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Quantum Matter at Ultralow Temperatures [Hardback]

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  • Formāts: Hardback, 592 pages
  • Izdošanas datums: 29-Sep-2016
  • Izdevniecība: IOS Press,US
  • ISBN-10: 1614996938
  • ISBN-13: 9781614996934
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Quantum Matter at Ultralow TemperaturesPalielināt
  • Formāts: Hardback, 592 pages
  • Izdošanas datums: 29-Sep-2016
  • Izdevniecība: IOS Press,US
  • ISBN-10: 1614996938
  • ISBN-13: 9781614996934
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781614996934.html
Keywords:
The Enrico Fermi summer school on Quantum Matter at Ultralow Temperatures held on 7-15 July 2014 at Varenna, Italy, featured important frontiers in the field of ultracold atoms. For the last 25 years, this field has undergone dramatic developments, which were chronicled by several Varenna summer schools, in 1991 on Laser Manipulation of Atoms, in 1998 on Bose-Einstein Condensation in Atomic Gases, and in 2006 on Ultra-cold Fermi Gases. The theme of the 2014 school demonstrates that the field has now branched out into many different directions, where the tools and precision of atomic physics are used to realise new quantum systems, or in other words, to quantum-engineer interesting Hamiltonians. The topics of the school identify major new directions: Quantum gases with long range interactions, either due to strong magnetic dipole forces, due to Rydberg excitations, or, for polar molecules, due to electric dipole interactions; quantum gases in lower dimensions; quantum gases with disorder; atoms in optical lattices, now with single-site optical resolution; systems with non-trivial topological properties, e.g. with spin-orbit coupling or in artificial gauge fields; quantum impurity problems (Bose and Fermi polarons); quantum magnetism. Fermi gases with strong interactions, spinor Bose-Einstein condensates and coupled multi-component Bose gases or Bose-Fermi mixtures continue to be active areas. The current status of several of these areas is systematically summarized in this volume.
Preface xv
M. Inguscio
W. Ketterle
S. Stringari
G. Roati
Course group shot xvi
Introduction to the physics of artificial gauge fields 1(62)
J. Dalibard
1 Magnetism and quantum physics
2(7)
1.1 Gauge invariance
2(2)
1.2 Cyclotron motion and Landau levels
4(1)
1.3 The Aharonov-Bohm effect
5(3)
1.4 Rotating gases
8(1)
2 Geometric phases and gauge fields for free atoms
9(11)
2.1 Berry's phase
9(2)
2.2 Adiabatic following of a dressed state
11(1)
2.3 The two-level case
12(4)
2.4 Validity of the adiabatic approximation
16(1)
2.5 Spontaneous emission and recoil heating
16(4)
3 Non-Abelian potentials and spin-orbit coupling
20(5)
3.1 Non-Abelian potentials in quantum optics
21(1)
3.2 Tripod configuration and 2D spin-orbit coupling
22(1)
3.3 1D version of spin-orbit coupling
23(2)
4 Gauge fields on a lattice
25(6)
4.1 Tight-binding model
26(1)
4.2 Hofstadter butterfly
27(4)
4.3 Chern number for an energy band
31(1)
5 Generation of lattice gauge fields via shaking or modulation
31(4)
5.1 Rapid shaking of a lattice
31(2)
