Thesis (pdf) - Swinburne University of Technology

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Here a model is presented which in contrast to most publications [Hin01, H¨01c] incorporates an unavoidable experimental effect: the imperfect symmetry of the double well potential. A two mode approximation is developed for this case. The analogy with all two-level systems allows the use of the Bloch equations. Their validity was checked with the numerical results of the full system, performed by S. Whitlock [Whi04] using the XMDS software developed at the University of Queensland. The simplicity of the Bloch model allows simula- tions on a much faster scale and application to many related problems. The presented two mode model is well known [All75, Mey91]. To the author’s knowledge the application to this kind of interferometer is new. The inter- pretation of the model using the Bloch sphere and the solutions of the Bloch equations give further insight into the physics that occurs in such an interferometer, identifying the main process as Larmor precessions. It is shown that an asymmetry is crucial and needed for an interferometer to work, and should be incorporated in any model, as it gives rise to the phase shift that the interferometer measures. The model also shows how experimental imperfections that translate into asymmetries in the potential can be overcome, clarifying a common misconception among experimental physicists about adiabatic processes and their role in atom interferometry. It also explains where and how the change from phase difference to measurable number difference is mani- fested. Although the model strictly is applicable to single atoms only, the main results have to be kept in mind for BEC-based interferometers. A/Prof. B. Dalton is acknowledged for correcting a factor in the Bloch equations. Two main limits of the model are identified by comparing the two mode model with the full numerical analysis. A new way to read out a double well atom interferometer was inspired by questions of Prof. P. Drummond of the Uni- versity of Queensland and is based on an idea of Prof. A. Sidorov. A related read out process was later successfully implemented in a BEC-based double 8
Chapter 1: Introduction well system [Hal07b] on the permanent magnetic chip described in chapters 4 and 5. The model is kept simple, so that different experimental parameters can be implemented easily. Even though it works with single atoms in double well, we find a surprisingly close match with the experimental data for a BEC in a double well [Jo07]. These two experimental publications emphasise the importance of this chapter, although it was mainly intended not as a tool for prediction, but to give a deeper understanding of the actual physical processes in double well potentials. Further applications to double well problems outside of atom optics are briefly discussed. Although the author is not first author on a publication that reports the early results [Sid06], the work on which this publication is based was mainly undertaken by him. Chapters 4 and 5 contain the description of the technical details and the results of the experiment which the author worked on at Swinburne University of Technology. Chapter 4 contains a full description of the experimental set-up of the permanent magnetic film atom-chip experiment. Here the experimental apparatus including the laser systems, the vacuum chamber and the novel hybrid atom chip with both current-carrying wires and a permanent magnetic film are presented and characterised. This work was done mainly in association with S. Whitlock and Dr. B. Hall. In the early stages this part of the work was supported by D. Gough and Prof. A. Sidorov. Results have been published covering the magnetic film and its properties [Wan05a] and experimental data with some technical details of the set-up [Hal06]. The TbGdFeCo magneto- optical film was fabricated by J. Wang, S. Whitlock and D. Gough. As the setting up of this unique experiment is an integral part of this thesis, the set-up and the individual parts are described in some detail. After the characterisation of the experimental set-up, the analysis of the data taken with the new permanent-magnetic-film atom-chip is presented in Chapter 5. With the help of this chip, atoms were first collected and cooled in a 9
Page 1: Bose-Einstein Condensation in Micro
Page 4 and 5: current carrying structures on the
Page 6 and 7: hear and speak German in my Hamburg
Page 8 and 9: viii
Page 11 and 12: Publications by the Candidate • A
Page 13 and 14: Contents Abstract iii Acknowledgeme
Page 15 and 16: CONTENTS 4.3.3 Procedure to reach U
Page 17 and 18: Chapter 1 Introduction One revoluti
Page 19 and 20: Chapter 1: Introduction physics tha
Page 21 and 22: Chapter 1: Introduction of micron-s
Page 23: Chapter 1: Introduction proposals u
Page 27: Chapter 1: Introduction [M¨05, Geh
Page 30 and 31: 2.1. Atoms and Electromagnetic Fiel
Page 44 and 45: 2.2. Atoms and Magnetic Fields 2.2
Page 46 and 47: 2.2. Atoms and Magnetic Fields Mini
Page 48 and 49: 2.2. Atoms and Magnetic Fields give
Page 50 and 51: 2.2. Atoms and Magnetic Fields 2.2.
