 Beyond The Lamb-Dicke 116 . . . . . . . . . . . . . . . . . 117 . . . . . . . . . . . . . . . . . 118 . . . . . . . . . . . . . . . . . 119 . . . . . . . . . . . . . . . . . 122 Photon Statistics of the Ion-Cavity Emission 8.1 Model . . . . . . . . . . . . . . . . . . . . . . 8.2 Experiments . . . . . . . . . . . . . . . . . . . 8.3 Results . . . . . . . . . . . . . . . . . . . . . . 8.4 Concluding Remarks . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 . 123 . 127 . 128 . 130 132 A Barium Atomic and Ionic Data 135 A.1 Basic Atomic Data . . . . . . . . . . . . . . . . . . . . . . . 135 v Contents A.2 Ionic Transition Data . . . . . . . . . . . . . . . . . . . . . . 136 B The Probability Distribution of a Leaky State 143 Bibliography 146 vi Abstract A trapped ion-cavity system is a potential candidate in quantum information processing (QIP) applications as it provides an efficient interface between ions (quantum memory) and photons (information carrier). In addition, a cavity also provides other useful functions for a trapped ion system such as ion cooling. This thesis explores various functionalities of a trapped ion-cavity system that highlight its potential as a practical tool for QIP applications. In this thesis, experiments are performed on a singly charged barium ion trapped within a high finesse cavity. The experiments make use of a vacuum stimulated Raman transition, which involves an exchange of one photon between the driving laser operating at 493 nm and the intra-cavity field with a resonance at the same wavelength. Depending on the experimental goal, the system can be manipulated to induce mechanical effects on the trapped ion or alter the properties of the cavity output. Using these approaches, the following experimental results are reported: efficient 3-D micromotion compensation despite optical access limitations imposed by the cavity mirrors, first demonstration of sub-Doppler cavity sideband cooling of trapped ions, and first proposal of ion temperature probing using a high finesse cavity. Additionally, a number of useful techniques such as cavity enhanced single ion spectroscopy and state detection using Raman repumping lasers were developed over the course of the experiments. vii List of Publications The following is a list of publications I have coauthored during my Ph.D. studies. 1. Boon Leng Chuah, Nicholas C. Lewty, and Murray D. Barrett. State detection using coherent raman repumping and two-color raman transfers. Physical Review A, 84:013411, Jul 2011. 2. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett. Spectroscopy on a single trapped 137 Ba+ ion for nuclear magnetic octupole moment determination. Optics Express, 20(19):21379–21384, Sep 2012. 3. Boon Leng Chuah, Nicholas C. Lewty, Radu Cazan, and Murray D. Barrett. Sub-doppler cavity cooling beyond the lamb-dicke regime. Physical Review A, 87:043420, Apr 2013. 4. Boon Leng Chuah, Nicholas C. Lewty, Radu Cazan, and Murray D. Barrett. Detection of ion micromotion in a linear paul trap with a high finesse cavity. Optics Express, 21(9):10632–10641, May 2013. 5. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett. Experimental determination of the nuclear magnetic octupole moment of 137 012518, Jul 2013. viii Ba+ ion. Physical Review A, 88: List of Tables 3.1 3.2 Properties of trap A and B . . . . . . . . . . . . . . . . . . . 32 The AOM frequencies of 650 nm repumper . . . . . . . . . . 53 A.1 A.2 A.3 A.4 . 135 . 136 . 