Comptes Rendus
Polariton physics/Physique des polaritons
Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light
Comptes Rendus. Physique, Volume 17 (2016) no. 8, pp. 808-835.

We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.

Nous passons en revue des développements récents concernant la dynamique quantique hors équilibre et la physique de la lumière dans des circuits supraconducteurs et analogues de Josephson, par analogie avec les systèmes de physique atomique. Nous commençons par des modèles quantiques d'impuretés reliés à des systèmes dissipatifs et contrôlés. Théoriciens et expérimentateurs accomplissent des efforts en vue de la caractérisation de ces systèmes quantiques hors équilibre. Nous montrons comment les systèmes de jonctions Josephson peuvent servir à implémenter l'équivalent de l'effet Kondo avec des photons micro-onde. L'effet Kondo peut se caractériser par une fréquence lumineuse renormalisée et par un pic dans la transmission élastique Rayleigh d'un photon. Nous nous intéressons aussi à la physique des systèmes hybrides comprenant des dispositifs à points quantiques mésoscopiques couplés à un résonateur électromagnétique. Ensuite, nous discuterons des modèles de réseaux d'électrodynamique quantiques (QED) permettant de concevoir des modèles de réseaux de Jaynes–Cummings et de Rabi, via la présence de qubits supraconducteurs dans les cavités. Ceci ouvre la porte nouvelle physique pour le problème à N-corps dans les systèmes lumineux hors équilibre, en relation avec la transition Mott-superfluide observée avec des atomes ultra-froids dans des réseaux optiques. Nous résumons aussi des prédictions théoriques récentes pour réaliser des phases topologiques avec de la lumière. Des champs de jauge synthétiques et des couplages spin–orbite ont été mis en œuvre avec succès dans les matériaux quantiques et dans les systèmes d'atomes ultra-froids piégés dans des réseaux optiques – en utilisant des perturbations de Floquet périodiques dans le temps – ainsi que dans les systèmes de réseaux photoniques artificiels. Finalement, nous discutons l'effet Josephson lié aux modèles de Bose–Hubbard dans des géométries en échelle ainsi qu'à deux dimensions, produisant de la cohérence de phase et des courants Meissner. Le modèle de Bose–Hubbard est aussi lié au modèle de Jaynes–Cummings sur réseau. En présence de champs de jauge synthétiques, nous montrons que les courants Meissner subsistent dans une phase de Mott isolante.

Published online:
DOI: 10.1016/j.crhy.2016.05.003
Keywords: Condensed-matter physics with light, Superconducting circuit quantum electrodynamics networks, Josephson effect and nanoscience, Dissipative and driven quantum impurity models, Jaynes–Cummings and Rabi lattices, Topological phases and synthetic gauge fields
Mot clés : Physique de la matière condensée avec la lumière, Réseaux électodynamiques quantiques à circuit supraconducteur, Effet Josephson et nanoscience, Modèles d'impuretés quantiques et contrôlés, Réseaux de Jaynes-Cummings et de Rabi, Phases topologiques et champs de jauge

Karyn Le Hur 1; Loïc Henriet 1; Alexandru Petrescu 1, 2; Kirill Plekhanov 1; Guillaume Roux 3; Marco Schiró 4

1 Centre de physique théorique, École polytechnique, CNRS, 91128 Palaiseau cedex, France
2 Department of Physics, Yale University, New Haven, CT 06520, USA
3 LPTMS, Université Paris-Sud and CNRS, UMR 8626, 91405 Orsay, France
4 Institut de physique théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
@article{CRPHYS_2016__17_8_808_0,
     author = {Karyn Le Hur and Lo{\"\i}c Henriet and Alexandru Petrescu and Kirill Plekhanov and Guillaume Roux and Marco Schir\'o},
     title = {Many-body quantum electrodynamics networks: {Non-equilibrium} condensed matter physics with light},
     journal = {Comptes Rendus. Physique},
     pages = {808--835},
     publisher = {Elsevier},
     volume = {17},
     number = {8},
     year = {2016},
     doi = {10.1016/j.crhy.2016.05.003},
     language = {en},
}
TY  - JOUR
AU  - Karyn Le Hur
AU  - Loïc Henriet
AU  - Alexandru Petrescu
AU  - Kirill Plekhanov
AU  - Guillaume Roux
AU  - Marco Schiró
TI  - Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light
JO  - Comptes Rendus. Physique
PY  - 2016
SP  - 808
EP  - 835
VL  - 17
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crhy.2016.05.003
LA  - en
ID  - CRPHYS_2016__17_8_808_0
ER  - 
%0 Journal Article
%A Karyn Le Hur
%A Loïc Henriet
%A Alexandru Petrescu
%A Kirill Plekhanov
%A Guillaume Roux
%A Marco Schiró
%T Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light
%J Comptes Rendus. Physique
%D 2016
%P 808-835
%V 17
%N 8
%I Elsevier
%R 10.1016/j.crhy.2016.05.003
%G en
%F CRPHYS_2016__17_8_808_0
Karyn Le Hur; Loïc Henriet; Alexandru Petrescu; Kirill Plekhanov; Guillaume Roux; Marco Schiró. Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light. Comptes Rendus. Physique, Volume 17 (2016) no. 8, pp. 808-835. doi : 10.1016/j.crhy.2016.05.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2016.05.003/

[1] C. Cohen-Tanoudji; J. Dupont-Roc; G. Grynberg Photons and Atoms, Introduction to Quantum Electrodynamics, Wiley, 1997

[2] Gilbert Grynberg, Alain Aspect, Claude Fabre, Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light, revised with help of Fabien Bretenaker and Antoine Browaeys. Foreword by Claude Cohen–Tannoudji. For more information see www.cambridge.org/9780521551120.

[3] J.-M. Raimond; M. Brune; S. Haroche Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys., Volume 73 (2001), p. 565

[4] S. Haroche; J.-M. Raimond Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press, 2006

[5] D. Leibfried; R. Blatt; C. Monroe; D. Wineland Quantum dynamics of single trapped ions, Rev. Mod. Phys., Volume 75 (2003), p. 281

[6] H. Ritsch; P. Domokos; F. Brennecke; T. Esslinger Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys., Volume 85 (2013), pp. 553-601

[7] K. Baumann; R. Mottl; F. Brennecke; T. Esslinger Exploring symmetry breaking at the Dicke quantum phase transition, Phys. Rev. Lett., Volume 107 (2011)

[8] R.J. Schoelkopf; S.M. Girvin Wiring up quantum systems, Nature, Volume 451 (2008), p. 664

[9] M.H. Devoret Quantum Fluctuations (S. Reynaud; E. Giacobino; J. Zinn-Justin, eds.), Elsevier, 1995 (Chap. 10)

[10] Michael J. Hartmann | arXiv

[11] D. Braak Integrability of the Rabi model, Phys. Rev. Lett., Volume 107 (2011)

[12] A.A. Houck; H.E. Türeci; J. Koch On-chip quantum simulation with superconducting circuits, Nat. Phys., Volume 8 (2012), pp. 292-299

[13] A. Tomadin; R. Fazio Many-body phenomena in QED-cavity arrays, J. Opt. Soc. Am., Volume 27 (2010)

[14] D.L. Underwood; W.E. Shanks; J. Koch; A.A. Houck Low-disorder microwave cavity lattices for quantum simulation with photons, Phys. Rev. A, Volume 86 (2012)

[15] Y. Salathé et al. Digital quantum simulation of spin models with circuit quantum electrodynamics, Phys. Rev. X, Volume 5 (2015)

[16] R. Barends et al. Digital quantum simulation of fermionic models with a superconducting circuit, Nat. Commun., Volume 6 (2015), p. 7654

[17] Y. Chen et al. Simulating weak localization using superconducting quantum circuits, Nat. Commun., Volume 5 (2014), p. 5184

[18] S.J. Weber; A. Chantasri; J. Dressel; A.N. Jordan; K.W. Murch; I. Siddiqi Mapping the optimal route between two quantum states, Nature, Volume 511 (2014), pp. 570-573

[19] N. Roch et al. Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits, Phys. Rev. Lett., Volume 112 (2014)

[20] I. Bloch; J. Dalibard; W. Zwerger Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008), p. 885

[21] I. Bloch; J. Dalibard; S. Nascimbène Quantum simulations with ultracold quantum gases, Nat. Phys., Volume 8 (2012), pp. 267-276

[22] M. Viteau; P. Huillery; M.G. Bason; N. Malossi; D. Ciampini; O. Morsch; E. Arimondo; D. Comparat; P. Pillet Cooperative excitation and many-body interactions in a cold Rydberg gas, Phys. Rev. Lett., Volume 109 (2012)

[23] H. Labuhn; S. Ravets; D. Barredo; L. Béguin; F. Nogrette; T. Lahaye; A. Browaeys Single-atom addressing in microtraps for quantum-state engineering using Rydberg atoms, Phys. Rev. A, Volume 90 (2014)

[24] V. Parigi; E. Bimbard; J. Stanojevic; A.J. Hilliard; F. Nogrette; R. Tualle-Brouri; A. Ourjoumtsev; P. Grangier Observation and measurement of interaction-induced dispersive optical nonlinearities in an ensemble of cold Rydberg atoms, Phys. Rev. Lett., Volume 109 (2012)

[25] Y. Kubo; C. Grezes; A. Dewes; T. Umeda; J. Isoya; H. Sumiya; N. Morishita; H. Abe; S. Onoda; T. Ohshima; V. Jacques; A. Dréau; J.-F. Roch; I. Diniz; A. Auffeves; D. Vion; D. Esteve; P. Bertet Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble, Phys. Rev. Lett., Volume 107 (2011)

