Ultracold Atoms in Optical Lattices Simulating quantum many-body systems
by Lewenstein, Maciej; Sanpera, Anna; Ahufinger, VeronicaFormat: Hardcover
Pub. Date: 2012-05-04
Publisher(s): Oxford University Press
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Summary
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.
Author Biography
Maciej Lewenstein is an ICREA professor at the Institut de Cincies Fotniques (ICFO) in Castelldefels (Barcelona), Spain, where he leads the quantum optics theory group. Anna Sanpera is an ICREA professor in the Quantum Information and Quantum Phenomena group in the Physics Department at the Universitat Autnoma de Barcelona, Spain. Veronica Ahufinger is an associate professor at the Optics group in the Physics Department at the Universitat Autnoma de Barcelona, Spain.
Table of Contents
| Abbreviations | p. xiii |
| Introduction | p. 1 |
| The third quantum revolution | p. 1 |
| Cold atoms from a historical perspective | p. 2 |
| Cold atoms and the challenges, of condensed matter physics | p. 5 |
| Plan of the book | p. 11 |
| Statistical physics of condensed matter: basic concepts | p. 13 |
| Classical phase transitions | p. 13 |
| Bose-Einstein condensation in non-interacting systems | p. 21 |
| Quantum phase transitions | p. 23 |
| One-dimensional systems | p. 27 |
| Two-dimensional systems | p. 32 |
| Ultracold gases in optical lattices: basic concepts | p. 36 |
| Optical potentials | p. 36 |
| Control of parameters in cold atom systems | p. 38 |
| Non-interacting particles in periodic lattices: band structure | p. 41 |
| Bose-Einstein condensates in optical lattices: weak interacting limit | p. 45 |
| From weakly interacting to strongly correlated regimes | p. 48 |
| Quantum simulators of condensed matter | p. 51 |
| Quantum simulators | p. 51 |
| Hubbard models | p. 53 |
| Spin models and quantum magnetism | p. 56 |
| Bose-Hubbard models: methods of treatment | p. 60 |
| Introduction | p. 60 |
| Weak interactions limit: the Bogoliubov approach | p. 62 |
| Strong interactions limit: strong coupling expansion | p. 64 |
| Perturbative mean-field approach | p. 68 |
| Gutzwiller approach | p. 69 |
| Exact diagonalization and the Lanczos method | p. 72 |
| Quantum Monte Carlo: path integral and worm algorithms | p. 75 |
| Phase-space methods | p. 81 |
| Analytic one-dimensional methods | p. 84 |
| Renormalization approaches in one dimension: DMRG and MPS | p. 89 |
| Renormalization approaches in two dimension: PEPS, MERA, and TNS | p. 94 |
| Fermi and Fermi-Bose Hubbard models: methods of treatment | p. 98 |
| Introduction | p. 98 |
| Fermi Hubbard model and BCS theory | p. 99 |
| Balanced BCS-BEC crossover | p. 101 |
| Mean-field description of unbalanced BCS-BEC crossover | p. 106 |
| Fermi Hubbard model and strongly correlated fermions | p. 109 |
| Hubbard models and effective Hamiltonians | p. 118 |
| Fermi-Bose Hubbard models | p. 121 |
| Ultracold spinor atomic gases | p. 125 |
| Introduction | p. 125 |
| Spinor interactions | p. 126 |
| Spinor Bose-Einstein condensates: mean-field phases | p. 128 |
| Spin textures and topological defects | p. 133 |
| Bosonic spinor gases in optical lattices | p. 137 |
| Spinor Fermi gases | p. 156 |
| Ultracold dipolar gases | p. 165 |
| Introduction | p. 165 |
| Properties of dipole-dipole interaction | p. 167 |
| Ultracold dipolar systems | p. 169 |
| Ultracold trapped dipolar gases | p. 171 |
| Dipolar gas in a lattice: extended Hubbard models | p. 182 |
| Dipolar bosons in a 2D optical lattice | p. 187 |
| Quantum Monte Carlo studies of dipolar gases | p. 196 |
| Further dipole effects | p. 202 |
| Disordered ultracold atomic gases | p. 205 |
| Introduction | p. 205 |
| Disorder in condensed matter | p. 206 |
| Realization of disorder in ultracold atomic gases | p. 224 |
| Disordered Bose-Einstein condensates | p. 228 |
| Disordered ultracold fermionic systems | p. 246 |
| Disordered ultracold Bose-Fermi and Bose-Bose mixtures | p. 248 |
| Spin glasses | p. 251 |
| Disorder-induced order | p. 258 |
| Frustrated ultracold atom systems | p. 264 |
| Introduction | p. 264 |
| Quantum antiferromagnets | p. 265 |
| Physics of frustrated quantum antiferromagnets | p. 270 |
| Realization of frustrated models with ultracold atoms | p. 282 |
| Ultracold atomic gases in 'artificial' gauge fields | p. 293 |
| Introduction | p. 293 |
| Ultracold atoms in rapidly rotating microtraps | p. 294 |
| Gauge symmetry in the lattice | p. 304 |
| Lattice gases in 'artificial' Abelian gauge fields | p. 310 |
| Lattice gases in 'artificial' non-Abelian gauge fields | p. 314 |
| Integer quantum Hall effect and emergence of Dirac fermions | p. 316 |
| Fractional quantum Hall effect in non-Abelian fields | p. 322 |
| Ultracold gases and lattice gauge theories | p. 326 |
| Generation of 'artificial' gauge fields | p. 328 |
| Many-body physics from a quantum information perspective | p. 340 |
| Introduction | p. 340 |
| Crash course on quantum information | p. 341 |
| Quantum phase transitions and entanglement | p. 355 |
| Area laws | p. 363 |
| The world according to tensor networks | p. 374 |
| Quantum information with lattice gases | p. 384 |
| Introduction | p. 384 |
| Quantum circuit model in optical lattices | p. 386 |
| One-way quantum computer with lattice gases | p. 394 |
| Topological quantum computing in optical lattices | p. 398 |
| Distributed quantum information | p. 409 |
| Detection of quantum systems realized with ultracold atoms | p. 412 |
| Introduction | p. 412 |
| Time of flight: first-order correlations | p. 415 |
| Time of flight and noise correlations: higher-order correlations | p. 417 |
| Bragg spectroscopy | p. 418 |
| Optical Bragg diffraction | p. 421 |
| Single-atom detectors | p. 423 |
| Quantum polarization spectroscopy | p. 424 |
| Perspectives: beyond standard optical lattices | p. 427 |
| Introduction | p. 427 |
| Beyond standard optical lattices: new trends | p. 428 |
| Standard optical lattices: what's new? | p. 432 |
| Bibliography | p. 439 |
| Index | p. 471 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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