136 Isotopes of barium . . . . . . . . . . . . . . . . . . . . . . Isotopes shift @ 493 nm and 455 nm . . . . . . . . . . . . . Isotopes shift @ 650 nm, 614 nm, and 585 nm . . . . . . . . Dipole matrix elements for transition J = 1/2 → J = 1/2 of isotopes with In = . . . . . . . . . . . . . . . . . . . . A.5 Dipole matrix elements for transition J = 3/2 → J = 1/2 of isotopes with In = . . . . . . . . . . . . . . . . . . . . A.6 135 Ba+ or 137 Ba+ relative hyperfine transition strength for P1/2 → S1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . A.7 135 Ba+ or 137 Ba+ relative hyperfine transition strength for P1/2 → D3/2 . . . . . . . . . . . . . . . . . . . . . . . . . . A.8 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition S1/2 | F = → P1/2 | F = . . . . . . . . . . . A.9 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition S1/2 | F = → P1/2 | F = . . . . . . . . . . . A.10 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition S1/2 | F = → P1/2 | F = . . . . . . . . . . . A.11 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition S1/2 | F = → P1/2 | F = . . . . . . . . . . . A.12 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . A.13 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . A.14 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . A.15 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . A.16 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . A.17 135 Ba+ or 137 Ba+ hyperfine dipole matrix elements for transition D3/2 | F = → P1/2 | F = . . . . . . . . . . . ix . 136 . 137 . 137 . 137 . 137 . 138 . 138 . 138 . 139 . 139 . 139 . 139 . 140 . 140 Bibliography [45] E. Mathieu. M´emoire sur le mouvement vibratoire dune membrane de forme elliptique. Journal de Math´ematiques Pures et Appliqu´ees, 13:137–203, 1868. Cited in page: [46] Theodor W H¨ansch and Arthur L Schawlow. Cooling of gases by laser radiation. Optics Communications, 13(1):68–69, 1975. Cited in page: [47] D Wineland and H Dehmelt. Proposed 1014 δν/ν laser fluorescence spectroscopy of Tl+ mono-ion oscillator iii (sideband cooling). Archives of the Bulletin of the American Physical Society, 637, 1975. Cited in page: [48] DJ Wineland, RE Drullinger, and FL Walls. Radiation-pressure cooling of bound resonant absorbers. Physical Review Letters, 40 (25):1639–1642, 1978. Cited in page: [49] DJ Wineland, Wayne M Itano, JC Bergquist, and Randall G Hulet. Laser-cooling limits and single-ion spectroscopy. Physical Review A, 36(5):2220, 1987. Cited in page: 10, 17 [50] HS Margolis, GP Barwood, G Huang, HA Klein, SN Lea, K Szymaniec, and P Gill. Hertz-level measurement of the optical clock frequency in a single 88 Sr+ ion. Science, 306(5700):1355–1358, 2004. Cited in page: 10 [51] C Monroe, DM Meekhof, BE King, SR Jefferts, WM Itano, DJ Wineland, and P Gould. Resolved-sideband raman cooling of a bound atom to the 3d zero-point energy. Physical Review Letters, 75(22), 1995. Cited in page: 10, 18, 66, 119 [52] Nicholas C Lewty, Boon Leng Chuah, Radu Cazan, BK Sahoo, and MD Barrett. Spectroscopy on a single trapped 137 Ba+ ion for nuclear 152 Bibliography magnetic octupole moment determination. Optics Express, 20(19): 21379–21384, 2012. Cited in page: 10, 142 [53] MR Dietrich, N. Kurz, T. Noel, G. Shu, and BB Blinov. Hyperfine and optical barium ion qubits. Physical Review A, 81(5):52328, 2010. Cited in page: 10, 89, 90, 99 [54] Harold J Metcalf and Peter Van der Straten. Laser cooling and trapping. Springer Verlag, 1999. Cited in page: 12, 13 [55] Bruce W Shore. The Theory of Coherent Atomic Excitation: Simple atoms and fields, volume 1. Wiley-Interscience, 1990. Cited in page: 12 [56] Chen Zhanjiang. Shelving of Barium Ion by Two Lasers Raman Transition. Undergraduate honours thesis, National University of Singapore, 2010. Cited in page: 13, 15, 56 [57] MJ McDonnell, DN Stacey, and AM Steane. Laser linewidth effects in quantum state discrimination by electromagnetically induced transparency. Physical Review A, 70(5):053802, 2004. Cited in page: 15 [58] SE Hamann, DL Haycock, G Klose, PH Pax, IH Deutsch, and PS Jessen. Resolved-sideband raman cooling to the ground state of an optical lattice. Physical Review Letters, 80:4149–4152, 1998. Cited in page: 18 [59] F Schmidt-Kaler, S Gulde, M Riebe, T Deuschle, A Kreuter, G Lancaster, C Becher, J Eschner, H H¨affner, and R Blatt. The coherence of qubits based on single Ca+ ions. Journal of Physics B: Atomic, Molecular and Optical Physics, 36(3):623, 2003. Cited in page: 18 153 Bibliography [60] Edwin T Jaynes and Frederick W Cummings. