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E-raamat: Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

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, (Institució Catalana de Recerca i Estudits Avançats (ICREA) and Departament de Física, Universitat Autònoma de Bar), (Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Ciències Fotòniques (ICFO), Barcelona, Spain)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 08-Mar-2012
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191627439
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Ultracold Atoms in Optical Lattices: Simulating quantum many-body systemsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 08-Mar-2012
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191627439
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Quantum computers, though not yet available on the market, will revolutionize the future of information processing. Quantum computers for special purposes like quantum simulators are already within reach. The physics of ultracold atoms, ions and molecules offer unprecedented possibilities of control of quantum many body systems and novel possibilities of applications to quantum information processing and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics.

This book provides a complete and comprehensive overview of ultracold lattice gases as quantum simulators. It opens up an interdisciplinary field involving atomic, molecular and optical physics, quantum optics, quantum information, condensed matter and high energy physics. The book includes some introductory chapters on basic concepts and methods, and then focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases. It reviews in detail the physics of artificial lattice gauge fields with ultracold gases. The last part of the book covers simulators of quantum computers. After a brief course in quantum information theory, the implementations of quantum computation with ultracold gases are discussed, as well as our current understanding of condensed matter from a quantum information perspective.

Arvustused

`Cold atoms and molecules is a hot topic at the interface between atomic physics, condensed matter physics and quantum information. This book belongs on the desk of every graduate student and postdoc in this field, and provides an excellent monograph for the experienced researcher who wants to get an overview of the various aspects of strongly interacting quantum degenerate gases.' Peter Zoller, Institute for Theoretical Physics, University of Innsbruck `This masterpiece is a unique opportunity to learn about the frontiers of quantum many-body physics, and how they can be explored with ultracold atoms in optical lattices. Some of the most talented theorists in the field guide the readers through the fascinating interplay of atomic, optical and condensed-matter physics, where old and new quantum many-body phenomena appear.' Giovanni Modugno, Università di Firenze