[26] M. Ludwig; F. Marquardt Quantum many-body dynamics in optomechanical arrays, Phys. Rev. Lett., Volume 111 (2013)

[27] M. Schmidt; V. Peano; F. Marquardt Optomechanical Dirac physics, New J. Phys., Volume 17 (2015)

[28] J. Kondo Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys., Volume 32 (1963), p. 37

[29] P.W. Anderson A poor man's derivation of scaling laws for the Kondo problem, J. Phys. C, Solid State Phys., Volume 3 (1970), pp. 2436-2441

[30] Ph. Nozières A Fermi-liquid description of the Kondo model at low temperatures, J. Low Temp. Phys., Volume 17 (1974), p. 31

[31] K. Wilson The renormalization group: critical phenomena and the Kondo problem, Rev. Mod. Phys., Volume 47 (1975) no. 4, pp. 773-840

[32] I. Affleck Conformal field theory approach to the Kondo effect, Acta Phys. Pol. B, Volume 26 (1995), pp. 1869-1932 (For a review:)

[33] A.M. Tsvelick; P. Wiegmann Exact results in the theory of magnetic alloys, Adv. Phys., Volume 32 (1983), p. 453

[34] K. Le Hur Kondo resonance of a microwave photon, Phys. Rev. B, Volume 85 (2012)

[35] M. Goldstein; M.H. Devoret; M. Houzet; L.I. Glazman Inelastic microwave photon scattering off a quantum impurity in a Josephson-junction array, Phys. Rev. Lett., Volume 110 (2013)

[36] A. Leclair; F. Lesage; S. Lukyanov; H. Saleur The Maxwell–Bloch theory in quantum optics and the Kondo model, Phys. Lett. A, Volume 235 (1997), pp. 203-208

[37] S. Camalet; J. Schriefl; P. Degiovanni; F. Delduc Quantum impurity approach to a coupled qubit problem, Europhys. Lett., Volume 68 (2004), p. 37

[38] L. Henriet; Z. Ristivojevic; P.P. Orth; K. Le Hur Quantum dynamics of the driven and dissipative Rabi model, Phys. Rev. A, Volume 90 (2014)

[39] P.P. Orth; A. Imambekov; K. Le Hur Universality in dissipative Landau-Zener transitions, Phys. Rev. A, Volume 82 (2010)

[40] P.P. Orth; A. Imambekov; K. Le Hur Non-perturbative stochastic method for driven spin–boson model, Phys. Rev. B, Volume 87 (2013)

[41] G.B. Lesovik; A.O. Lebedev; A.O. Imambekov Dynamics of two-level system interacting with random classical field, JETP Lett., Volume 75 (2002), p. 474

[42] A.O. Imambekov; V. Gritsev; E. Demler Varenna, 2006 (2008)

[43] A.D. Greentree; C. Tahan; J.H. Cole; L.C.L. Hollenberg Simulating quantum fields with cavity QED, Nat. Phys., Volume 2 (2006), p. 856

[44] D.G. Angelakis; M.F. Santos; S. Bose Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays, Phys. Rev. A, Volume 76 (2007)

[45] J. Cho; D.G. Angelakis; S. Bose Simulation of high-spin Heisenberg models in coupled cavities, Phys. Rev. A, Volume 78 (2008)

[46] M.J. Hartmann; F.G.S.L. Brandao; M.B. Plenio Quantum many-body phenomena in coupled cavity arrays, Nat. Phys., Volume 2 (2006), p. 849

[47] J. Koch; K. Le Hur Superfluid–Mott insulator transition of light in the Jaynes–Cummings lattice, Phys. Rev. A, Volume 80 (2009)

[48] S. Schmidt; G. Blatter Strong coupling theory for the Jaynes–Cummings–Hubbard model, Phys. Rev. Lett., Volume 103 (2009)

[49] S. Schmidt; G. Blatter Excitations of strongly correlated polaritons, Phys. Rev. Lett., Volume 104 (2010)

[50] M. Schiró; M. Bordyuh; B. Öztop; H.E. Türeci Phase transition of light in cavity QED lattices, Phys. Rev. Lett., Volume 109 (2012)

[51] M. Schiró; C. Joshi; M. Bordyuh; R. Fazio; J. Keeling; H.E. Türeci Exotic attractors of the non-equilibrium Rabi–Hubbard model | arXiv

[52] M. Hafezi; P. Adhikari; J.M. Taylor A chemical potential for light, Phys. Rev. B, Volume 92 (2015)

[53] K. Le Hur Quantum phase transitions in spin–boson systems: dissipation and light phenomena (Lincoln D. Carr, ed.), Understanding Quantum Phase Transitions, Taylor and Francis, Boca Raton, 2010 (see also) | arXiv

[54] A.J. Leggett; S. Chakravarty; A.T. Dorsey; M.P.A. Fisher; A. Garg; W. Zwerger Dynamics of the dissipative two-state system, Rev. Mod. Phys., Volume 59 (1987), p. 1

[55] U. Weiss Quantum Dissipative Systems, World Scientific, Singapore, 2008

[56] A. Moroz On solvability and integrability of the Rabi model, Ann. Phys., Volume 338 (2013), pp. 319-340

[57] H. Zhong; Q. Xie; M. Batchelor; C. Lee Analytical eigenstates for the quantum Rabi model, J. Phys. A, Math. Theor., Volume 46 (2013), p. 415302

[58] M. Tomka; O. El Araby; M. Pletyukhov; V. Gritsev Exceptional and regular spectra of a generalized Rabi model, Phys. Rev. A, Volume 90 (2014)

[59] J. Larson Dynamics of the Jaynes–Cummings and Rabi models: old wine in new bottles, Phys. Scr., Volume 76 (2007), p. 146

[60] P. Nataf; C. Ciuti Vacuum degeneracy of a circuit QED system in the ultrastrong coupling regime, Phys. Rev. Lett., Volume 104 (2010)

[61] Simone de Liberato Light-matter decoupling in the deep strong coupling regime: the breakdown of the Purcell effect, Phys. Rev. Lett., Volume 112 (2014)

[62] F.A. Wold; F. Vallone; G. Romero; M. Kollar; E. Solano; D. Braak Dynamical correlation functions and the quantum Rabi model, Phys. Rev. A, Volume 87 (2013)

[63] J. Koch; A.A. Houck; K. Le Hur; S.M. Girvin Time-reversal symmetry breaking in circuit-QED based photon lattices, Phys. Rev. A, Volume 82 (2010)

[64] A. Nunnenkamp; J. Koch; S.M. Girvin Synthetic gauge fields and homodyne transmission in Jaynes–Cummings lattices, New J. Phys., Volume 13 (2011)

[65] J. Kerckhoff; K. Lalumière; B.J. Chapman; A. Blais; K.W. Lehnert On-chip superconducting microwave circulator from synthetic rotation | arXiv

[66] A. Petrescu; A.A. Houck; K. Le Hur Anomalous hall effects of light and chiral edge modes on the Kagome lattice, Phys. Rev. A, Volume 86 (2012)

[67] A. Kamal; J. Clarke; M. Devoret Noiseless nonreciprocity in a parametric active device, Nat. Phys., Volume 7 (2011), pp. 311-315

[68] K. von Klitzing; G. Dorda; M. Pepper New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance, Phys. Rev. Lett., Volume 45 (1980), p. 494

[69] R.B. Laughlin Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett., Volume 50 (1983), p. 1395

[70] D.C. Tsui; H.L. Stormer; A.C. Gossard Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett., Volume 48 (1982), p. 1559

[71] M.Z. Hasan; C.L. Kane Topological insulators, Rev. Mod. Phys., Volume 82 (2010), p. 3045

[72] B.A. Bernevig; T.L. Hughes Topological Insulators and Topological Superconductors, Princeton University Press, 2013

[73] Xiao-Liang Qi; Shou-Cheng Zhang Topological insulators and superconductors, Rev. Mod. Phys., Volume 83 (2011), p. 1057

[74] Z. Wang; Y. Chong; J.D. Joannopoulos; M. Soljacic Observation of unidirectional backscattering-immune topological electromagnetic states, Nature, Volume 461 (2009), pp. 772-775

[75] M.C. Rechtsman; J.M. Zeuner; Y. Plotnik; Y. Lumer; D. Podolsky; F. Dreisow; S. Nolte; M. Segev; A. Szameit Photonic Floquet topological insulators, Nature, Volume 496 (2013), pp. 196-200

[76] M. Hafezi; J. Fan; A. Migdall; J. Taylor Observation of photonic edge states in a versatile silicon platform, Nat. Photonics, Volume 7 (2013), p. 1001

[77] M. Hafezi; E. Demler; M. Lukin; J. Taylor Robust optical delay lines via topological protection, Nat. Phys., Volume 7 (2011), pp. 907-912

[78] V.G. Sala; D.D. Solnyshkov; I. Carusotto; T. Jacqmin; A. Lemaître; H. Terças; A. Nalitov; M. Abbarchi; E. Galopin; I. Sagnes; J. Bloch; G. Malpuech; A. Amo Engineering spin–orbit coupling for photons and polaritons in microstructures, Phys. Rev. X, Volume 5 (2015)

[79] N. Goldman; J. Dalibard Periodically-driven quantum systems: effective Hamiltonians and engineered gauge fields, Phys. Rev. X, Volume 4 (2014)

[80] J. Cayssol; B. Dóra; F. Simon; R. Moessner Floquet topological insulators, Phys. Status Solidi RRL, Volume 7 (2013), pp. 101-108

[81] L. Lu; J.D. Joannopoulos; M. Soljacic Topological photonics, Nat. Photonics, Volume 8 (2014), pp. 821-829

