Quantum simulation of topological states of matter:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120726-1108417-0-4 Inhaltsverzeichnis |
| Physical Description: | XVIII, 143 S. graph. Darst. |
Staff View
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| 100 | 1 | |a Mazza, Leonardo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum simulation of topological states of matter |c Leonardo Mazza |
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
ABSTRACT V I I
Z U S A M M E N F A S S U N G I X
P U B L I C A T I O N S R E L A T E D T O T H I S T H E S I S X I
I N T R O D U C T I O N XIII
I QUANTUM SIMULATION W I T H COLD A T O M S 1
1 OPTICAL L A T T I C E S 3
1.1 OPTICAL POTENTIALS 3
1.2 THEORETICAL DESCRIPTION OF ATOMS IN OPTICAL LATTICES 5
1.3 MEASUREMENT TECHNIQUES 8
1.4 OPTICAL LATTICES AS QUANTUM SIMULATORS 10
1.4.1 VERSATILITY OF OPTICAL LATTICES 11
2 A N O P T I C A L S U P E R L A T T I C E S C H E M E 1 3
2.1 BEYOND STANDARD HOPPING PROCESSES 13
2.1.1 LASER-ASSISTED TUNNELING 14
2.1.2 DYNAMICAL SHAKING 14
2.1.3 ORBITAL PHYSICS 15
2.2 THE SETUP AND THE IDEA 15
2.3 REALIZATION OF SPIN-DEPENDENT HOPPING PROCESSES 19
2.3.1 COUPLING BETWEEN DIFFERENT HYPERFINE MANIFOLDS 19 2.3.2 DEVELOPING
AN EFFECTIVE 6-LEVEL MODEL 20
2.3.3 RANGE OF VALIDITY OF THE 6-LEVEL MODEL 23
2.3.4 DIAGONAL HOPPING MATRIX 24
2.3.5 NON-DIAGONAL HOPPING MATRIX 26
2.4 PROM A SPIN-DEPENDENT HOPPING TO A QUANTUM SIMULATOR . . . . 28
3 R E L A T I V I S T I C T H E O R I E S A N D TOPOLOGICAL INSULATORS 3
1
3.1 RELATIVISTIC LATTICE FERMIONS 32
3.1.1 MASSLESS AND MASSIVE DIRAC FERMIONS 32
3.1.2 WILSON FERMIONS 34
3.1.3 KAPLAN FERMIONS 35
3.2 TOPOLOGICAL INSULATORS 36
3.2.1 A MODEL FOR THE INTEGER QUANTUM HALL EFFECT 36
III
HTTP://D-NB.INFO/1033633593
IMAGE 2
C O N T E N T S
3.2.2 BOTTOM-UP APPROACH 40
3.2.3 SYMMETRY-BASED APPROACH 41
3.3 PERSPECTIVES 42
4 T H R E E - B O D Y INTERACTIONS W I T H SPIN-1 A T O M S 4 5
4.1 THE MAPPING 46
4.2 SPIN-1 ATOMS 48
4.3 THE PFAFFIAN WAVEFUNCTION 50
4.3.1 QUANTUM HALL EFFECT ON A LATTICE 50
4.3.2 TOPOLOGICAL PROPERTIES AS A BENCHMARK 51
4.3.3 TENTATIVES TOWARDS AN IMPLEMENTATION WITH SPIN-1 ATOMS 54 4.4
CONCLUSIONS AND PERSPECTIVES 56
5 P A R T I C L E - H O L E P A I R S A N D S T R I N G ORDER I N O N E
D I M E N S I O N 5 7
5.1 CORRELATED PARTICLE-HOLE PAIRS 58
5.2 A STRING ORDER PARAMETER 61
5.3 MULTI-SITE CORRELATIONS 65
5.4 FINITE-SIZE SCALING OF THE STRING ORDER PARAMETER 66
5.5 CONCLUSIONS AND PERSPECTIVES 68
I I QUANTUM INFORMATION APPLICATIONS 6 9
6 FERMIONIC G A U S S I A N S T A T E S 7 1
6.1 DIRAC AND MAJORANA FERMIONS 72
6.2 CANONICAL TRANSFORMATIONS 72
6.2.1 SINGLE-MODE AND MULTI-MODE CASES 73
6.2.2 COVARIANCE MATRIX 74
6.3 FERMIONIC GAUSSIAN STATES 75
6.3.1 SINGLE-MODE AND MULTI-MODE CASES 75
6.3.2 COVARIANCE MATRIX AND WICK S THEOREM 76
6.3.3 OVERLAP BETWEEN GAUSSIAN STATES 77
6.3.4 UHLMANN FIDELITY 78
6.4 QUADRATIC HAMILTONIANS 79
6.5 GAUSSIAN TIME EVOLUTION 80
6.5.1 HAMILTONIAN EVOLUTION 80
6.5.2 MASTER EQUATION WITH LINEAR JUMP OPERATORS 81
6.6 NON-GAUSSIAN TIME EVOLUTION 81
6.6.1 MASTER EQUATION WITH QUADRATIC JUMP OPERATORS 82
6.6.2 CONVEX-COMBINATION OF HAMILTONIAN TIME EVOLUTIONS . . 82 6.6.3
INTERACTIONS 83
7 Q U A N T U M M E M O R I E S W I T H M A J O R A N A M O D E S U N D
E R P E R T U R B A T I O N 8 5 7.1 SUMMARY OF THE MAIN RESULTS 87
7.2 THE KITAEV CHAIN: A ID TOPOLOGICAL SUPERCONDUCTOR 90
7.3 OPTIMAL RECOVERY OPERATION 92
7.3.1 PROPERTIES OF THE TRACE NORM 93
7.3.2 DERIVATION OF THE UPPER BOUND 93
7.3.3 EXPLICIT CONSTRUCTION OF A RECOVERY MAP 94