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proceedings of the IEEE, 51(1):89–109, 1963. Cited in page: 19 [61] Moorad Alexanian and Subir K Bose. Unitary transformation and the dynamics of a three-level atom interacting with two quantized field modes. Physical Review A, 52:2218–2224, 1995. Cited in page: 21 [62] Ying Wu. Effective raman theory for a three-level atom in the λ configuration. Physical Review A, 54(2):1586, 1996. Cited in page: 21 [63] C Russo. Photon statistics of a single ion coupled to a high-finesse cavity. PhD thesis, University of Innsbruck, 2008. Cited in page: 21 [64] Willard Miller. Symmetry groups and their applications. Academic Press, 1972. Cited in page: 21 [65] Stefano Zippilli and Giovanna Morigi. Mechanical effects of optical resonators on driven trapped atoms: Ground-state cooling in a high-finesse cavity. Physical Review A, 72:053408, Nov 2005. Cited in page: 27, 28, 29, 117, 121 [66] Stig Stenholm. The semiclassical theory of laser cooling. Reviews of Modern Physics, 58:699–739, Jul 1986. Cited in page: 27, 29 [67] F.E. Terman. Radio engineers’ handbook. McGraw-Hill Book Company Incorporated, 1943. Cited in page: 33 [68] W.M. Itano and DJ Wineland. Laser cooling of ions stored in harmonic and penning traps. Physical Review A, 25(1):35, 1982. Cited in page: 33 154 Bibliography [69] RWP Drever, John L Hall, FV Kowalski, J Hough, GM Ford, AJ Munley, and H Ward. Laser phase and frequency stabilization using an optical resonator. Applied Physics B: Lasers and Optics, 31 (2):97–105, 1983. Cited in page: 41, 110 [70] Bengt Edl´en. The refractive index of air. Metrologia, 2(2):71, 1966. Cited in page: 43 [71] KP Birch and MJ Downs. An updated edl´en equation for the refractive index of air. Metrologia, 30(3):155, 2005. Cited in page: 43 [72] KP Birch and MJ Downs. Correction to the updated edl´en equation for the refractive index of air. Metrologia, 31(4):315, 2005. Cited in page: 43 [73] Philip E Ciddor. Refractive index of air: new equations for the visible and near infrared. Applied Optics, 35(9):1566–1573, 1996. Cited in page: 43 [74] HN Rutt. A heterodyne frequency offset locking technique for pulsed or cw lasers. Journal of Physics E: Scientific Instruments, 17:704, 1984. Cited in page: 43, 53 [75] U Schunemann, H Engler, R Grimm, M Weidemuller, and M Zielonkowski. Simple scheme for tunable frequency offset locking of two lasers. Review of Scientific Instruments, 70(1):242–243, 1999. Cited in page: 43, 53 [76] Carl E Wieman and Leo Hollberg. Using diode lasers for atomic physics. Review of Scientific Instruments, 62(1):1–20, 1991. Cited in page: 48 [77] KB MacAdam, A Steinbach, and Carl Wieman. A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for cs and rb. American Journal of Physics, 155 Bibliography 60:1098–1098, 1992. Cited in page: 48 [78] PA Franken, AE Hill, CW el Peters, and G Weinreich. Generation of optical harmonics. Physical Review Letters, 7(4):118–119, 1961. Cited in page: 49 [79] ES Polzik and HJ Kimble. Frequency doubling with KNbO3 in an external cavity. Optics Letters, 16:1400–1402, 1991. Cited in page: 49 [80] A Hemmerich, DH McIntyre, C Zimmermann, and TW H¨ansch. Second-harmonic generation and optical stabilization of a diode laser in an external ring resonator. Optics Letters, 15(7):372–374, 1990. Cited in page: 49 [81] B Dahmani, L Hollberg, and R Drullinger. Frequency stabilization of semiconductor lasers by resonant optical feedback. Optics Letters, 12(11):876–878, 1987. Cited in page: 56 [82] P Laurent, A Clairon, and C Breant. of optically self-locked diode lasers. Frequency noise analysis IEEE Journal of Quantum Electronics, 25:1131–1142, 1989. Cited in page: 56 [83] HL Stover and WH Steier. Locking of laser oscillators by light injection. Applied Physics Letters, 8(4):91–93, 1966. Cited in page: 57 [84] KT Jacob and Y. Waseda. The vapour pressures of barium and strontium. Journal of the Less Common Metals, 139(2):249–259, 1988. Cited in page: 64 [85] AV Steele, LR Churchill, PF Griffin, and MS Chapman. Photoionization and photoelectric loading of barium ion traps. 