[82] I. Carusotto; C. Ciuti Quantum fluids of light, Rev. Mod. Phys., Volume 85 (2013), p. 299

[83] J. Dalibard; F. Gerbier; G. Juzeliūnas Patrik Öhberg, Artificial gauge potentials for neutral atoms, Rev. Mod. Phys., Volume 83 (2011), p. 1523

[84] N. Goldman; G. Juzeliunas; P. Ohberg; I.B. Spielman Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys., Volume 77 (2014), p. 126401

[85] Philipp Hauke; Olivier Tieleman; Alessio Celi; Christoph Ölschläger; Juliette Simonet; Julian Struck; Malte Weinberg; Patrick Windpassinger; Klaus Sengstock; Maciej Lewenstein; André Eckardt Non-Abelian gauge fields and topological insulators in shaken optical lattices, Phys. Rev. Lett., Volume 109 (2012)

[86] M. Aidelsburger; M. Atala; M. Lohse; J.T. Barreiro; B. Paredes; I. Bloch Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett., Volume 111 (2013)

[87] H. Miyake; G.A. Siviloglou; C.J. Kennedy; W.C. Burton; W. Ketterle Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett., Volume 111 (2013)

[88] D. Jaksch; P. Zoller Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms, New J. Phys., Volume 5 (2003), p. 56

[89] F.D.M. Haldane; S. Raghu Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett., Volume 100 (2008)

[90] B.I. Halperin Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B, Volume 25 (1982), p. 2185

[91] Chetan Nayak; Steven H. Simon; Ady Stern; Michael Freedman; Sankar Das Sarma Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys., Volume 80 (2008), p. 1083

[92] D.J. Thouless; M. Kohmoto; M.P. Nightingale; M. den Nijs Quantized hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett., Volume 49 (1982), pp. 405-408

[93] T. Ozawa; I. Carusotto Phys. Rev. Lett., 112 (2014)

[94] M. Hafezi Measuring topological invariants in photonic systems, Phys. Rev. Lett., Volume 112 (2014)

[95] H.M. Price; N.R. Cooper Mapping the berry curvature from semiclassical dynamics in optical lattices, Phys. Rev. A, Volume 85 (2012)

[96] R. Karplus; J.M. Luttinger Hall effect in ferromagnetics, Phys. Rev., Volume 95 (1954), p. 1154

[97] Marco Cominotti; Iacopo Carusotto Berry curvature effects in the Bloch oscillations of a quantum particle under a strong (synthetic) magnetic field, Europhys. Lett., Volume 103 (2013), p. 10001

[98] S.A. Skirlo; L. Lu; Y. Igarashi; J. Joannopoulos; M. Soljacic Experimental observation of large Chern numbers in photonic crystals | arXiv

[99] M.V. Berry Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., Volume 392 (1984) no. 1802, pp. 45-57

[100] S.S. Chern Characteristic classes of Hermitian manifolds, Ann. Math., Volume 47 (1948), p. 1

[101] P.J. Leek; J.M. Fink; A. Blais; R. Bianchetti; M. Göppl; J.M. Gambetta; D.I. Schuster; L. Frunzio; R.J. Schoelkopf; A. Wallraff Observation of Berry's phase in a solid state qubit, Science, Volume 318 (2007), p. 1889

[102] P. Roushan et al. Observation of topological transitions in interacting quantum circuits, Nature, Volume 515 (2014), pp. 241-244

[103] M.D. Schroer; M.H. Kolodrubetz; W.F. Kindel; M. Sandberg; J. Gao; M.R. Vissers; D.P. Pappas; Anatoli Polkovnikov; K.W. Lehnert Measuring a topological transition in an artificial spin 1/2 system, Phys. Rev. Lett., Volume 113 (2014)

[104] V. Gritsev; A. Polkovnikov Dynamical quantum Hall effect in the parameter space, Proc. Natl. Acad. Sci. USA, Volume 109 (2012), p. 6457

[105] M. Bellec; U. Kuhl; G. Montambaux; Fabrice Mortessagne Tight-binding couplings in microwave artificial graphene, Phys. Rev. B, Volume 88 (2013)

[106] L. Lu; Z. Wang; D. Ye; L. Ran; L. Fu; J.D. Joannopoulos; M. Soljaçic Experimental observation of Weyl points, Science, Volume 349 (2015) no. 6248, pp. 622-624

[107] Th. Jacqmin; I. Carusotto; I. Sagnes; M. Abbarchi; D. Solnyshkov; G. Malpuech; E. Galopin; A. Lemaître; J. Bloch; A. Amo Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons, Phys. Rev. Lett., Volume 112 (2014)

[108] P. Vignolo; M. Bellec; J. Boehm; A. Camara; J.-M. Gambaudo; U. Kuhl; F. Mortessagne Energy landscape in two-dimensional Penrose-tiled quasicrystal | arXiv

[109] M. Biondi; E.P.L. van Nieuwenburg; G. Blatter; S.D. Huber; S. Schmidt Incompressible polaritons in a flat band | arXiv

[110] Feng Mei; Jia-Bin You Wei Nie; R. Fazio; Shi-Liang Zhu; L.C. Kwek Simulation and detection of photonic Chern insulators in one-dimensional circuit quantum electrodynamics lattice | arXiv

[111] D. Tanese; E. Gurevich; F. Baboux; T. Jacqmin; A. Lemaître; E. Galopin; I. Sagnes; A. Amo; J. Bloch; E. Akkermans Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential, Phys. Rev. Lett., Volume 112 (2014)

[112] M. Schiró; K. Le Hur Tunable hybrid quantum electrodynamics from non-linear electron transport, Phys. Rev. B, Volume 89 (2014)

[113] A. Dousse; L. Lanco; J. Suffczynski; E. Semenova; A. Miard; A. Lemaître; I. Sagnes; C. Roblin; J. Bloch; P. Senellart Controlled light–matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography, Phys. Rev. Lett., Volume 101 (2008)

[114] T. Frey; P.J. Leek; M. Beck; J. Faist; A. Wallraff; K. Ensslin; T. Ihn; M. Büttiker Quantum dot admittance probed at microwave frequencies with an on-chip resonator, Phys. Rev. B, Volume 86 (2012)

[115] M.R. Delbecq; V. Schmitt; F.D. Parmentier; N. Roch; J.J. Viennot; G. Fève; B. Huard; C. Mora; A. Cottet; T. Kontos Coupling a quantum dot, fermionic leads and a microwave cavity on-chip, Phys. Rev. Lett., Volume 107 (2011)

[116] K.D. Petersson; L.W. McFaul; M.D. Schroer; M. Jung; J.M. Taylor; A.A. Houck; J.R. Petta Circuit quantum electrodynamics with a spin qubit, Nature, Volume 490 (2012), p. 380

[117] Z.-R. Lin; G.-P. Guo; T. Tu; F.-Y. Zhu; G.-C. Guo Generation of quantum-dot cluster states with a superconducting transmission line resonator, Phys. Rev. Lett., Volume 101 (2008)

[118] C.M. Wilson; G. Johansson; A. Pourkabirian; M. Simoen; J.R. Johansson; T. Duty; F. Nori; P. Delsing Observation of the dynamical Casimir effect in a superconducting circuit, Nature, Volume 479 (2011), pp. 376-379

[119] J.E. Mooij; T.P. Orlando; L. Levitov; L. Tian; C.H. Van der Wal; S. Lloyd Josephson persistent-current qubit, Science, Volume 285 (1999), pp. 1036-1039

[120] J.M. Martinis; S. Nam; J. Aumentado; C. Urbina Rabi oscillations in a large Josephson-junction qubit, Phys. Rev. Lett., Volume 89 (2002)

[121] D. Vion; A. Aassime; A. Cottet; P. Joyez; H. Pothier; C. Urbina; D. Esteve; M.H. Devoret Manipulating the quantum state of an electrical circuit, Science, Volume 296 (2002), p. 886

[122] J. Koch; T.M. Yu; J. Gambetta; A.A. Houck; D.I. Schuster; J. Majer; A. Blais; M.H. Devoret; S.M. Girvin; R.J. Schoelkopf Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A, Volume 76 (2007)

[123] H. Paik et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture, Phys. Rev. Lett., Volume 107 (2011)

[124] V.E. Manucharyan; J. Koch; L. Glazman; M. Devoret Fluxonium: single Cooper-pair circuit free of charge offsets, Science, Volume 326 (2009), pp. 113-116

[125] Y. Chen et al. Qubit architecture with high coherence and fast tunable coupling, Phys. Rev. Lett., Volume 113 (2014)

[126] S. Schmidt; J. Koch Circuit QED lattices: towards quantum simulation with superconducting circuits, Ann. Phys., Volume 525 (2013), pp. 395-412

[127] A. Blais; R.-S. Huang; A. Wallraff; S.M. Girvin; R.J. Schoelkopf Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation, Phys. Rev. A, Volume 69 (2004)

[128] A. Wallraff; D.I. Schuster; A. Blais; L. Frunzio; R.-S. Huang; J. Majer; S. Kumar; S.M. Girvin; R.J. Schoelkopf Circuit quantum electrodynamics: coherent coupling of a single photon to a Cooper pair box, Nature, Volume 431 (2004), pp. 162-167

[129] A.A. Clerk; M.H. Devoret; S.M. Girvin; F. Marquardt; R.J. Schoelkopf Introduction to quantum noise, measurement and amplification, Rev. Mod. Phys., Volume 82 (2010), p. 1155

[130] J. Casanova; G. Romero; I. Lizuain; J.J. Garcia-Ripoll; E. Solano Deep strong coupling regime of the Jaynes–Cummings model, Phys. Rev. Lett., Volume 105 (2010)