Abbreviations xiii
1 Introduction
1(12)
1.1 The third quantum revolution
1(1)
1.2 Cold atoms from a historical perspective
2(3)
1.3 Cold atoms and the challenges of condensed matter physics
5(6)
1.4 Plan of the book
11(2)
2 Statistical physics of condensed matter: basic concepts
13(23)
2.1 Classical phase transitions
13(8)
2.2 Bose-Einstein condensation in non-interacting systems
21(2)
2.3 Quantum phase transitions
23(4)
2.4 One-dimensional systems
27(5)
2.5 Two-dimensional systems
32(4)
3 Ultracold gases in optical lattices: basic concepts
36(15)
3.1 Optical potentials
36(2)
3.2 Control of parameters in cold atom systems
38(3)
3.3 Non-interacting particles in periodic lattices: band structure
41(4)
3.4 Bose-Einstein condensates in optical lattices: weak interacting limit
45(3)
3.5 From weakly interacting to strongly correlated regimes
48(3)
4 Quantum simulators of condensed matter
51(9)
4.1 Quantum simulators
51(2)
4.2 Hubbard models
53(3)
4.3 Spin models and quantum magnetism
56(4)
5 Bose-Hubbard models: methods of treatment
60(38)
5.1 Introduction
60(2)
5.2 Weak interactions limit: the Bogoliubov approach
62(2)
5.3 Strong interactions limit: strong coupling expansion
64(4)
5.4 Perturbative mean-field approach
68(1)
5.5 Gutzwiller approach
69(3)
5.6 Exact diagonalization and the Lanczos method
72(3)
5.7 Quantum Monte Carlo: path integral and worm algorithms
75(6)
5.8 Phase-space methods
81(3)
5.9 Analytic one-dimensional methods
84(5)
5.10 Renormalization approaches in one dimension: DMRG and MPS
89(5)
5.11 Renormalization approaches in two dimension: PEPS, MERA, and TNS
94(4)
6 Fermi and Fermi-Bose Hubbard models: methods of treatment
98(27)
6.1 Introduction
98(1)
6.2 Fermi Hubbard model and BCS theory
99(2)
6.3 Balanced BCS-BEC crossover
101(5)
6.4 Mean-field description of imbalanced BCS-BEC crossover
106(3)
6.5 Fermi Hubbard model and strongly correlated fermions
109(9)
6.6 Hubbard models and effective Hamiltonians
118(3)
6.7 Fermi-Bose Hubbard models
121(4)
7 Ultracold spinor atomic gases
125(40)
7.1 Introduction
125(1)
7.2 Spinor interactions
126(2)
7.3 Spinor Bose-Einstein condensates: mean-field phases
128(5)
7.4 Spin textures and topological defects
133(4)
7.5 Bosonic spinor gases in optical lattices
137(19)
7.6 Spinor Fermi gases
156(9)
8 Ultracold dipolar gases
165(40)
8.1 Introduction
165(2)
8.2 Properties of dipole-dipole interaction
167(2)
8.3 Ultracold dipolar systems
169(2)
8.4 Ultracold trapped dipolar gases
171(11)
8.5 Dipolar gas in a lattice: extended Hubbard models
182(5)
8.6 Dipolar bosons in a 2D optical lattice
187(9)
8.7 Quantum Monte Carlo studies of dipolar gases
196(6)
8.8 Further dipole effects
202(3)
9 Disordered ultracold atomic gases
205(59)
9.1 Introduction
205(1)
9.2 Disorder in condensed matter
206(18)
9.3 Realization of disorder in ultracold atomic gases
224(4)
9.4 Disordered Bose-Einstein condensates
228(18)
9.5 Disordered ultracold fermionic systems
246(2)
9.6 Disordered ultracold Bose-Fermi and Bose-Bose mixtures
248(3)
9.7 Spin glasses
251(7)
9.8 Disorder-induced order
258(6)
10 Frustrated ultracold atom systems
264(29)
10.1 Introduction
264(1)
10.2 Quantum antiferromagnets
265(5)
10.3 Physics of frustrated quantum antiferromagnets
270(12)
10.4 Realization of frustrated models with ultracold atoms
282(11)
11 Ultracold atomic gases in `artificial' gauge fields
293(47)
11.1 Introduction
293(1)
11.2 Ultracold atoms in rapidly rotating microtraps
294(10)
11.3 Gauge symmetry in the lattice
304(6)
11.4 Lattice gases in `artificial' Abelian gauge fields
310(4)
11.5 Lattice gases in `artificial' non-Abelian gauge fields
314(2)
11.6 Integer quantum Hall effect and emergence of Dirac fermions
316(6)
11.7 Fractional quantum Hall effect in non-Abelian fields
322(4)
11.8 Ultracold gases and lattice gauge theories
326(2)
11.9 Generation of `artificial' gauge fields
328(12)
12 Many-body physics from a quantum information perspective
340(44)
12.1 Introduction
340(1)
12.2 Crash course on quantum information
341(14)
12.3 Quantum phase transitions and entanglement
355(8)
12.4 Area laws
363(11)
12.5 The world according to tensor networks
374(10)
13 Quantum information with lattice gases
384(28)
13.1 Introduction
384(2)
13.2 Quantum circuit model in optical lattices
386(8)
13.3 One-way quantum computer with lattice gases
394(4)
13.4 Topological quantum computing in optical lattices
398(11)
13.5 Distributed quantum information
409(3)
14 Detection of quantum systems realized with ultracold atoms
412(15)
14.1 Introduction
412(3)
14.2 Time of flight: first-order correlations
415(2)
14.3 Time of flight and noise correlations: higher-order correlations
417(1)
14.4 Bragg spectroscopy
418(3)
14.5 Optical Bragg diffraction
421(2)
14.6 Single-atom detectors
423(1)
14.7 Quantum polarization spectroscopy
424(3)
15 Perspectives: beyond standard optical lattices
427(12)
15.1 Introduction
427(1)
15.2 Beyond standard optical lattices: new trends
428(4)
15.3 Standard optical lattices: what's new?
432(7)
Bibliography 439(32)
Index 471
Maciej Lewenstein has been an ICREA professor at the Institut de Ciències Fotòniques in Castelldefels since 2005 where he leads the quantum optics theory group. In 2007 he won the Humbolt research award, Germany. In 2008 he obtained the Advance Research Grant from the European Community and in 2010 he won the first Harmburger Prize for his contributions in theoretical physics. His interests range from traditional quantum optics through to physics of cold gases and quantum information to physics of ultra intense laser fields.

Anna Sanpera has been an ICREA professor in the newly formed group of Quantum Information and Quantum Phenomena at the Universitat Autònoma of Barcelona, Spain, since 2005. She is currently working on quantum information theory, physics ultra-cold gases and the interface between quantum theory and condensed matter. She is also interested in the connection between quantum mechanics and biology.

Verònica Ahufinger obtained an ICREA researcher position in 2005 and moved to the Universitat Autònoma of Barcelona. Since 2010 she has been a professor at the Universitat Autònoma of Barcelona. She is interested in the interplay between the physics of ultracold atoms, quantum optics and condensed matter.
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