Quantum Phase Transitions in Cold Atoms and Low Temperature Solids:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Schriftenreihe: | Springer Theses
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 233 S. Ill., graph. Darst. |
| ISBN: | 9781441981783 |
Internformat
MARC
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| 245 | 1 | 0 | |a Quantum Phase Transitions in Cold Atoms and Low Temperature Solids |c Kaden Richard Alan Hazzard |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XVIII, 233 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer Theses | |
| 502 | |a Ithaca, Cornell Univ., Department of Physics, 2010 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1
Introduction
to Many-Body Physics in Ultracold Atomic Gases
...
ł
1.1
Motivation: Many-Body Physics
.....................
I
1.2
Motivation: General Atomic Physics
.................. 4
1.3
History and Introduction to Many-Body Physics
in Cold Atomic Systems
.......................... 5
1.3.1
Background and Achievements
............... 5
1.4
Challenges and Outline of Thesis
.................... 7
References
......................................... 9
2
Theoretical and Experimental Techniques Used
to Explore Many-Body Physics in Cold Atoms,
Especially Optical Lattices
............................. 11
2.1
Experimental Techniques
.......................... 11
2.1.1
Common Experimental Techniques for all Cold
Atoms Experiments: Trapping and Cooling
...... 11
2.1.2
Optical Lattice Experimental Techniques
........ 14
2.1.3
Detection
.............................. 16
2.2
Theoretical Techniques
........................... 18
2.2.1
Interactions in Cold Atom Systems
............ 18
2.2.2
Weak Interactions: Mean Field Theory
and Fluctuations
......................... 22
2.2.3
Bosons in an Optical Lattice
and the Bose-Hubbard Model
............... 24
2.2.4
Gutzwiller Mean Field
.................... 26
2.2.5
Fluctuations in Strong Lattice Potentials:
Beyond Gutzwiller
....................... 29
2.2.6
Extracting Information About Homogeneous
Systems from Trapped Systems
.............. 30
References
......................................... 31
xiv
Contents
3
Radio-Frequency Spectroscopy: Broad Introduction
.......... 33
3.1
Motivation and Background
........................ 33
3.2
Two Differing Pictures of RF Spectroscopy
............. 34
References
......................................... 35
4
RF Spectra: A Sum Rule Approach to Trapped Bosons
in an Optical Lattice
.................................. 37
4.1
Chapter Overview
............................... 37
4.2
Introduction
................................... 37
4.3
Spectrum of Harmonically Trapped Gas
............... 39
4.3.1
Hamiltonian and Approximations
............. 39
4.3.2
Homogeneous Clock Shifts
................. 41
4.3.3
Calculation of Spectrum in a Trap
............ 42
4.3.4
Analytic Results
......................... 44
4.3.5
Intermediate Coupling
..................... 45
4.4
Refinements
................................... 46
4.4.1
Anharmonicity
.......................... 47
4.4.2
Alternative Explanations of Enhanced Low-Density
Spectral Weight
......................... 48
4.5
Summary
..................................... 49
References
......................................... 50
5
RF Spectra: Multiple Peaked Spectrum
in a Homogeneous System
.............................. 51
5.1
Chapter Overview
............................... 51
5.2
Introduction
................................... 52
5.2.1
RF Spectroscopy
......................... 52
5.3
Bose-Hubbard Model
............................ 54
5.3.1
Model and RF Spectra
.................... 54
5.3.2
Sum Rules
............................. 55
5.4
Random Phase Approximation
...................... 55
5.4.1
General Setup and Solution
................. 55
5.4.2
Limiting Cases and Dependence
on Final State Interactions
.................. 58
5.4.3
Inhomogeneous Spectrum
.................. 59
5.5
Conclusions and Discussion
........................ 61
References
......................................... 62
6
Radio-Frequency Spectra at Finite Temperature,
Fluctuation-Response Relations, and Proposed Applications
..... 63
6.1
Chapter Overview
............................... 63
6.2
Introduction
................................... 63
6.3
RF Spectra Introduction
........................... 64
6.4
Finite Temperature Superfluid
...................... 65
Contents xv
6.5 Applications................................... 67
6.5.1 Thermometry
with the
Mott
Insulator
.......... 67
6.5.2
Number Correlations and Local Compressibility.
