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State-selective transport of single neutral atoms [Elektronische Ressource] / vorgelegt von Michał Karski

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252 pages
State-selective transportof single neutral atomsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen FakultatderRheinischen Friedrich-Wilhelms-Universitat Bonnvorgelegt vonMicha l KarskiausBial ystok (Polen)Bonn 2010Angefertigt mit Genehmigungder Mathematisch-Naturwissenschaftlichen Fakultat¨der Rheinischen Friedrich-Wilhelms-Universit¨at Bonn1. Gutachter: Prof. Dr. Dieter Meschede2. Gutachter: Prof. Dr. Reinhard F. WernerTag der Promotion: 20.10.2010Erscheinungsjahr: 2010Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonnhttp://hss.ulb.uni-bonn.de/diss_onlineelektronisch publiziertSummaryThe present work investigates the state-selective transport of single neutral cesiumatoms in a one-dimensional optical lattice. It demonstrates experimental appli-cations of this transport, including a single atom interferometer, a quantum walkand controlled two-atom collisions. The atoms are stored one by one in an opticallattice formed by a standing wavedipole trap. Their positions are determined withsub-micrometer precision, while atom pair separations are reliably inferred downto neighboring lattice sites using real-time numerical processing. Using microwavepulsesinthepresenceofamagneticfieldgradient,theinternalqubitstates,encodedin the hyperfinelevels of the atoms, can be separately initialized and manipulated.
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State-selective transport
of single neutral atoms
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakultat
der
Rheinischen Friedrich-Wilhelms-Universitat Bonn
vorgelegt von
Micha l Karski
aus
Bial ystok (Polen)
Bonn 2010Angefertigt mit Genehmigung
der Mathematisch-Naturwissenschaftlichen Fakultat¨
der Rheinischen Friedrich-Wilhelms-Universit¨at Bonn
1. Gutachter: Prof. Dr. Dieter Meschede
2. Gutachter: Prof. Dr. Reinhard F. Werner
Tag der Promotion: 20.10.2010
Erscheinungsjahr: 2010
Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn
http://hss.ulb.uni-bonn.de/diss_onlineelektronisch publiziertSummary
The present work investigates the state-selective transport of single neutral cesium
atoms in a one-dimensional optical lattice. It demonstrates experimental appli-
cations of this transport, including a single atom interferometer, a quantum walk
and controlled two-atom collisions. The atoms are stored one by one in an optical
lattice formed by a standing wavedipole trap. Their positions are determined with
sub-micrometer precision, while atom pair separations are reliably inferred down
to neighboring lattice sites using real-time numerical processing. Using microwave
pulsesinthepresenceofamagneticfieldgradient,theinternalqubitstates,encoded
in the hyperfinelevels of the atoms, can be separately initialized and manipulated.
This allows us to perform arbitrary single-qubit operations and prepare arbitrary
patterns of atoms in the lattice with single-site precision.
Chapter1presentstheexperimentalsetupfortrappingasmallnumberofcesium
atoms in a one-dimensional optical lattice. Chapter 2 is devoted to fluorescence
imaging of atoms, discussing the imaging setup, numeric methods and their per-
formance in detail. Chapter 3 focuses on engineering of internal states of trapped
atoms in the lattice using optical methods and microwave radiation. It provides a
detailed investigation of coherence properties of our experimental system. Finally
manipulationofindividualatomswithalmostsingle-siteresolutionandpreparation
of regular strings of atoms with predefined distances are presented.
InChapter4,basicconcepts,theexperimentalrealizationandtheperformanceof
thestate-selective transportofneutralatoms overseverallattice sites arepresented
and discussed in detail. Coherence properties of this transport are investigated in
Chapter 5, using various two-arms single atom interferometer sequences in which
atomic matter waves are split, delocalized, merged and recombined on the initial
latticesite,whiletheinterferencecontrastandtheaccumulatedphasedifferenceare
measured. By delocalizing a single atom over several lattice sites, possible spatial
inhomogeneities of fields along the lattice axis in the trapping region are probed.
In Chapter 6, experimental realization of a discrete time quantum walk on a line
with single optically trapped atoms is presentedas an advanced application of mul-
tiple path quantum interference in the context of quantum information processing.
