Ultracold gases and quantum information: École d'été de physique des Houches in Singapore, session XCI, 29 June-24 July, July 2009, École thématique du CNRS / ed. by C.Miniatura et al. - Oxford; New York: Oxford University Press, 2011. - xxxi, 630 p.: ill., ports. - Other titles: Les Houches 2009 - session XCI. - Incl. bibl. ref. - ISBN 978-0-19-960365-7  Место хранения:   016 | Библиотека Института ядерной физики СО РАН | Новосибирск

Оглавление / Contents

List of participants .......................................... xxv 1 Basics on Bose—Einstein condensation ......................... 1 1.1 Introduction ............................................ 2 1.2 Ideal Bose-Einstein condensates ......................... 3 1.3 Mean-field theory ...................................... 15 1.4 Beyond mean-field theory ............................... 39 1.5 Bimodal condensates .................................... 51 Notes ....................................................... 60 Acknowledgments ............................................. 62 References .................................................. 62 2 Degenerate Fermi gases ...................................... 66 2.1 Introduction ........................................... 67 2.2 Ideal Fermi gas ........................................ 69 2.3 Two-component Fermi gas ................................ 84 Appendix A: The renormalization procedure .................. 100 Notes ...................................................... 101 Acknowledgments ............................................ 101 References ................................................. 102 3 Quantum information: primitive notions and quantum correlations ............................................... 105 3.1 Quantum theory ........................................ 106 3.2 Primitives of quantum information (I) ................. 120 3.3 Primitives of quantum information (II) ................ 131 3.4 Quantum correlations (I): the failure of alternative descriptions .......................................... 143 3.5 Quantum correlations (II): the mathematics of no-signalling ......................................... 156 3.6 Quantum correlations (III): the power of Bell ......... 165 Notes ...................................................... 170 References ................................................. 173 4 Quantum computing and entanglement ......................... 178 4.1 Introduction .......................................... 179 4.2 Quantum networks ...................................... 181 4.3 Quantum algorithms .................................... 183 4.4 Quantum error correction .............................. 190 4.5 Entanglement: introduction and basic definitions ...... 195 4.6 Entanglement and quantum algorithms ................... 203 4.7 One-way quantum computing ............................. 209 Acknowledgments ............................................ 216 References ................................................. 216 5 Quantum computation with trapped ions and atoms ............ 218 Preface .................................................... 219 5.1 Ion (and atom) quantum logic .......................... 219 5.2 Scalability ........................................... 234 5.3 Qubit interfacing ..................................... 236 Note ....................................................... 241 References ................................................. 241 6 Quantum Hall effects ....................................... 253 Preface .................................................... 254 6.1 Introduction .......................................... 255 6.2 Landau quantization ................................... 267 6.3 Integer quantum Hall effect ........................... 287 6.4 Strong correlations and the fractional quantum Hall effect ................................................ 305 6.5 Brief overview of multicomponent quantum Hall systems ............................................... 327 Appendix A: Electronic band structure of graphene .......... 341 Appendix B: Landau levels of massive Dirac particles ....... 345 Notes ...................................................... 347 References ................................................. 352 7 Quantum phase transitions .................................. 356 7.1 Introduction .......................................... 357 7.2 Quantum Ising model ................................... 362 7.3 Hubbard model ......................................... 369 7.4 Conclusions ........................................... 390 7.5 Appendix: The Jordan-Wigner transformation ............ 390 References ................................................. 393 8 Interactions in quantum fluids ............................. 395 8.1 Introduction .......................................... 396 8.2 Fermi liquids ......................................... 397 8.3 Beyond Fermi liquid ................................... 413 8.4 One-dimensional systems ............................... 426 8.5 Conclusions ........................................... 438 Acknowledgments ............................................ 439 References ................................................. 439 9 Disorder and interference: localization phenomena .......... 441 9.1 Introduction .......................................... 442 9.2 Transfer-matrix description of transport and Anderson localization in ID systems ................... 446 9.3 Scaling theory of localization ........................ 456 9.4 Key numerical and experimental results ................ 465 9.5 Microscopic description of quantum transport .......... 480 9.6 Coherent backscattering (CBS) ......................... 495 9.7 Weak localization (WL) ................................ 509 9.8 Kicked rotor .......................................... 517 Notes ...................................................... 526 References ................................................. 527 10 Quantum information processing and quantum optics devices .................................................... 534 10.1 Basic field quantization - the foundations ............ 535 10.2 A silly question: what is a photon? ................... 555 10.3 Parametric-down conversion: a common workhouse ........ 589 10.4 Quantum information with photons ...................... 605 Notes ......................................................... 628 References .................................................... 628