. . 72
6.6
Determining Density Profiles from RF Spectra
........... 75
6.6.1
Determining Density Profiles from Spectra
When Mean Energy Shift is Proportional to the
Density Plus a Constant
.................... 76
6.6.2
Determining Density Profiles from RF Spectra
in the General Case
...................... 77
6.6.3
Cooling and Quantum Register Initialization
..... 77
6.6.4
Measuring Spatial Correlations; Quantum
Computer Readout
....................... 78
6.7
Conclusions
................................... 83
References
......................................... 84
7
RF Spectra: Summary, Conclusions, and the Future
.......... 85
References
......................................... 86
8
Rotation, Inducing Gauge Fields, and Exotic States
of Matter in Cold Atoms
............................... 87
8.1
Physics of Rotating Particles/Particles in Gauge Fields
..... 88
8.1.1
Vortices
............................... 89
8.1.2
Vortices in Lattices:
Hofstadter
Butterfly
........ 89
8.1.3
Quantum Hall Effect
...................... 90
8.2
Rotation
..................................... 92
8.2.1
Rotation and Angular Momentum Boosts
—
Principles and Experimental Techniques
........ 92
8.2.2
Rotation Leads to an Effective Magnetic Field
(Gauge Field) and Limitations of Rotation
for Inducing Exotic States
.................. 92
8.3
Other Methods of Inducing Gauge Fields
.............. 93
8.4
On-Site
Correlations
............................. 94
References
......................................... 94
9
Stirring up Fractional Quantum Hall Puddles
............... 97
9.1
Chapter Overview
............................... 97
9.2
Introduction
................................... 97
9.3
Summary
..................................... 103
References
......................................... 104
10
Incorporating Arbitrarily Strong
On-Site
Correlations
into Lattice Models
................................... 105
10.1
Chapter Overview
............................... 106
xvi Contents
10.2
Body
........................................ 106
References
.........................................
ИЗ
11
Quantitative Calculation of Parameters for a Model Sufficiently
General to Capture all
On-Site
Correlations
................ 115
11.1
Background
................................... 115
11.2
Introduction, Notation, and Set Up
................... 115
11.3
Quantitative Estimates of the Hamiltonian Parameters
with Quantum Monte Carlo
........................ 116
11.3.1
General Idea
........................... 116
11.3.2
Relating Response to Correlation Functions
...... 117
11.3.3
Implementation of Correlation Function in PIMC
... 117
11.4
Solutions for Various Values of t(mn) and Em
............ 118
11.4.1
Non-Interacting Case
...................... 118
11.4.2
Strong Coupling t/U
-> 0
Limit
............. 122
11.4.3
General
—
Correlation Functions
from Exact Diagonalization
................. 129
11.5
Note on Temperature Dependence of Response Functions
... 129
Reference
.......................................... 129
12
Summary, Conclusions, and the Future of Induced Gauge
Fields and Lattices with
On-Site
Correlations
............... 131
References
......................................... 131
13
Techniques to Measure Quantum Criticality in Cold Atoms
..... 133
13.1
Introduction
................................... 133
13.2
Note and Summary
.............................. 139
References
......................................... 140
14
Quantum Criticality: More Detailed Information
............. 143
14.1
Bose-Hubbard Model
............................ 143
14.2
Finite Temperature Gutzwiller Theory
................. 144
14.3
Non-Universal Contributions
....................... 144
14.4
Time of Flight Expansion
......................... 145
14.5
Finite Density O(2) Model
......................... 146
14.6
Calculating Density Profiles of One-Dimensional
Hardcore Bosons
............................... 147
14.7
Other Cold Atoms Systems Displaying Quantum Criticality
... 148
14.8
Precise Definition of Universality
.................... 148
14.9
Quantum Monte Carlo Parameters and Signal-to-Noise
..... 150
14.10
Finite-Size Scaling
.............................. 151
References
......................................... 151
Contents xvii
15 Systems
Other than Cold Atoms
......................... 153
16
Film Mediated Interactions Alter Correlations and Spectral
Shifts of Hydrogen Adsorbed on Helium Films
.............. 155