Using this simple example of a quantum walk, fundamental properties of and dif-
ferences between the quantum and classical regimes are investigated and discussed
in detail. Finally, by combining preparation of atom strings, position-dependent
manipulation of qubitstates and state-selective transport, in Chapter 7, twoatoms
are deterministically broughttogether into contact, forming a starting point for in-
vestigating two-atom interactions on the most fundamentallevel. Future prospects
and suggestions are finally presented in Chapter 8.
iSummary
Parts of this thesis have been published in the following journal articles:
1. M. Karski, L. Forster, J.-M. Choi, W. Alt, A. Widera and D. Meschede,¨
Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence
Imaging, Phys. Rev. Lett. 102, 053001 (2009)
2. M. Karski, L. F¨orster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede and
A. Widera, Quantum Walk in Position Space with Single Optically Trapped
Atoms, Science 325, 174 (2009)
3. M. Karski, L. Forster, J.-M. Choi, A. Steffen, N. Belmechri, W. Alt, D. Me-¨
schede and A. Widera, Imprinting patterns of neutral atoms in an optical
lattice usingmagnetic resonance techniques,toappearinNew.J.Phys.(2010)
iiContents
Summary i
Introduction 1
1. Trapping of single atoms 5
1.1. A magneto-optical trap . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1. Principle of operation . . . . . . . . . . . . . . . . . . . . . . 6
1.1.2. Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.3. Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.4. Magnetic coil system . . . . . . . . . . . . . . . . . . . . . . . 12
1.2. A one-dimensional optical lattice . . . . . . . . . . . . . . . . . . . . 16
1.2.1. Classical model of a dipole potential . . . . . . . . . . . . . . 17
1.2.2. Periodic array of trapping potentials . . . . . . . . . . . . . . 19
1.2.3. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 20
1.3. Computer control system . . . . . . . . . . . . . . . . . . . . . . . . 22
2. Fluorescence detection of neutral atoms in an optical lattice 23
2.1. The deconvolution problem . . . . . . . . . . . . . . . . . . . . . . . 23
2.2. Imaging setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1. Optical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.2. The EMCCD detector . . . . . . . . . . . . . . . . . . . . . . 27
2.3. Determining the number and positions of the atoms . . . . . . . . . 29
2.3.1. Counting atoms in an optical lattice . . . . . . . . . . . . . . 31
2.3.2. Determining the line spread function with sub-pixel accuracy 35
2.3.3. Determining the isoplanatic patch . . . . . . . . . . . . . . . 38
2.3.4. Characterizing the line spread function. . . . . . . . . . . . . 40
2.3.5. Parametric deconvolution . . . . . . . . . . . . . . . . . . . . 44
2.3.6. Inferring the signal-noise relation . . . . . . . . . . . . . . . . 46
2.3.7. Filtering of erroneous results . . . . . . . . . . . . . . . . . . 52
2.3.8. Remarks on implementation and performance . . . . . . . . . 53
2.4. Detecting atoms on neighboring lattice sites . . . . . . . . . . . . . . 55
2.4.1. Parametric deconvolution of atom clusters . . . . . . . . . . . 56
2.4.2. Calibration of the image scale . . . . . . . . . . . . . . . . . . 60
2.4.3. Parametric deconvolution of atom pairs . . . . . . . . . . . . 62
2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
iiiContents
3. Engineering internal states of neutral atoms in an optical lattice 67
3.1. State preparation and detection . . . . . . . . . . . . . . . . . . . . . 67
3.1.1. State initialization by optical pumping . . . . . . . . . . . . . 67
3.1.2. State-selective detection . . . . . . . . . . . . . . . . . . . . . 69
3.2. Quantum state manipulation using microwave radiation . . . . . . . 71
3.2.1. The Bloch sphere representation . . . . . . . . . . . . . . . . 71
3.2.2. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 75
3.2.3. Microwave spectroscopy . . . . . . . . . . . . . . . . . . . . . 77
3.2.4. Quantum state tomography . . . . . . . . . . . . . . . . . . . 82
3.3. Coherence properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3.1. Classification of decoherence effects . . . . . . . . . . . . . . . 87
3.3.2. Ramsey spectroscopy. . . . . . . . . . . . . . . . . . . . . . . 88
3.3.3. Spin-echo spectroscopy . . . . . . . . . . . . . . . . . . . . . . 94