156 Bibliography Physical Review A, 75(5):053404, 2007. Cited in page: 65 [86] DM Lucas, A Ramos, JP Home, MJ McDonnell, S Nakayama, J-P Stacey, SC Webster, DN Stacey, and AM Steane. Isotope-selective photoionization for calcium ion trapping. Physical Review A, 69(1): 012711, 2004. Cited in page: 65 [87] S Gulde, D Rotter, P Barton, F Schmidt-Kaler, R Blatt, and W Hogervorst. Simple and efficient photo-ionization loading of ions for precision ion-trapping experiments. Applied Physics B: Lasers and Optics, 73(8):861–863, 2001. Cited in page: 65 [88] B Wang, JW Zhang, C Gao, and LJ Wang. Highly efficient and isotope selective photo-ionization of barium atoms using diode laser and led light. Optics Express, 19(17):16438–16447, 2011. Cited in page: 65 [89] Nicholas C. Lewty. Experimental Determination of The Nuclear Magnetic Octupole Moment of 137 Ba+ . PhD thesis, National University of Singapore, 2014. Cited in page: 66, 70 [90] Goh Wei Na. Photoionization of Neutral Barium. Undergraduate honours thesis, National University of Singapore, 2011. Cited in page: 66 [91] A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger. Controlling fast transport of cold trapped ions. Physical Review Letters, 109:080501, Aug 2012. Cited in page: 68, 131 [92] R. Bowler, J. Gaebler, Y. Lin, T. R. Tan, D. Hanneke, J. D. Jost, J. P. Home, D. Leibfried, and D. J. Wineland. Coherent diabatic ion 157 Bibliography transport and separation in a multizone trap array. Physical Review Letters, 109:080502, Aug 2012. Cited in page: 68 [93] Ralph G DeVoe and Christian Kurtsiefer. Experimental study of anomalous heating and trap instabilities in a microscopic 137 Ba ion trap. Physical Review A, 65(6):063407, 2002. Cited in page: 72, 84, 87, 91, 95 [94] WW Macalpine and RO Schildknecht. Coaxial resonators with helical inner conductor. Proceedings of the IRE, 47(12):2099–2105, 1959. Cited in page: 74 [95] Aiden J Lockwood, Jing Jing Wang, Ralph Gay, and Beverley J Inkson. Characterising performance of tem compatible nanomanipulation slip-stick inertial sliders against gravity. In Journal of Physics: Conference Series, volume 126, page 012096. IOP Publishing, 2008. Cited in page: 76 [96] David Jacob, Marc Vallet, Fabien Bretenaker, Albert Le Floch, and Roger Le Naour. Small faraday rotation measurement with a fabry-p´erot cavity. Applied Physics Letters, 66:3546–3548, 1995. Cited in page: 79 [97] S Moriwaki, H Sakaida, T Yuzawa, and N Mio. Measurement of the residual birefringence of interferential mirrors using fabry-perot cavity. Applied Physics B: Lasers and Optics, 65:347–350, 1997. Cited in page: 79 [98] Jae Yong Lee, Hai-Woong Lee, Jae Wan Kim, Yong Shim Yoo, and Jae Won Hahn. Measurement of ultralow supermirror birefringence by use of the polarimetric differential cavity ringdown technique. Applied Optics, 39:1941–1945, 2000. Cited in page: 79 [99] Jun Ye and Theresa W Lynn. Applications of optical cavities in modern atomic, molecular, and optical physics. Advances in Atomic, 158 Bibliography Molecular, and Optical Physics, 49:1–83, 2003. Cited in page: 81 [100] MD Davidson, LC Snoek, H Volten, and A D¨onszelmann. Oscillator strengths and branching ratios of transitions between low-lying levels in the barium ii spectrum. Astronomy and Astrophysics, 255:457, 1992. Cited in page: 81, 82, 141 [101] Peter Horak, Bruce G. Klappauf, Albrecht Haase, Ron Folman, J¨org Schmiedmayer, Peter Domokos, and E. A. Hinds. Possibility of single-atom detection on a chip. Physical Review A, 67:043806, Apr 2003. Cited in page: 81, 117 [102] JL Hall, L Hollberg, T Baer, and HG Robinson. Optical heterodyne saturation spectroscopy. Applied Physics Letters, 39:680–682, 1981. Cited in page: 83 [103] Ch Raab, J Bolle, H Oberst, J Eschner, F