5.2 Resonant shaking/modulation
33(2)
6 Generation of lattice gauge fields via internal atomic transitions
35(6)
6.1 Laser-assisted tunneling in a 1D ladder
35(2)
6.2 Lattice with artificial dimension
37(1)
6.3 Laser-induced tunneling in a 2D lattice
38(1)
6.4 Optical flux lattices
39(2)
7 Conclusion
41(2)
Appendix A. Landau levels
43(3)
Eigenstates with the Landau gauge
43(2)
Probability current in a Landau state
45(1)
Eigenstates with the symmetric gauge
45(1)
Appendix B. Topology in the square lattice
46(17)
Band structure and periodicity in reciprocal space
47(3)
Constant force and unitary transformation
50(1)
Bloch oscillations and adiabatic following
51(1)
The velocity operator and its matrix elements
52(1)
The Berry curvature
53(1)
Conduction from a filled band and Chern number
54(1)
The Chern number is an integer
55(8)
Strongly interacting Fermi gases 63(80)
W. Zwerger
1 Feshbach resonances
63(13)
1.1 Two-body scattering
64(1)
1.2 Feshbach resonances
65(5)
1.3 Three-body losses
70(3)
1.4 Unitary bosons and the Efimov effect
73(3)
2 Tan relations
76(15)
2.1 Thermodynamic relations
77(2)
2.2 Quantitative results for the contact
79(3)
2.3 Closed-channel fraction
82(2)
2.4 Single-channel model and zero-range limit
84(3)
2.5 Short-distance correlations
87(4)
3 Unitary fermions: universality and scale invariance
91(25)
3.1 Quantum critical point and universality
92(7)
3.2 Thermodynamics of the unitary Fermi gas
99(5)
3.3 Luttinger-Ward theory
104(4)
3.4 Scale invariance
108(6)
3.5 Broken scale invariance and conformal anomaly in 2D
114(2)
4 RF-spectroscopy and transport
116(28)
4.1 RF-spectroscopy
117(9)
4.2 Quantum limited viscosity and spin diffusion
126(17)
Thermodynamics of strongly interacting Fermi gases 143(78)
M.W. Zwierlein
1 Introduction
144(1)
2 Universal thermodynamics
145(48)
2.1 Thermodynamics of trapped gases
148(3)
2.1.1 Zero-temperature equation of state
149(1)
2.1.2 Viral theorem for the trapped gas at unitarity
150(1)
2-2 General thermodynamic relations
151(2)
2.2.1 Obtaining the pressure from density profiles
152(1)
2.2.2 "Magic formula" for harmonic trapping
153(1)
2.3 Universal thermodynamics of the unitary Fermi gas
153(9)
2.3.1 Compressibility equation of state
154(1)
2.3.2 Specific heat versus temperature-the Lambda transition in a gas
155(2)
2.3.3 Chemical potential, energy and free energy
157(3)
2.3.4 Entropy, density and pressure
160(1)
2.3.5 Importance of cross-validation with theory
161(1)
2.3.6 Further applications of the "fit-free" method
161(1)
2.4 Equation of state in the BEC-BCS crossover-The contact
162(7)
2.4.1 Energy of molecular Bose-Einstein condensates
165(1)
2.4.2 Energy of weakly interacting Fermi gas
166(1)
2.4.3 Near unitarity
167(1)
2.4.4 Pressure relation
167(1)
2.4.5 General Virial theorem
168(1)
2.5 Equation of state in the BEC-BCS crossover Experiments
169(21)
2.5.1 Equation of state from density profiles
169(1)
2.5.2 Momentum distribution
170(1)
2.5.3 Radiofrequency spectroscopy
171(8)
2.5.4 Photoassociation
179(2)
2.5.5 Bragg spectroscopy
181(4)
2.5.6 Temperature dependence of the homogeneous contact
185(1)
2.5.7 Collective oscillations
186(1)
2.5.8 Condensation energy
187(3)