3.3.4. Carr-Purcell sequence . . . . . . . . . . . . . . . . . . . . . . 96
3.4. Position-dependent quantum state manipulation . . . . . . . . . . . 101
3.4.1. Position-dependent Zeeman shift . . . . . . . . . . . . . . . . 101
3.4.2. Microwave spectroscopy in position space . . . . . . . . . . . 102
3.4.3. Calibration of the frequency shift . . . . . . . . . . . . . . . . 105
3.4.4. Preparation of predefined patterns of atoms . . . . . . . . . . 106
3.5. Composite pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4. State-selective transport of neutral atoms 123
4.1. State-selective potentials . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.2. Moving atoms in state-selective potentials . . . . . . . . . . . . . . . 127
4.3. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.4. Excitation of motional states in moving potentials . . . . . . . . . . 132
4.4.1. State-dependent shift dynamics . . . . . . . . . . . . . . . . . 134
4.4.2. Excitations for linear and cosinusoidal driving ramps . . . . . 136
4.4.3. Effect of limited bandwidth . . . . . . . . . . . . . . . . . . . 139
4.5. Transporting atoms over several lattice sites . . . . . . . . . . . . . . 141
4.5.1. Dirac representation of state-selective transport . . . . . . . . 141
4.5.2. Adjusting settling time and half-wave voltage . . . . . . . . . 143
4.5.3. Analyzing transport data . . . . . . . . . . . . . . . . . . . . 145
4.6. Transport efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.6.1. Effect of state initialization errors and photon scattering . . . 149
4.6.2. Effect of microwave pulse errors. . . . . . . . . . . . . . . . . 150
4.6.3. Effect of decoherence . . . . . . . . . . . . . . . . . . . . . . . 152
4.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5. Coherent state-selective transport — A single atom interferometer 155
5.1. Coherence properties of state-selective transport . . . . . . . . . . . 156
5.1.1. Dephasing of thermal atoms . . . . . . . . . . . . . . . . . . . 156
5.1.2. Detecting vibrational excitations . . . . . . . . . . . . . . . . 160
ivContents
5.1.3. Determining the optimum ramp time. . . . . . . . . . . . . . 162
5.2. Delocalizing of a matter wave over several lattice sites . . . . . . . . 164
5.2.1. Accumulation of phase . . . . . . . . . . . . . . . . . . . . . . 166
5.2.2. Experimental results . . . . . . . . . . . . . . . . . . . . . . . 168
5.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6. Quantum walks in position space 179
6.1. Random walk and quantum walk on a line . . . . . . . . . . . . . . . 180
6.1.1. Random walk on a line . . . . . . . . . . . . . . . . . . . . . 180
6.1.2. Quantum Walk on a line . . . . . . . . . . . . . . . . . . . . . 181
6.2. Experimental realization . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.2.1. Effect of limitations imposed by the state-selective transport 184
6.2.2. Experimental sequence . . . . . . . . . . . . . . . . . . . . . . 188
6.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6.3.1. Quantum-to-classical transition . . . . . . . . . . . . . . . . . 191
6.3.2. Quantum state reconstruction . . . . . . . . . . . . . . . . . . 193
6.3.3. Reversing the quantum walk . . . . . . . . . . . . . . . . . . 195
6.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7. Controlled two-atom collisions 201
7.1. State-selective transport in a magnetic field gradient . . . . . . . . . 202
7.1.1. Experimental sequence . . . . . . . . . . . . . . . . . . . . . . 203
7.1.2. Revealing drifts of the magnetic quadrupole field . . . . . . . 204
7.1.3. Transport efficiency in a magnetic field gradient . . . . . . . 204
7.2. Transporting atoms to a common lattice site . . . . . . . . . . . . . 206
7.2.1. Experimental results . . . . . . . . . . . . . . . . . . . . . . . 208
7.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8. Perspectives 215
8.1. Anderson localization in disordered quantum walks . . . . . . . . . . 215
8.2. Implementation of a two-qubit gate . . . . . . . . . . . . . . . . . . . 216
A. Software 219
A.1. Control Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.2. iXacq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
A.3. WaveGen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
A.4. Post Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Bibliography 229
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