[131] I.I. Rabi; I.I. Rabi Space quantization in a gyrating magnetic field, Phys. Rev., Volume 49 (1936), p. 324

[132] V. Bouchiat; D. Vion; Ph. Joyez; D. Esteve; M.H. Devoret Quantum coherence with a single Cooper pair, Phys. Scr. T, Volume 76 (1998), pp. 165-170

[133] Y. Nakamura; Yu.A. Pashkin; J.S. Tsai Coherent control of macroscopic quantum states in a single-Cooper-pair box, Nature, Volume 398 (1999), pp. 786-788

[134] G. Ithier; E. Collin; P. Joyez; P.J. Meeson; D. Vion; D. Esteve; F. Chiarello; A. Shnirman; Y. Makhlin; J. Schriefl; G. Schön Decoherence in a superconducting quantum bit circuit, Phys. Rev. B, Volume 72 (2005)

[135] O. Buisson; F.W.J. Hekking Entangled states in a Josephson charge qubit coupled to a superconducting resonator, Naples, Italy ( June 2000 )

[136] P. Forn-Diaz; J. Lisenfeld; D. Marcos; J.J. Garcia-Ripoll; E. Solano; C.J.P.M. Harmans; J.E. Mooij Observation of the Bloch–Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime, Phys. Rev. Lett., Volume 105 (2010)

[137] T. Niemczyk; F. Deppe; F. Deppe; H. Huebl; E.P. Menzel; F. Hocke; M.J. Schwarz; J.J. Garcia-Ripoll; D. Zueco; T. Hümmer; E. Solano; A. Marx; R. Gross Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys., Volume 6 (2010), pp. 772-776

[138] O. Babelon; L. Cantini; B. Douçot A semiclassical study of the Jaynes–Cummings model, J. Stat. Mech. (2009)

[139] O. Babelon; B. Douçot Classical Bethe ansatz and normal forms in the Jaynes–Cummings model | arXiv

[140] H. Tschirhart; A. Faribault Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke–Jaynes–Cummings–Gaudin quantum integrable models, J. Phys. A, Math. Theor., Volume 47 (2014), p. 405204

[141] S. Schweber On the application of Bargmann Hilbert spaces to dynamical problems, Ann. Phys. (N.Y.), Volume 41 (1967), p. 205

[142] E.K. Irish; J. Gea-Banacloche; I. Martin; K.C. Schwab Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator, Phys. Rev. B, Volume 72 (2005)

[143] R.H. Dicke Coherence in spontaneous radiation processes, Phys. Rev., Volume 93 (1954), pp. 99-110

[144] K. Hepp; E.H. Lieb On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model, Ann. Phys., Volume 76 (1973), pp. 360-404

[145] Philipp Strack; Subir Sachdev Dicke quantum spin glass of atoms and photons, Phys. Rev. Lett., Volume 107 (2011)

[146] P. Nataf; C. Ciuti Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED?, Nat. Commun., Volume 1 (2010), p. 72

[147] O. Viehmann; J. von Delft; F. Marquardt Superradiant phase transitions and the standard description of circuit QED, Phys. Rev. Lett., Volume 107 (2011)

[148] P. Nataf; M. Dogan; K. Le Hur Heisenberg uncertainty principle as a probe of entanglement entropy: application to superradiant quantum phase transitions, Phys. Rev. A, Volume 86 (2012)

[149] S. Dusuel; J. Vidal Finite-size scaling exponents of the Lipkin–Meshkov–Glick model, Phys. Rev. Lett., Volume 93 (2004)

[150] H. Francis Song; Stephan Rachel; Christian Flindt; Israel Klich; Nicolas Laflorencie; Karyn Le Hur Bipartite fluctuations as a probe of many-body entanglement, Phys. Rev. B, Volume 85 (2012) (Editors' Suggestion)

[151] Israel Klich; Leonid Levitov Quantum noise as an entanglement meter, Phys. Rev. Lett., Volume 102 (2009)

[152] E.T. Jaynes; F.W. Cummings Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE, Volume 51 (1963), p. 89

[153] A. Imamoglu; H. Schmidt; G. Woods; M. Deutsch Strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett., Volume 79 (1998), p. 1467

[154] A. Verger; C. Ciuti; I. Carusotto Polariton quantum blockade in a photonic dot, Phys. Rev. B, Volume 73 (2006)

[155] M. Boissonneault; J. Gambetta; A. Blais Dispersive regime of CQED: photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A, Volume 79 (2009)

[156] K.M. Birnbaum et al. Photon blockade in an optical cavity with one trapped atom, Nature, Volume 436 (2005), p. 87

[157] L.S. Bishop et al. Nonlinear response of the vacuum Rabi resonance, Nat. Phys., Volume 5 (2008), pp. 105-109

[158] J.M. Fink et al. Climbing the Jaynes–Cummings ladder and observing its n nonlinearity in a cavity QED system, Nature, Volume 454 (2008), pp. 315-318

[159] M. Hofheinz et al. Generation of Fock states in a superconducting quantum circuit, Nature, Volume 454 (2008), pp. 310-314

[160] A.J. Hoffman; S.J. Srinivasan; S. Schmidt; L. Spietz; J. Aumentado; H.E. Türeci; A.A. Houck Dispersive photon blockade in a superconducting circuit, Phys. Rev. Lett., Volume 107 (2011)

[161] C. Cohen-Tannoudji; J. Dupont-Roc; C. Fabre A quantum calculation of the higher order terms in the Bloch–Siegert shift, J. Phys. B, At. Mol. Phys., Volume 6 ( August 1973 )

[162] M. Hofheinz et al. Synthesizing arbitrary quantum states in a superconducting resonator, Nature, Volume 459 ( 28 May 2009 ), pp. 546-549

[163] C.W. Gardiner; M.J. Collett Input and ouptut in damped quantum systems: quantum stochastic differential equations and the master equation, Phys. Rev. A, Volume 31 (1985), p. 3761

[164] R.P. Feynman; F.L. Vernon The theory of a general quantum system interacting with a linear dissipative system, Ann. Phys. (N.Y.), Volume 24 (1963), p. 118

[165] A.O. Caldeira; A.J. Leggett Path integral approach to quantum Brownian motion, Physica, Volume 121A (1983), p. 587

[166] G. Lindblad On the generators of quantum dynamical semigroups, Commun. Math. Phys., Volume 48 (1976), p. 119

[167] F. Bloch Generalized theory of relaxation, Phys. Rev., Volume 105 (1957), p. 1206

[168] A.G. Redfield On the theory of relaxation processes, IBM J. Res. Dev., Volume 1 (1957), p. 19

[169] M. Blume; V.J. Emery; A. Luther Spin–boson systems: one-dimensional equivalents and the Kondo problem, Phys. Rev. Lett., Volume 25 (1970), p. 450

[170] K. Le Hur Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system, Ann. Phys. (N.Y.), Volume 323 (2008), p. 2208

[171] M. Vojta Impurity quantum phase transitions, Philos. Mag., Volume 86 (2006), p. 1807

[172] R. Dümcke; H. Spohn Quantum tunneling with dissipation and the Ising model over R, J. Stat. Phys., Volume 41 (1985), p. 389

[173] P.W. Anderson; G. Yuval; D.R. Hamann Exact results in the Kondo problem. II. Scaling theory, qualitatively correct solution, and some new results on one-dimensional classical statistical models, Phys. Rev. B, Volume 1 (1970), p. 4464

[174] S. Chakravarty Quantum fluctuations in the tunneling between superconductors, Phys. Rev. Lett., Volume 49 (1982), p. 681

[175] A.J. Bray; M.A. Moore Influence of dissipation on quantum coherence, Phys. Rev. Lett., Volume 49 (1982), p. 681

[176] S. Jezouin; M. Albert; F.D. Parmentier; A. Anthore; U. Gennser; A. Cavanna; I. Safi; F. Pierre Tomonaga–Luttinger physics in electronic quantum circuits, Nat. Commun., Volume 4 (2013), p. 1802

[177] H.T. Mebrahtu; I.V. Borzenets; D.E. Liu; H. Zheng; Y.V. Bomze; A.I. Smirnov; H.U. Baranger; G. Finkelstein Quantum phase transition in a resonant level coupled to interacting leads, Nature, Volume 488 (2012), p. 61

[178] K. Le Hur; K. Le Hur; M.-R. Li; M.-R. Li; K. Le Hur; W. Hofstetter Hidden Caldeira–Leggett dissipation in a Bose–Fermi Kondo model, Phys. Rev. Lett., Volume 92 (2004)

[179] I. Safi; H. Saleur A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics, Phys. Rev. Lett., Volume 93 (2004) (See also)

[180] L. Borda; G. Zarand; P. Simon Dissipation-induced quantum phase transition in a quantum box, Phys. Rev. B, Volume 72 (2005)

[181] P. Cedraschi; M. Büttiker Quantum coherence of the ground state of a mesoscopic ring, Ann. Phys. (N.Y.), Volume 289 (2001), pp. 1-23

[182] A. Furusaki; K. Matveev Occupation of a resonant level coupled to a chiral Luttinger liquid, Phys. Rev. Lett., Volume 88 (2002)

[183] G. Toulouse Expression exacte de l'énergie de l'état de base de l'hamiltonien de Kondo pour une valeur particulière de Jz, C. R. Acad. Sci. Paris, Volume 268 (1969), p. 1200

[184] F. Guinea; V. Hakim; A. Muramatsu Bosonization of a two-level system with dissipation, Phys. Rev. B, Volume 32 (1985), p. 4410

[185] I. Affleck; A.A. Ludwig; B.A. Jones Conformal-field-theory approach to the two-impurity Kondo problem: comparison with numerical renormalization-group results, Phys. Rev. B, Volume 52 (1995), p. 9528