Page 52 and 53: 2.3. Evaporative Cooling The light
Page 54 and 55: 2.3. Evaporative Cooling The change
Page 56 and 57: 2.4. Bose-Einstein Condensation Thi
Page 58 and 59: 2.5. The Magneto-Optical Trap σ ±
Page 60 and 61: 2.5. The Magneto-Optical Trap two p
Page 62 and 63: 2.6. Atom Interferometry beamsplitt
Page 64 and 65: 2.6. Atom Interferometry of the spa
Page 66 and 67: 2.6. Atom Interferometry 50
Page 68 and 69: Localised wavefunctions were also u
Page 70 and 71: 3.1. Introduction general form, so
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3.2. Two Mode Approximation and the
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3.3. The Results of the Model V; Y
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3.3. The Results of the Model the a
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3.3. The Results of the Model a red
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3.3. The Results of the Model max(
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3.3. The Results of the Model used
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3.3. The Results of the Model uses
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3.4. Summary excited states do not
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3.4. Summary pendent on the atomic
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4.1. Overview current-carrying wire
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4.2. The Laser Systems • The opti
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4.2. The Laser Systems light is the
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4.2. The Laser Systems photodiode
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4.2. The Laser Systems double-passi
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4.2. The Laser Systems To the light
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4.3. The Vacuum System are mounted
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4.3. The Vacuum System produced fro
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4.4. The Magnetic Field Coils tempe
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4.4. The Magnetic Field Coils tempe
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4.5. The Atom Chip and as a heat si
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4.5. The Atom Chip are 2.0 mm and 1
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4.5. The Atom Chip Cr Au Glass MO f
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4.5. The Atom Chip 108
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5.1. Overview and Timing Sequence w
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5.2. The Magneto-Optical Traps in t
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5.2. The Magneto-Optical Traps Numb
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5.2. The Magneto-Optical Traps nume
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5.2. The Magneto-Optical Traps at a
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5.2. The Magneto-Optical Traps (b))
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5.2. The Magneto-Optical Traps Appl
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5.3. The Wire Magnetic Trap as a qu
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5.3. The Wire Magnetic Trap follow
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5.3. The Wire Magnetic Trap s −1
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5.3. The Wire Magnetic Trap number
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5.3. The Wire Magnetic Trap distrib
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5.3. The Wire Magnetic Trap of the
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5.3. The Wire Magnetic Trap corresp
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5.3. The Wire Magnetic Trap other s
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5.3. The Wire Magnetic Trap atomic
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5.3. The Wire Magnetic Trap All fig
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5.3. The Wire Magnetic Trap integra
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5.4. The Permanent Magnetic Trap Fi
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5.4. The Permanent Magnetic Trap 0
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5.4. The Permanent Magnetic Trap (d
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5.4. The Permanent Magnetic Trap 15
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6.1. Overview using a degenerate at
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6.2. The Vacuum System used for tra
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6.3. The Diode Laser Systems for Ma
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6.3. The Diode Laser Systems for Ma
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6.5. Detection of Atoms beam splitt
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6.5. Detection of Atoms 164
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7.2. The Magneto-Optical Trap of 10
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7.3. Loading the Dipole Trap from t
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7.3. Loading the Dipole Trap number
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7.3. Loading the Dipole Trap number
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7.4. Evaporative Cooling in the Dip
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8.1. Summary and Discussion to Bose
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8.2. Outlook and Future Jo07]. Here
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8.2. Outlook and Future BEC can be
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A.1. Asymmetric double-well potenti
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A.2. A permanent magnetic film atom
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A.2. A permanent magnetic film atom
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A.3. Perpendicularly magnetized, gr
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A.3. Perpendicularly magnetized, gr
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temperature in µK 300 250 200 150
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Figure C.1: The energy levels of th
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The bias field coils Coils inner di
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[E 15]: diaphragm pump: MD4T (3.3 m
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BIBLIOGRAPHY [Bar01] M. Barrett, J.
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BIBLIOGRAPHY [D¨98] S. Dürr, T. N
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BIBLIOGRAPHY [Fey57] R. Feynman, F.
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BIBLIOGRAPHY [Hal05] B. Hall, S. Wh
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BIBLIOGRAPHY [Kok98] S. Kokkelmans,
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BIBLIOGRAPHY [Mom03] J. Mompart, K.
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BIBLIOGRAPHY [Ryc04] D. Rychtarik,
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BIBLIOGRAPHY [Tab91] J. Tabosa, G.
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BIBLIOGRAPHY [Xin04] Y. Xing, A. El
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