2.6 The normal state above Tc: Pseudo-gap phase, Fermi liquid, or Fermi gas?
190(3)
3 Fermionic superfluidity with spin imbalance
193(15)
3.1 Chandrasekhar-Clogston limit
195(3)
3.2 Phase separation
198(1)
3.3 Limit of high imbalance-the Fermi polaron
199(3)
3.4 Fermi liquid of polarons
202(1)
3.5 Thermodynamics of spin-imbalanced Fermi mixtures
202(4)
3.5.1 Equation of state at unitarity
203(3)
3.6 Prospects for observing the FFLO state
206(2)
4 Conclusion and perspectives
208(13)
Spinor Bose-Einstein gases 221(78)
G. Edward Marti
D.M. Stamper-Kurn
1 Basic properties
222(9)
1.1 The quantum fluids landscape
222(3)
1.2 Atomic species
225(4)
1.2.1 Alkali atoms
225(1)
1.2.2 High-spin atoms
226(1)
1.2.3 Stability against dipolar relaxation
227(2)
1.3 Rotationally symmetric interactions
229(2)
2 Magnetic order of spinor Bose-Einstein condensates
231(17)
2.1 Bose-Einstein magnetism in a non-interacting spinor gas
232(5)
2.2 Spin-dependent s-wave interactions in more recognizable form
237(2)
2.3 Ground states in the mean-field and single-mode approximations
239(1)
2.4 Mean-field ground states under applied magnetic fields
240(4)
2.5 Experimental evidence for magnetic order of ferromagnetic and anti-ferromagnetic F=1 spinor condensates
244(1)
2.6 Correlations in the exact many-body ground state of the F=1 spinor gas
245(3)
3 Imaging spinor condensates
248(16)
3.1 Stern-Gerlach imaging
249(1)
3.2 Dispersive birefringent imaging
250(3)
3.2.1 Circular birefringent imaging
250(3)
3.3 Projective imaging
253(5)
3.3.1 Absorptive spin-sensitive in situ imaging (ASSISI)
255(2)
3.3.2 Noise in dispersive imaging and ASSISI
257(1)
3.4 Spin-spin correlations and magnetic susceptibility
258(1)
3.5 Multi-axis imaging and topological invariants
259(5)
3.5.1 Multi-axis imaging of ferromagnetic structures
260(3)
3.5.2 Magnetization curvature
263(1)
4 Spin dynamics
264(14)
4.1 Microscopic spin dynamics
264(2)
4.2 Mean-field picture of collective spin dynamics
266(3)
4.3 Spin-mixing instability
269(9)
4.3.1 Experiments in the single-mode regime
273(1)
4.3.2 Quantum quenches in spatially extended spinor Bose-Einstein condensates
274(4)
5 Magnetic excitations
278(13)
5.1 Quasiparticles of a spin-1 spinor condensate
279(1)
5.2 Linearized Schrodinger equation
280(3)
5.2.1 Ferromagnetic F=1 condensate
280(2)
5.2.2 Polar F=1 condensate
282(1)
5.3 Making and detecting magnons
283(3)
5.4 Magnon propagation
286(2)
5.5 Magnon contrast interferometry and recoil frequency
288(3)
6 Conclusion
291(8)
Probing and controlling quantum many-body systems in optical lattices 299(26)
I. Bloch
1 Introduction
299(1)
2 Bose and Fermi Hubbard models
300(4)
2.1 Bose-Hubbard model
301(2)
2.2 Fermi-Hubbard model
303(1)
3 Quantum magnetism with ultracold atoms in optical lattices
304(5)
3.1 Superexchange spin interactions
305(3)
3.1.1 Superexchange interactions in a double well
305(1)
3.1.2 Superexchange interactions on a lattice
306(2)
3.2 Resonating valence bond states in a plaquette
308(1)
4 Site-resolved imaging
309(2)
5 Thermometry at the limit of individual thermal excitations
311(3)
6 Single-site-resolved addressing of individual atoms
314(1)
7 Quantum gas microscopy-new possibilities for cold quantum gases
315(4)
7.1 Using quantum gas microscopes to probe quantum magnetism
317(1)
7.2 Long-range-interacting quantum magnets