[186] M. Garst; S. Kehrein; T. Pruschke; A. Rosch; M. Vojta Quantum phase transition of Ising-coupled Kondo impurities, Phys. Rev. B, Volume 69 (2004)

[187] P.P. Orth; D. Roosen; W. Hofstetter; K. Le Hur Dynamics, synchronization and quantum phase transitions of two dissipative spins, Phys. Rev. B, Volume 82 (2010)

[188] J. Raftery; D. Sadri; S. Schmidt; H.E. Türeci; A.A. Houck Observation of a dissipation-induced classical to quantum transition, Phys. Rev. X, Volume 4 (2014)

[189] Karyn Le Hur; Bernard Coqblin The underscreened Kondo effect: a two S=1 impurity model, Phys. Rev. B, Volume 56 (1997), p. 668

[190] Karyn Le Hur The underscreened Kondo effect in ladder systems, Phys. Rev. Lett., Volume 83 (1999), p. 848

[191] C.-H. Chung; K. Le Hur; M. Vojta; P. Wölfle Non-equilibrium transport at a dissipative quantum phase transition, Phys. Rev. Lett., Volume 102 (2009)

[192] H. Carmichael An Open System Approach to Quantum Optics, Springer, Berlin, 1994

[193] M. Carrega; P. Solinas; A. Braggio; M. Sassetti; U. Weiss Functional integral approach to time-dependent heat exchange in open quantum systems: general method and applications | arXiv

[194] J. Dalibard; I. Castin; K. Molmer Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett., Volume 68 (1992), p. 580

[195] R. Dum; P. Zoller; H. Ritsch Monte Carlo simulation of the atomic master equation for spontaneous emission, Phys. Rev. A, Volume 45 (1992), p. 4879

[196] W.T. Strunz; L. Diosi; N. Gisin Open system dynamics with non-Markovian quantum trajectories, Phys. Rev. Lett., Volume 82 (1999), p. 1801

[197] F.B. Anders; A. Schiller Spin precession and real time dynamics in the Kondo model: a time-dependent numerical renormalization-group study, Phys. Rev. B, Volume 74 (2006)

[198] A.B. Anders; R. Bulla; M. Vojta Equilibrium and non-equilibrium dynamics of the sub-ohmic spin–boson model, Phys. Rev. Lett., Volume 98 (2007)

[199] Soumya Bera; Ahsan Nazir; Alex W. Chin; Harold U. Baranger; Serge Florens A generalized multi-polaron expansion for the spin–boson model: environmental entanglement and the biased two-state system, Phys. Rev. B, Volume 90 (2014)

[200] Z. Cai; U. Schollwoeck; L. Pollet Identifying a bath-induced Bose liquid in interacting spin–boson models, Phys. Rev. Lett., Volume 113 (2014)

[201] E. Sanchez-Burillo; D. Zueco; J.J. Garcia-Ripoll; L. Martin-Moreno Scattering in the ultrastrong regime: nonlinear optics with one photon, Phys. Rev. Lett., Volume 113 (2014)

[202] Igor Lesanovsky; Merlijn van Horssen; Madalin Guta; Juan P. Garrahan Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state, Phys. Rev. Lett., Volume 110 (2013)

[203] Marco Schiró; Michele Fabrizio Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport, Phys. Rev. B, Volume 79 (2009)

[204] Philipp Werner; Takashi Oka; Andrew J. Millis Diagrammatic Monte Carlo simulation of non-equilibrium systems, Phys. Rev. B, Volume 79 (2009)

[205] T.L. Schmidt; P. Werner; L. Muehlbacher; A. Komnik Transient dynamics of the Anderson impurity model out of equilibrium, Phys. Rev. B, Volume 78 (2008)

[206] Rosario E.V. Profumo; Christoph Groth; Laura Messio; Olivier Parcollet; Xavier Waintal Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices | arXiv

[207] M. Bauer; D. Bernard; A. Tilloy The open quantum Brownian motion, J. Stat. Mech. P, Volume 09001 (2014)

[208] D.M. Kennes; O. Kashuba; M. Pletyukhov; H. Schoeller; V. Meden Oscillatory dynamics and non-Markovian memory in dissipative quantum systems, Phys. Rev. Lett., Volume 110 (2013)

[209] Loic Henriet; Karyn Le Hur Many-body stochastic dynamics: quenches in dissipative quantum spin arrays, Phys. Rev. B, Volume 93 (2016)

[210] G. Kulaitis; F. Krüger; F. Nissen; J. Keeling Disordered driven coupled cavity arrays: non-equilibrium stochastic mean-field theory, Phys. Rev. A, Volume 87 (2013)

[211] S. Mandt; D. Sadri; A.A. Houck; H. Türeci Stochastic differential equations for quantum dynamics of spin–boson networks, New J. Phys., Volume 17 (2015) no. 5

[212] C. Xu; A. Poudel; M.G. Vavilov Nonadiabatic dynamics of a dissipative two-level system, Phys. Rev. A, Volume 89 (2014)

[213] Jiasen Jin; Alberto Biella; Oscar Viyuela; Leonardo Mazza; Jonathan Keeling; Rosario Fazio; Davide Rossini Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems | arXiv

[214] J.T. Stockburger; H. Grabert Exact c-number representation of non-Markovian quantum dissipation, Phys. Rev. Lett., Volume 88 (2002)

[215] A. Winter; H. Rieger Quantum phase transition and correlations in the multi-spin–boson model, Phys. Rev. B, Volume 90 (2014)

[216] Peter P. Orth; Ivan Stanic; Karyn Le Hur Dissipative quantum Ising model in a cold atomic spin–boson mixture, Phys. Rev. A, Volume 77 (2008)

[217] B.D. Josephson Possible new effects in superconductive tunnelling, Phys. Lett., Volume 1 (1962), p. 251

[218] V. Ambegaokar; B.I. Halperin Voltage due to thermal noise in the dc Josephson effect, Phys. Rev. Lett., Volume 22 (1969), p. 1364

[219] P.W. Anderson; J.M. Rowell Probable observation of the Josephson tunnel effect, Phys. Rev. Lett., Volume 10 (1963), p. 230

[220] S. Shapiro Josephson currents in superconducting tunneling: the effect of microwaves and other observations, Phys. Rev. Lett., Volume 11 (1963), p. 80

[221] T.A. Fulton et al. Observation of combined Josephson and charging effects in small tunnel junction circuits, Phys. Rev. Lett., Volume 63 (1989), p. 1307

[222] M.R. Andrews; C.G. Townsend; H.J. Miesner; D.S. Durfee; D.M. Kurn; W. Ketterle Observation of interference between two Bose condensates, Science, Volume 275 (1997), p. 637

[223] M. Albiez et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett., Volume 95 (2005)

[224] K. Sukhatme et al. Observation of the ideal Josephson effect in superfluid 4He, Nature, Volume 411 (2001), pp. 280-283

[225] M. Abbarchi et al. Macroscopic quantum self-trapping and Josephson oscillations of exciton–polaritons, Nat. Phys., Volume 9 (2013), p. 275

[226] D. Goldhaber-Gordon; H. Shtrikman; D. Mahalu; D. Abusch-Magder; U. Meirav; M.A. Kastner Nature, 391 (1998), pp. 156-159

[227] L.P. Kouwenhoven; C.M. Marcus Quantum dots, Phys. World, Volume 11 (1998), pp. 35-39

[228] Leo Kouwenhoven; Leonid Glazman Revival of the Kondo effect, Phys. World, Volume 14 (2001), pp. 33-38

[229] A. Recati; P.O. Fedichev; W. Zwerger; J. von Delft; P. Zoller Atomic quantum dots coupled to BEC reservoirs, Phys. Rev. Lett., Volume 94 (2005)

[230] M.-R. Li; K. Le Hur Double-dot charge qubit and transport via dissipative cotunneling, Phys. Rev. Lett., Volume 93 (2004)

[231] J. Koch; K. Le Hur Discontinuous current-phase relations in small 1D Josephson junction arrays, Phys. Rev. Lett., Volume 101 (2008)

[232] H. Zheng; D.J. Gauthier; H. Baranger Waveguide QED: many-body bound state effects on coherent and fock state scattering from a two-level system, Phys. Rev. A, Volume 82 (2010)

[233] Izak Snyman; Serge Florens Josephson–Kondo screening cloud in circuit quantum electrodynamics | arXiv

[234] Johannes Bauer; Christophe Salomon; Eugene Demler Realizing a Kondo-correlated state with ultracold atoms, Phys. Rev. Lett., Volume 111 (2013)

[235] Michael Knap; Dmitry A. Abanin; Eugene Demler Dissipative dynamics of a driven quantum spin coupled to a bath of ultracold fermions, Phys. Rev. Lett., Volume 111 (2013)

[236] C. Altimiras; O. Parlavecchio; Ph. Joyez; D. Vion; P. Roche; D. Esteve; F. Portier Fluctuation–dissipation relations of a tunnel junction driven by a quantum circuit, Appl. Phys. Lett., Volume 103 (2013), p. 212601

[237] Max Haeberlein; Frank Deppe; Andreas Kurcz; Jan Goetz; Alexander Baust; Peter Eder; Kirill Fedorov; Michael Fischer; Edwin P. Menzel; Manuel J. Schwarz; Friedrich Wulschner; Edwar Xie Ling Zhong; Enrique Solano; Achim Marx; Juan-José Garcia-Ripoll; Rudolf Gross Spin–boson model with an engineered reservoir in circuit quantum electrodynamics | arXiv