Schmidt-Kaler, and R Blatt. Diode laser spectrometer at 493 nm for single trapped Ba+ ions. Applied Physics B: Lasers and Optics, 67(6):683–688, 1998. Cited in page: 84 [104] N Kurz, MR Dietrich, Gang Shu, R Bowler, J Salacka, V Mirgon, and BB Blinov. Measurement of the branching ratio in the 6P3/2 decay of baii with a single trapped ion. Physical Review A, 77(6):060501, 2008. Cited in page: 84 [105] W Neuhauser, M Hohenstatt, P Toschek, and H Dehmelt. Optical-sideband cooling of visible atom cloud confined in parabolic well. Physical Review Letters, 41(4):233–236, 1978. Cited in page: 84 [106] G Janik, W Nagourney, and H Dehmelt. Doppler-free optical spectroscopy on the Ba+ mono-ion oscillator. Journal of the Optical 159 Bibliography Society of America B, 2(8):1251–1257, 1985. Cited in page: 84 [107] A Kastler. Atomes a` i’lnt´erieur d’un interf´erom`etre perot-fabry. Applied Optics, 1(1):17–24, 1962. Cited in page: 84 [108] Norman C Peterson, Michael J Kurylo, Walter Braun, Arnold M Bass, and Richard A Keller. Enhancement of absorption spectra by dye-laser quenching. Journal of the Optical Society of America (1917-1983), 61:746, 1971. Cited in page: 84 [109] Giel Berden, Rudy Peeters, and Gerard Meijer. Cavity ring-down spectroscopy: experimental schemes and applications. International Reviews in Physical Chemistry, 19(4):565–607, 2000. Cited in page: 84 [110] Michael Fleischhauer, Atac Imamoglu, and Jonathan P Marangos. Electromagnetically induced transparency: Optics in coherent media. Reviews of Modern Physics, 77(2):633, 2005. Cited in page: 84, 86 [111] Sze M Tan. A computational toolbox for quantum and atomic optics. Journal of Optics B: Quantum and Semiclassical Optics, 1(4):424, 1999. Cited in page: 85 [112] Sebastian Reick. Internal and external dynamics of a strongly-coupled atom-cavity system. PhD thesis, Universit¨ats-und Landesbibliothek Bonn, 2009. Cited in page: 86 [113] Tobias Kampschulte. Coherently driven three-level atoms in an optical cavity. PhD thesis, Universit¨ats-und Landesbibliothek Bonn, 2011. Cited in page: 86 160 Bibliography [114] C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband. Frequency comparison of two high-accuracy Al+ optical clocks. Physical Review Letters, 104:070802, Feb 2010. Cited in page: 89, 102, 115 [115] DJ Wineland, JC Bergquist, W.M. Itano, and RE Drullinger. Double-resonance and optical-pumping electromagnetically confined, laser-cooled ions. experiments on Optics Letters, 5(6):245–247, 1980. Cited in page: 89 [116] W. Nagourney, J. Sandberg, and H. Dehmelt. Shelved optical electron amplifier: Observation of quantum jumps. Physical Review Letters, 56(26):2797–2799, 1986. Cited in page: 89 [117] JC Bergquist, R.G. Hulet, W.M. Itano, and DJ Wineland. Observation of quantum jumps in a single atom. Physical Review Letters, 57(14):1699–1702, 1986. Cited in page: 89 [118] P. A. Barton, C. J. S. Donald, D. M. Lucas, D. A. Stevens, A. M. Steane, and D. N. Stacey. Measurement of the lifetime of the 3d2 D5/2 state in 40 Ca+ . Physical Review A, 62:032503, Aug 2000. Cited in page: 89, 90 [119] S. Olmschenk, KC Younge, DL Moehring, DN Matsukevich, P. Maunz, and C. Monroe. Manipulation and detection of a trapped Yb+ hyperfine qubit. Physical Review A, 76(5):052314, 2007. Cited in page: 90, 101 [120] DJ Berkeland and MG Boshier. Destabilization of dark states and optical spectroscopy in zeeman-degenerate atomic systems. Physical Review A, 65(3):033413, 2002. Cited in page: 90 [121] AH Myerson, DJ Szwer, SC Webster, DTC Allcock, MJ Curtis, G. Imreh, JA Sherman, DN Stacey, AM Steane, and DM Lucas. 161 Bibliography High-fidelity readout of trapped-ion qubits. Physical Review Letters, 100(20):200502, 2008. Cited in page: 95 [122] M. Acton. Detection and control of individual trapped ions and neutral atoms. PhD thesis, University of Michigan, 2008. Cited in page: 95, 101, 143 [123] D.J. Wineland, M. Barrett, J. Britton, J. Chiaverini, B. DeMarco, WM Itano, B. Jelenkovi´c, C. Langer, D. Leibfried, V. Meyer, et al. Quantum information processing with trapped ions. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 361(1808):1349–1361, 2003. Cited in page: 97 [124] MJ McDonnell, DN Stacey, and AM Steane. Laser linewidth effects in quantum state discrimination by electromagnetically induced transparency. Physical Review A, 70(5):053802, 2004. Cited in page: 99 [125] William H Press, Brian P Flannery, Saul A Teukolsky, and William T Vetterling. Numerical recipes in C: the art of scientific computation, volume 1. Cambridge university press, 1992. Cited in page: 100 [126] D.J. Wineland and W.M. Itano. Laser cooling of atoms. Physical Review A, 20(4):1521–1540, 1979. Cited in page: 100 [127] Rachel Noek, Geert Vrijsen, Daniel Gaultney, Emily Mount, Taehyun Kim, Peter Maunz, and Jungsang Kim. High speed, high fidelity detection of an atomic hyperfine qubit. Opt. Lett., 38(22):4735–4738, Nov 2013. Cited in page: 101 [128] J.G. Danzl, M.J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Aldegunde, J.M. Hutson, and H.C. N¨agerl. 162 An ultracold Bibliography high-density sample of rovibronic ground-state molecules in an optical lattice. Nature Physics, 6(4):265–270, 2010. Cited in page: 101 [129] T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science, 319(5871):1808–1812, 2008. Cited in page: 102 [130] F. Schmidt-Kaler, H. H¨affner, M. Riebe, S. Gulde, G.P.T. Lancaster, T. Deuschle, C. Becher, C.F. Roos, J. Eschner, and R. Blatt. Realization of the cirac–zoller controlled-not quantum gate. Nature, 422(6930):408–411, 2003. Cited in page: 102 [131] R J´auregui, J R´ecamier, and P A Quinto-Su. On decoherence and nonlinear effects in the generation of quantum states of motion in paul traps. Journal of Optics B: Quantum Semiclassical Optics, (4):194, 2001. Cited in page: 103 [132] S. Brouard and J. Plata. Heating of a trapped ion by random fields: The influence of the micromotion. Physical Review A, 63:043402, Mar 2001. Cited in page: 103 [133] M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenkovi´c, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland. Sympathetic cooling of Be+ and 24 Mg+ for quantum logic. Physical Review A, 68:042302. Cited in page: 103 [134] Ch. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt. Motional sidebands and direct measurement of the cooling 163 Bibliography rate in the resonance fluorescence of a single trapped ion. Physical Review Letters, 85:538–541, Jul 2000. Cited in page: 103 [135] J.T H¨offges, H.W Baldauf, T Eichler, S.R Helmfrid, and H Walther. Heterodyne measurement of the fluorescent radiation of a single trapped ion. Optics Communications, 133(16):170 – 174, 1997. Cited in page: 103 [136] Y. Ibaraki, U. Tanaka, and S. Urabe. Detection of parametric resonance of trapped ions for micromotion compensation. Applied Physics B, 105:219–223, 2011. Cited in page: 103 [137] S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner. Electric field compensation and sensing with a single ion in a planar trap. Journal of Applied Physics, 110(11):114909, 2011. Cited in page: 103 [138] K. Pyka, N. Herschbach, J. Keller, and T.E. Mehlst¨aubler. A high-precision rf trap with minimized micromotion for an In+ multiple-ion clock. arXiv preprint arXiv:1206.5111, 2012. Cited in page: 113 [139] Peter F. Herskind, Shannon X. Wang, Molu Shi, Yufei Ge, Marko Cetina, and Isaac L. Chuang. Microfabricated surface ion trap on a high-finesse optical mirror. Optics Letters, 36(16):3045–3047, Aug 2011. Cited in page: 115 [140] Hauke Doerk, Zbigniew Idziaszek, and Tommaso Calarco. Atom-ion quantum gate. Physical Review A, 81:012708, Jan 2010. Cited in page: 115 [141] Lˆe Huy Nguyˆen, Amir Kalev, Murray D. Barrett, and Berthold-Georg Englert. Micromotion in trapped atom-ion systems. Physical Review 164 Bibliography A, 85:052718, May 2012. Cited in page: 115 [142] P. Maunz, T. Puppe, I. Schuster, N. Syassen, P.W.H. Pinkse, and G. Rempe. Cavity cooling of a single atom. Nature, 428(6978):50–52, 2004. Cited in page: 116 [143] A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble. Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity. Physical Review Letters, 97:083602, Aug 2006. Cited in page: 116 [144] Vladan Vuleti´c and Steven Chu. Laser cooling of atoms, ions, or molecules by coherent scattering. Physical Review Letters, 84: 3787–3790, Apr 2000. Cited in page: 116 [145] Vladan Vuleti´c, Hilton W. Chan, and Adam T. Black. Three-dimensional cavity doppler cooling and cavity sideband cooling by coherent scattering. Physical Review A, 64:033405, Aug 2001. Cited in page: 116, 117 [146] Stefano Zippilli and Giovanna Morigi. Cooling trapped atoms in optical resonators. Physical Review Letters, 95:143001, Sep 2005. Cited in page: 117 [147] L. Mandel. Sub-poissonian photon statistics in resonance fluorescence. Optics Letters, 4(7):205–207, Jul 1979. Cited in page: 124 [148] R. Short and L. Mandel. Observation of sub-poissonian photon statistics. Physical Review Letters, 51:384–387, Aug 1983. Cited in page: 124 [149] W Vogel and R. L. de Matos Filho. Nonlinear jaynes-cummings dynamics of a trapped ion. Physical Review A, 52:4214–4217, Nov 165 Bibliography 1995. Cited in page: 125 [150] S. Wallentowitz and W. Vogel. Quantum-mechanical counterpart of nonlinear optics. Physical Review A, 55:4438–4442, Jun 1997. Cited in page: 125 [151] U. Fano. Ionization yield of radiations. ii. the fluctuations of the number of ions. Physical Review, 72:26–29, Jul 1947. Cited in page: 127 [152] National Institute of Standards and Technology (An Agency of U.S. Department of Commerce). Handbook of basic atomic spectroscopic data: Atomic data for barium (ba), 2013. URL http://physics. nist.gov/PhysRefData/Handbook/Tables/bariumtable1.htm. Cited in page: 135 [153] K Wendt, SA Ahmad, F Buchinger, AC Mueller, R Neugart, and E-W Otten. Relativistic j-dependence of the isotope shift in the 6s-6p doublet of Ba-II. Zeitschrift fur Physik, 318:125–129, 1984. Cited in page: 136 [154] Petrine Villemoes, Arne Arnesen, Filip Heijkenskjold, A Wannstrom. Isotope shifts and hyperfine structure of 134−138 and Ba II by fast ion beam-laser spectroscopy. Journal of Physics B: Atomic, Molecular and Optical Physics, 26(22):4289, 1993. Cited in page: 136 [155] Hans Karlsson and Ulf Litz´en. Revised Ba-I and Ba-II wavelengths and energy levels derived by fourier transform spectroscopy. Physica Scripta, 60:321–328, 1999. Cited in page: 141 [156] N Yu, W Nagourney, and H Dehmelt. Radiative lifetime measurement of the Ba+ metastable D3/2 state. 4898–4901, 1997. Cited in page: 141 166 Physical Review Letters, 78: Bibliography [157] AA Madej and JD Sankey. Quantum jumps and the single trapped barium ion: Determination of collisional quenching rates for the 5d2 D5/2 level. Physical Review A, 41:2621–2630, 1990. Cited in page: 141 [158] JZ Klose, JR Fuhr, and WL Wiese. Critically evaluated atomic transition probabilities for Ba-I and Ba-II. Journal of Physical and Chemical Reference Data, 31:217, 2002. Cited in page: 141 [159] Jeffrey Aaron Sherman. Single barium ion spectroscopy: light shifts, hyperfine structure, and progress on an optical frequency standard and atomic parity violation. PhD thesis, University of Washington, 2007. Cited in page: 142 [160] Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, Murray D. Barrett, and B. K. Sahoo. Experimental determination of the nuclear magnetic octupole moment of 137 012518, Jul 2013. Cited in page: 142 167 Ba+ ion. Physical Review A, 88: [...]