16.1
Chapter Overview
............................... 155
16.2
Results
...................................... 156
References
......................................... 162
17
Candidate Theories to Explain the Anomalous
Spectroscopie
Signatures of Atomic
H
in Molecular H2 Crystals
............ 165
17.1
Introduction and Motivation
........................ 165
17.2
Experiments
................................... 166
17.2.1
General Introduction: Physics of Atomic Hydrogen
Embedded in Solid Hydrogen
................ 166
17.2.2
Anomalies and Experimental Results
.......... 168
17.3
Scenarios
..................................... 168
17.3.1
Bose
Statistics and Bose-Einstein Condensation
. . . 169
17.3.2
Local Bose-Einstein Condensation
............ 173
17.3.3
Nuclear Spin Dependent Density-of-States
....... 174
17.4
Other Observations
.............................. 175
17.5
Summary, Conclusions, and Consequences
............. 176
References
......................................... 177
18
Helium and Hydrogen
(superľ)Solids
..................... 179
18.1
Background
................................... 179
18.2
Chapter Overview
............................... 179
18.3
Introduction
................................... 180
18.4
Torsionai
Oscillator NCRI
......................... 181
18.5
Two Supersolid Features
.......................... 181
18.6
Blocked Annulus
Torsionai
Oscillators
................ 182
18.7
Dissipation Peaks
............................... 182
18.8
H2 Experiments
................................ 183
18.9
Frequency Dependence
........................... 186
18.10
Thermodynamics: Specific Heat and Pressure
........... 187
18.11
3He Doping
................................... 188
18.11.1
Frozen Link Model
....................... 188
18.11.2
Dynamic Link Model
..................... 189
18.12
Anomalous Critical Velocity
....................... 191
18.13
DC Flow
..................................... 191
18.14
Shear
........................................ 191
18.15
Implications for Mechanism
........................ 192
18.16
Future Directions
............................... 192
18.17
Conclusions
................................... 193
References
......................................... 193
xviii Contents
Appendix
A: Relating Scattering Amplitudes and
ľ-Matrix
........ 195
Appendix B: Ward Identities for the RF Spectrum
for the Bose-Hubbard Model
—
Vertex Corrections,
Symmetries, and Conservation Laws
......................... 197
Biographical Sketch
...................................... 229
Curriculum
Vitae
....................................... 231
|
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| spelling | Hazzard, Kaden Richard Alan Verfasser aut Quantum Phase Transitions in Cold Atoms and Low Temperature Solids Kaden Richard Alan Hazzard New York, NY [u.a.] Springer 2011 XVIII, 233 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Theses Ithaca, Cornell Univ., Department of Physics, 2010 Tieftemperaturphysik (DE-588)4185450-0 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Phasenumwandlung (DE-588)4132140-6 s Tieftemperaturphysik (DE-588)4185450-0 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024378041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hazzard, Kaden Richard Alan Quantum Phase Transitions in Cold Atoms and Low Temperature Solids Tieftemperaturphysik (DE-588)4185450-0 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| subject_GND | (DE-588)4185450-0 (DE-588)4132140-6 (DE-588)4113937-9 |
| title | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids |
| title_auth | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids |
| title_exact_search | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids |
| title_full | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids Kaden Richard Alan Hazzard |
| title_fullStr | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids Kaden Richard Alan Hazzard |
| title_full_unstemmed | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids Kaden Richard Alan Hazzard |
| title_short | Quantum Phase Transitions in Cold Atoms and Low Temperature Solids |
| title_sort | quantum phase transitions in cold atoms and low temperature solids |
| topic | Tieftemperaturphysik (DE-588)4185450-0 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| topic_facet | Tieftemperaturphysik Phasenumwandlung Hochschulschrift |
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