[238] Y.A. Pashkin; T. Yamamoto; O. Astafiev; Y. Nakamura; D.V. Averin; J.S. Tsai Quantum oscillations in two coupled charge qubits, Nature (London), Volume 421 (2003), p. 823

[239] E. Bibow; P. Lafarge; L. Levy Resonant Cooper pair tunneling through a double-island qubit, Phys. Rev. Lett., Volume 88 (2001)

[240] O. Astafiev; A.M. Zagoskin; A.A. Abdumalikov; Yu.A. Pashkin; T. Yamamoto; K. Inomata; Y. Nakamura; J.-S. Tsai Resonance fluorescence of a single artificial atom, Science, Volume 327 (2010), p. 840

[241] M. Sassetti; U. Weiss Universality in the dissipative two-state system, Phys. Rev. Lett., Volume 65 (1990), p. 2262

[242] H. Shiba The Korringa relation for the impurity nuclear spin-lattice relaxation in dilute Kondo alloys, Prog. Theor. Phys., Volume 54 (1975), p. 967

[243] M. Garst; P. Wolfle; L. Borda; J. von Delft; L. Glazman Energy-resolved inelastic electron scattering off a magnetic impurity, Phys. Rev. B, Volume 72 (2005)

[244] C. Mora; K. Le Hur Universal resistances of the quantum RC circuit, Nat. Phys., Volume 6 (2010), p. 697

[245] M. Filippone; C. Mora Fermi liquid approach to the quantum RC circuit: renormalization-group analysis of the Anderson and Coulomb blockade models, Phys. Rev. B, Volume 86 (2012)

[246] M. Filippone; K. Le Hur; C. Mora Giant charge relaxation resistance in the Anderson model, Phys. Rev. Lett., Volume 107 (2011)

[247] M. Büttiker; A. Prêtre; H. Thomas; M. Büttiker; H. Thomas; A. Prêtre Mesoscopic capacitors, Phys. Lett. A, Volume 70 (1993), p. 4114

[248] S.E. Nigg; R. Lopez; M. Büttiker Mesoscopic charge relaxation, Phys. Rev. Lett., Volume 97 (2006)

[249] J. Gabelli; et al.; G. Fève et al. An on-demand coherent single electron source, Science, Volume 313 (2006), p. 499

[250] J. Gabelli; G. Fève; J.-M. Berroir; B. Plaçais A coherent RC circuit, Rep. Prog. Phys., Volume 75 (2012), p. 126504

[251] Y. Hamamoto; T. Jonckheere; T. Kato; T. Martin Dynamic response of a mesoscopic capacitor in the presence of strong electron interactions, Phys. Rev. B, Volume 81 (2010)

[252] Y. Etzioni; B. Horovitz; P. Le Doussal; Y. Etzioni; B. Horovitz; P. Le Doussal Rings and boxes in dissipative environments, Phys. Rev. B, Volume 106 (2011)

[253] P. Dutt; T.L. Schmidt; C. Mora; K. Le Hur Strongly correlated dynamics in multichannel quantum RC circuits, Phys. Rev. B, Volume 87 (2013)

[254] C. Texier Wigner time delay and related concepts – application to transport in coherent conductors | arXiv

[255] P. Nozières; A. Blandin Kondo effect in real metals, J. Phys., Volume 41 (1980), p. 193

[256] R.M. Potok; I.G. Rau; H. Shtrikman; Y. Oreg; D. Goldhaber-Gordon Observation of the two-channel Kondo effect, Nature, Volume 446 (2007), p. 167

[257] H.T. Mebrahtu et al. Observation of Majorana quantum critical behavior in a resonant level coupled to a dissipative environment, Nat. Phys., Volume 9 (2013), p. 732

[258] A.J. Keller et al. Universal Fermi liquid crossover and quantum criticality in a mesoscopic device, Nature, Volume 526 (2015), pp. 237-240

[259] Z. Iftikhar et al. Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states, Nature, Volume 526 (2015), pp. 233-236

[260] C. Mora; K. Le Hur Probing dynamics of Majorana fermions in quantum impurity systems, Phys. Rev. B, Volume 88 (2013)

[261] P. Dutt; T.L. Schmidt; C. Mora; K. Le Hur Strongly correlated dynamics in multichannel quantum RC circuits, Phys. Rev. B, Volume 88 (2013)

[262] J. Majer et al. Coupling superconducting qubits via a cavity bus, Nature, Volume 449 (2007), pp. 443-447

[263] M.R. Delbecq; L.E. Bruhat; J.J. Viennot; S. Datta; A. Cottet; T. Kontos Photon mediated interaction between distant quantum dot circuits, Nat. Commun., Volume 4 (2013), p. 1400

[264] G.-W. Deng et al. Coupling two distant double quantum dots to a microwave resonator | arXiv

[265] L. DiCarlo et al. Demonstration of two-qubit algorithms with a superconducting quantum processor, Nature, Volume 460 (2009), pp. 240-244

[266] S. Shankar et al. Stabilizing entanglement autonomously between two superconducting qubits, Nature, Volume 504 (2013), pp. 419-422

[267] A. Aspect; P. Grangier; G. Roger; A. Aspect; J. Dalibard; G. Roger Experimental test of Bell's inequalities using time-varying analyzers, Phys. Rev. Lett., Volume 49 (1982) no. 2, pp. 91-94

[268] L.N. Cooper Bound electron pairs in a degenerate Fermi gas, Phys. Rev., Volume 104 (1956), pp. 1189-1190

[269] Christophe Arnold; Justin Demory; Vivien Loo; Aristide Lemaître; Isabelle Sagnes; Mikhaïl Glazov; Olivier Krebs; Paul Voisin; Pascale Senellart; Loïc Lanco Macroscopic polarization rotation induced by a single spin, Nat. Commun. (2015)

[270] J.J. Viennot; M.C. Dartiailh; A. Cottet; T. Kontos Coherent coupling of a single spin to microwave cavity photons, Science, Volume 349 (2015), p. 408

[271] E. Bocquillon; V. Freulon; F.D. Parmentier; J.-M. Berroir; B. Plaçais; C. Wahl; J. Rech; T. Jonckheere; T. Martin; C. Grenier; D. Ferraro; P. Degiovanni; G. Fève Electron quantum optics in ballistic chiral conductors, Ann. Phys., Volume 526 (2014), p. 1

[272] P.W. Anderson Model for the electronic structure of amorphous semiconductors, Phys. Rev. Lett., Volume 34 (1975), p. 953

[273] T. Holstein Ann. Phys., 8 (1959), p. 325 (ISSN: 0003-4916)

[274] A. Mitra; I. Aleiner; A.J. Millis Phonon effects in molecular transistors: quantum and classical treatment, Phys. Rev. B, Volume 69 (2004)

[275] P.S. Cornaglia; H. Ness; D.R. Grempel Many body effects on the transport properties of single-molecule devices, Phys. Rev. Lett., Volume 93 (2004)

[276] Y. Vinkler; A. Schiller; N. Andrei Quantum quenches and driven dynamics in a single-molecule device, Phys. Rev. B, Volume 85 (2012)

[277] G.-W. Deng; L. Henriet; D. Wei; S.-X. Li; H.-O. Li; G. Cao; M. Xiao; G.-C. Guo; M. Schiro; K. Le Hur; G.-P. Guo A quantum electrodynamics Kondo circuit with orbital and spin entanglement | arXiv

[278] A. Cottet; T. Kontos; B. Douçot Electron–photon coupling in mesoscopic quantum electrodynamics, Phys. Rev. B, Volume 91 (2015)

[279] O. Dmytruk; M. Trif; C. Mora; P. Simon Cavity quantum electrodynamics with an out-of-equilibrium quantum dot | arXiv

[280] K. Hennessy; A. Badolato; M. Winger; D. Gerace; M. Atatüre; S. Gulde; S. Fält; E.L. Hu; A. Imamoglu Quantum nature of a strongly coupled single quantum dot-cavity system, Nature, Volume 445 ( 22 February 2007 ), pp. 896-899

[281] I. Kozinsky; H.W.Ch. Postma; O. Kogan; A. Husain; M.L. Roukes Basins of attraction of a nonlinear nanomechanical resonator, Phys. Rev. Lett., Volume 99 (2007)

[282] Christian Bergenfeldt; Peter Samuelsson; Björn Sothmann; Christian Flindt; Markus Büttiker Hybrid microwave-cavity heat engine, Phys. Rev. Lett., Volume 112 (2014)

[283] Björn Sothmann; Rafael Sanchez; Andrew N. Jordan Thermoelectric energy harvesting with quantum dots, Nanotechnology, Volume 26 (2015)

[284] L. Henriet; A.N. Jordan; K. Le Hur Electrical current from quantum vacuum fluctuations in nano-engines, Phys. Rev. B, Volume 92 (2015)

[285] M. Kulkarni; O. Cotlet; H.E. Tureci Cavity-coupled double-quantum dot at finite bias: analogy with lasers and beyond, Phys. Rev. A, Volume 90 (2014)

[286] B. Sbierski; M. Hanl; A. Weichselbaum; H.E. Türeci; M. Goldstein; L.I. Glazman; J. von Delft; A. Imamoglu Proposed Rabi–Kondo correlated state in a laser-driven semiconductor quantum dot, Phys. Rev. Lett., Volume 111 (2013)

[287] F. Mei; V.M. Stojanovic; I. Siddiqi; L. Tian Analog superconducting quantum simulator for Holstein polarons, Phys. Rev. B, Volume 88 (2013)

[288] Jason Alicea; C.W.J. Beenakker New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys., Volume 75 (2012), p. 113 (For recent reviews: See also Search for Majorana fermions in superconductors Annu. Rev. Condens. Matter Phys., 4, 2013)