... generations of entanglement between two trapped ions [11], creations of a quantum byte by deterministically entangling eight calcium ions [12], quantum teleportations [13] and implementations of Grovers search algorithm [14] have all been realized experimentally with trapped ions Moreover, recent demonstrations of entanglements between trapped ions and photons [15], and between distant trapped ions [16,... ideal system for such an interface is based on an ion trapped within a high finesse cavity [20–22] The cavity enhances the interaction between the ion and a single photon, and enables efficient collection of the ion emissions Proposed applications of trapped ion- cavity systems in QIP include quantum repeaters [23, 24], entanglement of distant ions [25–27] and quantum logic gates [28–31] To date, remarkable... sources [21, 32], single ion lasers [33] and ion- photon entanglement [22] have all been demonstrated with trapped ion- cavity setups In addition to QIP applications, a cavity also provides other useful functions for a trapped ion system such as enhanced photon collection efficiency [34] and a means for cooling ions [35] As a progression in exploring the various functionalities of a cavity, this thesis presents... of an ion trap for confining singly charged barium ions is described Afterwards, the principle of ion trap Doppler cooling is presented in Section 2.2 In Section 2.3, a brief introduction of coherent population transfer is discussed Then a theoretical overview of cavity QED is presented in Section 2.4, which is followed by two sections discussing the thermal effects on ion- cavity coupling and cavity. .. the phases determined by the initial conditions of the ion position and velocity The solutions of Equation 2.7 and Equation 2.8 comprise motions in two timescales, corresponding to the secular motion and the micromotion The secular motion is the harmonic oscillation of the ion with the amplitude Ax,y,z and the frequency ωx,y,z , while the micromotion is motion driven by the RF field and is scaled by... Photo-ionization scheme Temperature measurement procedure Raman spectra of vibrational modes Raman cooling scheme Cavity birefringence Cavity output vs Attocube motion Ion- cavity emission profiles Birefringence induced phase retardation Single atom cooperativity Cavity- enhanced single ion spectroscopy setup Cavity- enhanced... Paul trap Stable zone of an ion trap The Λ-type Raman Transition Ion- cavity Raman coupling The setup for ion- cavity coupling 6 7 11 20 23 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 The trap picture A schematic diagram of trap B Home-build transformer Experimental cavity Trap. .. used such as ion trapping using radio frequency (RF) traps, Doppler cooling of trapped ions and atomic state manipulation Then the theory for an ideal two-level atom in an optical cavity is presented The description is later extended to include the realistic considerations, such as cavity and excited state dissipations, and the effects due to external driving lasers Before 2 Chapter 1 Introduction the chapter... used to further reduce the ion temperature As seen in the previous section, a Λ-type Raman transition could be motional sensitive depending on the laser configuration With an appropriate setting, the Raman transition can transfer the ion from a higher vibration quantum to a lower one and reduce the ion temperature 17 Chapter 2 Theoretical Considerations Here, a brief description of the cooling process... 6.4 Micromotion detection by cavity: setup Relevant transitions and level structure Micromotion sidebades at different stages Cavity profile when fully compensated 105 109 112 113 7.1 7.2 7.3 Cavity cooling setup 118 Relevant transitions 119 Cavity cooling data 120 8.1 8.2 Cavity emission profile . enhances the interaction between the ion and a single photon, and enables efficient collection of the ion emissions. Proposed applications of trapped ion- cavity systems in QIP include quantum repeaters. demonstrated with trapped ion- cavity setups. In addition to QIP applications, a cavity also provides other useful functions for a trapped ion system such as enhanced photon collection efficiency [34]. generations of entanglement between two trapped ions [11], creations of a quantum byte by deterministically entangling eight calcium ions [12], quantum teleportations [13] and implementations of