318(1)
8 Outlook
319(6)
New theoretical approaches to Bose polarons 325(88)
F. Grusdt
E. Demler
1 Introduction
326(4)
2 Derivation of the Frohlich Hamiltonian
330(9)
2.1 Microscopic Hamiltonian: Impurity in a BEC
330(1)
2.2 Frohlich Hamiltonian in a BEC
331(1)
2.3 Microscopic derivation of the Frohlich model
332(3)
2.4 Characteristic scales and the polaronic coupling constant
335(2)
2.5 Lippmann-Schwinger equation
337(2)
3 Overview of common theoretical approaches
339(16)
3.1 Perturbative approaches s
339(3)
3.1.1 Rayleigh-Schrodinger perturbation theory
339(1)
3.1.2 Green's function perturbation theory and self-consistent Born
340(2)
3.2 Exact solution for infinite mass
342(1)
3.3 Lee-Low-Pines treatment
343(1)
3.4 Weak coupling mean-field theory
344(4)
3.4.1 Self-consistency equation
346(1)
3.4.2 Polaron energy
346(1)
3.4.3 Polaron mass
347(1)
3.5 Strong coupling Landau-Pekar approach
348(3)
3.5.1 Polaron energy
350(1)
3.5.2 Polaron mass
351(1)
3.6 Feynman path integral approach
351(3)
3.6.1 Jensen-Feynman variational principle
352(1)
3.6.2 Feynman's trial action
352(2)
3.6.3 Polaron mass
354(1)
3.7 Monte Carlo approaches
354(1)
4 Renormalization group approach >>
355(19)
4.1 Frohlich model and renormalized coupling constants
358(2)
4.2 Renormalization group formalism for the Frohlich model
360(7)
4.2.1 Dimensional analysis
360(2)
4.2.2 Formulation of the RG
362(4)
4.2.3 RG flow equations
366(1)
4.2.4 Solutions of RG flow equations
367(1)
4.3 Polaron ground state energy in the renormalization group approach
367(4)
4.3.1 Logarithmic UV divergence of the polaron energy
368(3)
4.4 Ground state polaron properties from RG
371(2)
4.4.1 Polaron mass
371(1)
4.4.2 Phonon number
372(1)
4.4.3 Quasiparticle weight
372(1)
4.5 Gaussian variational approach
373(1)
5 UV regularization and log-divergence
374(3)
5.1 Regularization of the power-law divergence
375(1)
5.2 Explanation of the logarithmic divergence
376(1)
6 Results for experimentally relevant parameters
377(10)
6.1 Experimental considerations
377(3)
6.1.1 Conditions for the Frohlich model
378(1)
6.1.2 Experimentally achievable coupling strengths
379(1)
6.2 RF spectroscopy
380(3)
6.2.1 Basic theory of RF spectroscopy
380(2)
6.2.2 Basic properties of RF spectra
382(1)
6.3 Properties of polarons
383(4)
6.3.1 Polaronic mass
383(3)
6.3.2 Phonon number
386(1)
6.3.3 Quasiparticle weight
387(1)
7 Example of a dynamical problem: Bloch oscillations of Bose polarons
387(10)
7.1 Time-dependent mean-field approach
388(2)
7.1.1 Equations of motion-Dirac's time-dependent variational principle
389(1)
7.2 Bloch oscillations of polarons in lattices
390(8)
7.2.1 Model
390(2)
7.2.2 Time-dependent mean-field description
392(1)
7.2.3 Adiabatic approximation and polaron dynamics
392(2)
7.2.4 Polaron transport properties
394(3)
8 Outlook
397(1)
Appendix A
398(15)
A.1 Lee-Low-Pines formalism in a lattice
398(3)
A.1.1 Coupling constant and relation to experiments
399(1)
A.1.2 Time-dependent Lee-Low-Pines transformation in the lattice
399(2)
A.2 Renormalized impurity mass
401(1)
A.3 Polaron properties from the RG-derivations
402(14)
A.3.1 Polaron phonon number
402(1)
A.3.2 Polaron momentum
403(1)
A.3.3 Quasiparticle weight
404(9)
Clean and dirty one-dimensional systems 413(30)
T. Giamarchi
1 Introduction
413(1)
2 Why one dimension
414(2)
3 1D basics
416(12)