[289] A. Kitaev Unpaired Majorana fermions in quantum wires, Phys. Usp., Volume 44 (2001), p. 131

[290] N. Read; D. Green Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect, Phys. Rev. B, Volume 61 (2000), p. 10267

[291] T.L. Schmidt; A. Nunnenkamp; C. Bruder Majorana qubit rotations in microwave cavities, Phys. Rev. Lett., Volume 110 (2013)

[292] T.L. Schmidt; A. Nunnenkamp; C. Bruder Microwave-controlled coupling of Majorana bound states, New J. Phys., Volume 15 (2013)

[293] A. Cottet; T. Kontos; B. Douçot Squeezing light with Majorana fermions, Phys. Rev. B, Volume 88 (2013)

[294] M. Trif; Y. Tserkovnyak Resonantly tunable Majorana polariton in a microwave cavity, Phys. Rev. Lett., Volume 109 (2012)

[295] O. Dmytruk; M. Trif; P. Simon Cavity quantum electrodynamics with mesoscopic topological superconductors | arXiv

[296] E. Ginossar; E. Grosfeld; K. Yavilberg; E. Ginossar; E. Grosfeld Fermion parity measurement and control in Majorana circuit quantum electrodynamics, Nat. Commun., Volume 5, 2014, p. 4772 | arXiv

[297] D.M. Badiane; L.I. Glazman; M. Houzet; J.S. Meyer Ac Josephson effect in topological Josephson junctions, C. R. Physique, Volume 14 (2013), p. 840

[298] B. Béri; N.R. Cooper Topological Kondo effect with Majorana fermions, Phys. Rev. Lett., Volume 109 (2012)

[299] A. Altland; B. Beri; R. Egger; A.M. Tsvelik Bethe ansatz solution of the topological Kondo model, J. Phys. A, Volume 47 (2014), p. 265001

[300] Erik Eriksson; Christophe Mora; Alex Zazunov; Reinhold Egger Non-Fermi liquid manifold in a Majorana device, Phys. Rev. Lett., Volume 113 (2014)

[301] A. Altland; B. Beri; R. Egger; A.M. Tsvelik Multi-channel Kondo impurity dynamics in a Majorana device, Phys. Rev. Lett., Volume 113 (2014)

[302] I. Carusotto; D. Gerace; H.E. Tureci; S. De Liberato; C. Ciuti; A. Imamoglu Fermionized photons in an array of driven dissipative nonlinear cavities, Phys. Rev. Lett., Volume 103 (2009)

[303] C.-E. Bardyn; A. Imamoglu Majorana-like modes of light in a one-dimensional array of nonlinear cavities, Phys. Rev. Lett., Volume 109 (2012)

[304] N. Roch; E. Flurin; F. Nguyen; P. Morfin; P. Campagne-Ibarcq; M.H. Devoret; B. Huard Widely tunable, non-degenerate three-wave mixing microwave device operating near the quantum limit, Phys. Rev. Lett., Volume 108 (2012)

[305] E. Flurin; N. Roch; F. Mallet; M.H. Devoret; B. Huard Generating entangled microwave radiation over two transmission lines, Phys. Rev. Lett., Volume 109 (2012)

[306] C. Aron; M. Kulkarni; H. Türeci Steady-state entanglement of spatially separated qubits via quantum bath engineering, Phys. Rev. A, Volume 90 (2014)

[307] A. Tomadin; V. Giovannetti; R. Fazio; D. Gerace; I. Carusotto; H.E. Tureci; A. Imamoglu Signatures of the super fluid–insulator phase transition in laser driven dissipative nonlinear cavity arrays, Phys. Rev. A, Volume 81 (2010)

[308] A. Georges; G. Kotliar; W. Krauth; M. Rozenberg et al. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys., Volume 68 (1996), p. 13

[309] Markus Greiner; Olaf Mandel; Tilman Esslinger; Theodor W. Hänsch; Immanuel Bloch Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, Volume 415 ( 3 January 2002 ), pp. 39-44

[310] M.P.A. Fisher; P.B. Weichman; G. Grinstein; D.S. Fisher Boson localization and the superfluid–insulator transition, Phys. Rev. B, Volume 40 (1989), p. 546

[311] T. Giamarchi; H.J. Schulz Localization and interaction in one-dimensional quantum fluids, Europhys. Lett., Volume 3 (1987), p. 1287

[312] M. Hohenadler; M. Aichhorn; S. Schmidt; L. Pollet Dynamical critical exponent of the Jaynes–Cummings–Hubbard model, Phys. Rev. A, Volume 84 (2011)

[313] D. Rossini; R. Fazio Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities, Phys. Rev. Lett., Volume 99 (2007)

[314] M. Pasek; Y.D. Chong Network models of photonic Floquet topological insulators, Phys. Rev. B, Volume 89 (2014)

[315] C. Aron; M. Kulkarni; H. Tureci Photon-mediated interactions: a scalable tool to create and sustain entangled many-body states | arXiv

[316] A. Baust et al. Ultrastrong coupling in two-resonator circuit QED | arXiv

[317] G.M. Reuther et al. Two-resonator circuit QED: dissipative theory, Phys. Rev. B, Volume 81 (2010)

[318] F. Nissen; S. Schmidt; M. Biondi; G. Blatter; H.E. Türeci; J. Keeling Non-equilibrium dynamics of coupled qubit-cavity arrays, Phys. Rev. Lett., Volume 108 (2012)

[319] A. Le Boité; G. Orso; C. Ciuti Bose–Hubbard model: relation between driven-dissipative steady-states and equilibrium quantum phases | arXiv

[320] S. Finazzi; A. Leboité; F. Storme; A. Baksic; C. Ciuti Corner space renormalization method for driven-dissipative 2D correlated systems | arXiv

[321] Chaitanya Joshi; Felix Nissen; Jonathan Keeling Quantum correlations in the 1-D driven dissipative transverse field XY model, Phys. Rev. A, Volume 88 (2013)

[322] A. Biella; L. Mazza; I. Carusotto; D. Rossini; R. Fazio Photon transport in a dissipative chain of nonlinear cavities | arXiv

[323] P. Nalbach; S. Vishveshwara; A.A. Clerk Quantum Kibble–Zurek physics in the presence of spatially-correlated dissipation, Phys. Rev. B, Volume 92 (2015)

[324] G. Goldstein; C. Aron; C. Chamon Driven-dissipative Ising model: mean field solution, Phys. Rev. B, Volume 92 (2015)

[325] Anders S. Sorensen; Eugene Demler; Mikhail D. Lukin Fractional quantum hall states of atoms in optical lattices, Phys. Rev. Lett., Volume 94 (2005)

[326] M. Hafezi; A.S. Sorensen; E. Demler; M.D. Lukin Fractional quantum Hall effect in optical lattices, Phys. Rev. A, Volume 76 (2007)

[327] L. Hormozi; G. Möller; S.H. Simon Fractional quantum Hall effect of lattice bosons near commensurate flux, Phys. Rev. Lett., Volume 108 (2012)

[328] R.N. Palmer; D. Jaksch High-field fractional quantum Hall effect in optical lattices, Phys. Rev. Lett., Volume 96 (2003)

[329] Nigel R. Cooper; Jean Dalibard Reaching fractional quantum Hall states with optical flux lattices, Phys. Rev. Lett., Volume 110 (2013)

[330] N.Y. Yao; A.V. Gorshkov; C.R. Laumann; A.M. Laüchli; J. Ye; M.D. Lukin Realizing fractional Chern insulators in dipolar spin systems, Phys. Rev. Lett., Volume 110 (2013)

[331] A. Sterdyniak; B.A. Bernevig; N.R. Cooper; N. Regnault Interacting bosons in topological optical flux lattices, Phys. Rev. B, Volume 91 (2015)

[332] J. Cho; D.G. Angelakis; S. Bose Fractional quantum Hall state in coupled cavities, Phys. Rev. Lett., Volume 101 (2008)

[333] A.L.C. Hayward; A.M. Martin; A.D. Greentree Fractional quantum Hall physics in Jaynes–Cummings–Hubbard lattices, Phys. Rev. Lett., Volume 108 (2012)

[334] R.O. Umucalilar; I. Carusotto Fractional quantum Hall states of photons in an array of dissipative coupled cavities, Phys. Rev. Lett., Volume 108 (2012)

[335] M. Hafezi; M.D. Lukin; J.M. Taylor Non-equilibrium fractional quantum Hall state of light, New J. Phys., Volume 15 (2013)

[336] David Carpentier; Pierre Delplace; Michel Fruchart; Krzysztof Gawedzki; Clément Tauber Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals, Nucl. Phys. B, Volume 896 (2015), pp. 779-834

[337] Mark S. Rudner; Netanel H. Lindner; Erez Berg; Michael Levin Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems, Phys. Rev. X, Volume 3 (2013)

[338] Ningyuan Jia; Clai Owens; Ariel Sommer; David Schuster; Jonathan Simon Time reversal invariant topologically insulating circuits, Phys. Rev. X, Volume 5 (2015)

[339] A.B. Khanikaev; S.H. Mousavi; W.-K. Tse; M. Kargarian; A.H. MacDonald; G. Shvets Photonic analogue of two-dimensional topological insulators and helical one-way edge transport in bi-anisotropic metamaterials, Nat. Mater., Volume 12 (2013), p. 233

[340] V.V. Albert; L.I. Glazman; L. Jiang Topological properties of linear circuit lattices, Phys. Rev. Lett., Volume 114 (2015)

[341] Y. Plotnik et al. Observation of unconventional edge states in photonic graphene, Nat. Mater., Volume 13 (2014), p. 57