7.4 OPTIMAL GAUSSIAN RECOVERY OPERATION 95
IMAGE 3
C O N T E N T S V
7.4.1 DEFINITION OF NEW PAULI OPERATORS 95
7.4.2 GENERALITIES OF GAUSSIAN CHANNELS AND NOTATION 95
7.4.3 DERIVATION OF THE UPPER BOUND 96
7.4.4 EXPLICIT CONSTRUCTION OF A RECOVERY MAP 97
7.4.5 CONVEX-COMBINATION OF TRACE-PRESERVING GAUSSIAN RE COVERY
OPERATIONS 98
7.5 GAUSSIAN DECOHERENCE CHANNEL 98
7.6 MASTER EQUATION WITH LINEAR JUMP OPERATORS 100
7.6.1 UNIQUENESS OF THE STEADY STATE 101
7.6.2 ONE DECOHERENCE-FREE FERMIONIC MODE 102
7.6.3 DEPENDENCE ON THE SYSTEM SIZE 103
7.6.4 TRANSLATIONALLY-INVARIANT LINDBLAD OPERATORS 103
7.6.5 IMPOSSIBILITY OF PROTECTION VIA ENGINEERED DISSIPATION . . 105 7.7
MASTER EQUATION WITH QUADRATIC LINDBLAD OPERATORS 105
7.7.1 UNIQUENESS OF THE STEADY COVARIANCE MATRIX 105
7.8 KITAEV CHAIN COUPLED TO A SMALL FERMIONIC ENVIRONMENT . . . . 106
7.9 CONVEX-COMBINATION OF HAMILTONIAN TIME EVOLUTIONS 108 7.9.1 THE CASE
OF P INDEPENDENT FROM F I 109
7.9.2 THE CASE OF P DEPENDENT ON P, I L L
7.10 CONCLUSIONS AND PERSPECTIVES 113
A M A G N E T I C F L U X Q U A N T I Z A T I O N C O N D I T I O N 1 1
5
A.L INFINITE SYSTEM 115
A.2 FINITE SYSTEM WITH PERIODIC BOUNDARY CONDITIONS 116
B S O M E A D D I T I O N A L R E S U L T S O N F E R M I O N I C G A U
S S I A N S T A T E S 1 1 9
B . L EXPECTATION VALUE OF A CANONICAL TRANSFORMATION 119
B.2 TRACE OF THE PRODUCT OF TWO UNITARY OPERATORS 120
B.3 DISTANCE BETWEEN CONVEX-COMBINATIONS OF GAUSSIAN STATES . . . 121
C A N EIGENVALUE R E S U L T 1 2 5
C O N C L U S I O N S A N D P E R S P E C T I V E S 1 2 7
A C K N O W L E D G E M E N T S 1 3 1
B I B L I O G R A P H Y 1 3 3
|
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| spelling | Mazza, Leonardo Verfasser aut Quantum simulation of topological states of matter Leonardo Mazza 2012 XVIII, 143 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Quantenzustand (DE-588)4176600-3 gnd rswk-swf Topologische Phase (DE-588)113303408X gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantenzustand (DE-588)4176600-3 s Topologische Phase (DE-588)113303408X s Simulation (DE-588)4055072-2 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20120726-1108417-0-4 http://mediatum.ub.tum.de/node?id=1108417 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120726-1108417-0-4 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025690724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazza, Leonardo Quantum simulation of topological states of matter Quantenzustand (DE-588)4176600-3 gnd Topologische Phase (DE-588)113303408X gnd Simulation (DE-588)4055072-2 gnd |
| subject_GND | (DE-588)4176600-3 (DE-588)113303408X (DE-588)4055072-2 (DE-588)4113937-9 |
| title | Quantum simulation of topological states of matter |
| title_auth | Quantum simulation of topological states of matter |
| title_exact_search | Quantum simulation of topological states of matter |
| title_full | Quantum simulation of topological states of matter Leonardo Mazza |
| title_fullStr | Quantum simulation of topological states of matter Leonardo Mazza |
| title_full_unstemmed | Quantum simulation of topological states of matter Leonardo Mazza |
| title_short | Quantum simulation of topological states of matter |
| title_sort | quantum simulation of topological states of matter |
| topic | Quantenzustand (DE-588)4176600-3 gnd Topologische Phase (DE-588)113303408X gnd Simulation (DE-588)4055072-2 gnd |
| topic_facet | Quantenzustand Topologische Phase Simulation Hochschulschrift |
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