3.1 What are one-dimensional systems?
416(1)
3.2 Some realizations with cold atoms or CM
417(1)
3.3 Universal physics in one dimension (Luttinger liquid)
418(7)
3.4 Fermions and spins
425(1)
3.5 Luttinger parameters
426(2)
4 Experimental tests of TLL
428(4)
4.1 Magnetic insulators
428(1)
4.2 Cold atomic systems
428(1)
4.3 Other experimental features of 1d: Fractionalization of excitations
429(3)
5 TLL and beyond
432(6)
5.1 Effect of a lattice: Mott transition
433(2)
5.2 Disorder
435(3)
6 Wishes and open problems
438(5)
Spectroscopy of Rydberg atoms in dense ultracold gases 443(20)
J. Balewski
T. Pfau
1 Introduction
443(2)
2 Electron-atom scattering
445(6)
2.1 Fermi pseudopotential
445(5)
2.2 Higher-order contributions
450(1)
3 Rydberg spectroscopy
451(5)
3.1 Ultracold but thermal gases
451(4)
3.2 Bose-Einstein condensates
455(1)
4 Lifetime of Rydberg atoms in dense gases
456(3)
4.1 Dependence on principal quantum number and density
457(1)
4.2 Possible decay processes
458(1)
4.3 Dependence on spectral position
459(1)
5 Conclusion
459(4)
Coherently coupled Bose gases 463(22)
A. Recati
1 Introduction
463(1)
2 Model
464(1)
3 Mean-field Gross-Pitaevskii equations
465(2)
3.1 Ground state
465(2)
4 Excitation spectra
467(8)
4.0 Spin structure factor and magnetic fluctuations
471(1)
4.1 Trapped gas
472(2)
4.2 Relation to Josephson dynamics
474(1)
5 Soliton and vortex dimers
475(2)
6 Tight-binding model for gases in optical lattices
477(8)
Does an isolated quantum system relax? 485(20)
B. Rauer
T. Schweigler
T. Langen
J. Schmiedmayer
1 Motivation
485(1)
2 One-dimensional Bose gases
486(2)
3 Creating a non-equilibrium state
488(2)
4 Probing the quantum state
490(6)
4.1 Density ripples
491(1)
4.2 Phase correlation functions
492(3)
4.3 Full distribution functions
495(1)
5 Generalized Gibbs ensemble
496(1)
6 Dynamics beyond prethermalization
497(3)
6.1 Recurrences
498(1)
6.2 Imbalanced splitting
498(2)
7 Application: Interferometry with squeezed states
500(1)
8 Conclusion
501(4)
Entanglement and non-locality in many-body systems: A primer 505(32)
J. Tura
A. B. Sainz
T. Grass
R. Agusiak
A. Acin
M. Lewen-Stein
1 Introduction
506(2)
2 Crash course on entanglement
508(5)
2.1 Bipartite pure states: Schmidt decomposition
508(1)
2.2 Bipartite mixed states: Separable and entangled states
509(1)
2.3 Entanglement criteria
510(2)
2.4 Entanglement measures
512(1)
2.5 von Neumann entropy
512(1)
3 Entanglement in many-body systems
513(1)
3.1 Computational complexity
513(1)
3.2 Entanglement of a generic state
513(1)
4 Area laws
514(7)
4.1 Quantum area laws in 1D
515(1)
4.2 Higher-dimensional systems
516(3)
4.2.1 Area laws for mutual information-classical and quantum Gibbs states
517(2)
4.3 The world according to tensor networks
519(2)
5 Non-locality in many-body systems
521(8)
5.1 Probabilities and correlations-DIQIP approach
522(3)
5.2 Detecting non-locality in many-body systems with two-body correlators
525(1)
5.3 Permutational invariance
526(1)
5.4 Symmetric two-body Bell inequalities: example
527(1)
5.5 Many-body symmetric states
527(2)
6 Conclusions
529(8)
Majorana fermions in atomic wire networks as non-Abelian anyons 537(28)
M.A. Baranov
1 Introduction
537(1)
2 Exchange and statistics
538(8)
2.1 Braid group, representations, and exchange statistics
542(1)
2.2 Physical requirements for non-Abelian anyons
543(3)
3 Majorana fermions as non-Abelian anyons
546(4)
4 Majorana fermions in Kitaev wire
550(3)
5 Majorana fermions in systems of cold atoms
553(7)
5.1 Braiding Majorana fermions in wires setup
554(3)
5.2 Physics behind the braiding
557(1)
5.3 Demonstration of non-Abelian statistics
558(2)
6 Using Majorana fermions for quantum computation
560(3)
7 Summary
563(2)
List of participants 565