[342] Mikael C. Rechtsman; Yonatan Plotnik; Julia M. Zeuner; Daohong Song; Zhigang Chen; Alexander Szameit; Mordechai Segev Topological creation and destruction of edge states in photonic graphene, Phys. Rev. Lett., Volume 111 (2013)

[343] M. Milicevic; T. Ozawa; P. Andreakou; I. Carusotto; T. Jacqmin; E. Galopin; A. Lemaître; L. Le Gratiet; I. Sagnes; J. Bloch Edge states in polariton honeycomb lattices, 2D Materials, Volume 2 (2015)

[344] Eliot Kapit; Mohammad Hafezi; Steven H. Simon Induced self-stabilization in fractional quantum Hall states of light, Phys. Rev. X, Volume 4 (2014)

[345] J. Lebreuilly; M. Wooters; I. Carusotto Strongly interacting photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping | arXiv

[346] M. Bellec; U. Kuhl; G. Montambaux; F. Mortessagne Topological transition of Dirac points in a microwave experiment, Phys. Rev. Lett., Volume 110 (2013)

[347] M. Polini; F. Guinea; M. Lewenstein; Hari C. Manoharan; V. Pellegrini Artificial graphene as a tunable Dirac material, Nat. Nanotechnol., Volume 8 (2013), p. 625

[348] F.D.M. Haldane Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “Parity Anomaly”, Phys. Rev. Lett., Volume 61 (1988), p. 2015

[349] G.W. Semenoff Condensed-matter simulation of a three-dimensional anomaly, Phys. Rev. Lett., Volume 53 (1984), p. 2449

[350] T.O. Wehling; A.M. Black-Schaffer; A.V. Balatsky Dirac materials, Adv. Phys., Volume 76 (2014), p. 1

[351] P.R. Wallace The band theory of graphite, Phys. Rev., Volume 71 (1947), p. 622

[352] J. Cayssol Introduction to Dirac materials and topological insulators, C. R. Physique, Volume 14 (2013), pp. 760-778

[353] J.S. Pedernales; R. Di Candia; D. Ballester; E. Solano Quantum simulations of relativistic quantum physics in circuit QED, New J. Phys., Volume 15 (2013)

[354] S. Raghu; Xiao-Liang Qi; C. Honerkamp; Shou-Cheng Zhang Topological Mott insulators, Phys. Rev. Lett., Volume 100 (2008)

[355] T. Liu; B. Douçot; K. Le Hur Realizing topological Mott insulators from the RKKY interaction, Phys. Rev. B, Volume 93 (2016)

[356] K. Fang; Z. Yu; S. Fan Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nature, Volume 782 (2012), p. 6

[357] W. Wu; S. Rachel; W.-M. Liu; K. Le Hur Quantum spin Hall insulators with interactions and lattice anisotropy, Phys. Rev. B, Volume 85 (2012)

[358] G. Kotliar; S.Y. Savrasov; K. Haule; V.S. Oudovenko; O. Parcollet; C.A. Marianetti Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys., Volume 78 (2006), p. 865

[359] G. Jotzu; M. Messer; R. Desbuquois; M. Lebrat; T. Uehlinger; D. Greif; T. Esslinger Experimental realisation of the topological Haldane model, Nature, Volume 515 (2014), pp. 237-240

[360] J. Struck; C. Ölschläger; M. Weinberg; P. Hauke; J. Simonet; A. Eckardt; M. Lewenstein; K. Sengstock; P. Windpassinger Tunable gauge potential for neutral and spinless particles in driven lattices, Phys. Rev. Lett., Volume 108 (2012)

[361] L. Tarruell; D. Greif; T. Uehlinger; G. Jotzu; T. Esslinger Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, Volume 483 (2012), pp. 302-305

[362] G. Montambaux; F. Piechon; J.-N. Fuchs; M.O. Goerbig Merging of Dirac points in a two-dimensional crystal, Phys. Rev. B, Volume 80 (2009)

[363] M. Aidelsburger; M. Lohse; C. Schweizer; M. Atala; J.T. Barreiro; S. Nascimbène; N.R. Cooper; I. Bloch; N. Goldman Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms, Nat. Phys., Volume 11 (2015), pp. 162-166

[364] M. Atala; M. Aidelsburger; J.T. Barreiro; D. Abanin; T. Kitagawa; E. Demler; I. Bloch Direct measurement of the Zak phase in topological Bloch bands, Nat. Phys., Volume 9 (2013), pp. 795-800

[365] P. Delplace; D. Ullmo; G. Montambaux The Zak phase and the existence of edge states in graphene, Phys. Rev. B, Volume 84 (2011)

[366] C.-Z. Chang et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science, Volume 340 (2013), p. 167

[367] D. Green; L. Santos; C. Chamon Isolated flat bands and spin-1 conical bands in two-dimensional lattices, Phys. Rev. B, Volume 82 (2010)

[368] H.H. Lieb Two theorems on the Hubbard model, Phys. Rev. Lett., Volume 62 (1989), p. 1201

[369] A. Mielke Ferromagnetic ground states for the Hubbard model on line graphs, J. Phys. A, Math. Gen., Volume 24 (1991)

[370] Hiroyuki Tamura; Kenji Shiraishi; Takashi Kimura; Hideaki Takayanagi Flat-band ferromagnetism in quantum dot superlattices, Phys. Rev. B, Volume 65 (2002)

[371] F. Baboux; L. Ge; T. Jacqmin; M. Biondi; A. Lemaître; L. Le Gratiet; I. Sagnes; S. Schmidt; H.E. Türeci; A. Amo; J. Bloch Bosonic condensation in a flat energy band, Phys. Rev. Lett., Volume 116 (2016)

[372] Matteo Biondi; Evert P.L. van Nieuwenburg; Gianni Blatter; Sebastian D. Huber; Sebastian Schmidt Incompressible polaritons in a flat band, Phys. Rev. Lett., Volume 115 (2015)

[373] B. Pannetier; J. Chaussy; R. Rammal; J.C. Villegier Experimental fine tuning of frustration: two-dimensional superconducting network in a magnetic field, Phys. Rev. Lett., Volume 53 (1984), p. 1845

[374] Y. Xiao; D.A. Huse; P.M. Chaikin; M.J. Higgins; S. Bhattacharya; D. Spencer Comparison of phase boundaries between Kagome and honeycomb superconducting wire networks, Phys. Rev. B, Volume 65 (2002)

[375] J. Vidal; R. Mosseri; B. Douçot Aharonov–Bohm cages in two-dimensional structures, Phys. Rev. Lett., Volume 81 (1998), p. 5888

[376] G.-Boong Jo; J. Guzman; C.K. Thomas; P. Hosur; A. Vishwanath; D.M. Stamper-Kurn Ultracold atoms in a tunable optical Kagome lattice, Phys. Rev. Lett., Volume 108 (2012)

[377] B. Fak et al. Kapellasite: a Kagome quantum spin liquid with competing interactions, Phys. Rev. Lett., Volume 109 (2012)

[378] P. Lecheminant; B. Bernu; C. Lhuillier; L. Pierre; P. Sindzingre Order versus disorder in the quantum Heisenberg antiferromagnet on the Kagome lattice: an approach through exact spectra analysis, Phys. Rev. B, Volume 56 (1997), p. 2521

[379] P. Azaria; C. Hooley; P. Lecheminant; C. Lhuillier; A.M. Tsvelik Kagome lattice antiferromagnet stripped to its basics, Phys. Rev. Lett., Volume 81 (1998), p. 1694

[380] Shou-Shu Gong; Wei Zhu; Leon Balents; D.N. Sheng Global phase diagram of competing ordered and quantum spin liquid phases on the Kagome lattice, Phys. Rev. B, Volume 91 (2015)

[381] Simeng Yan; David A. Huse; Steven R. White Spin liquid ground state of the S=1/2 Kagome Heisenberg model, Science, Volume 332 (2011), pp. 1173-1176

[382] Fabian Kolley; Stefan Depenbrock; Ian P. McCulloch; Ulrich Schollwöck; Vincenzo Alba Phase diagram of the J1–J2 Heisenberg model on the Kagome lattice, Phys. Rev. B, Volume 91 (2015)

[383] Laura Messio; Bernard Bernu; Claire Lhuillier The Kagome antiferromagnet: a chiral topological spin liquid?, Phys. Rev. Lett., Volume 108 (2012)

[384] A. Wietek; A. Sterdyniak; A.M. Läuchli Nature of chiral spin liquids on the Kagome lattice, Phys. Rev. B, Volume 92 (2015)

[385] C. Repellin; B. Andrei Bernevig; N. Regnault Z2 fractional topological insulators in two dimensions, Phys. Rev. B, Volume 90 (2014)

[386] Yu Chen et al. Simulating weak localization using superconducting quantum circuits, Nat. Commun., Volume 5 (2014), p. 5184

[387] P.G. Harper Single band motion of conduction electrons in a uniform magnetic field, Proc. Phys. Soc. A, Volume 68 (1955), p. 874

[388] D.R. Hofstadter Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B, Volume 14 (1976), p. 2239

[389] K. Fang; S. Fan Photonic de Haas–van Alphen effect, Opt. Express, Volume 21 (2013), p. 18216

[390] Takuya Kitagawa; Erez Berg; Mark Rudner; Eugene Demler Topological characterization of periodically-driven quantum systems, Phys. Rev. B, Volume 82 (2010)

[391] Netanel H. Lindner; Gil Refael; Victor Galitski Floquet topological insulator in semiconductor quantum wells, Nat. Phys., Volume 7 (2011), pp. 490-495

[392] C.L. Kane; E.J. Mele Quantum spin Hall effect in graphene, Phys. Rev. Lett., Volume 95 (2005)

[393] C.L. Kane; E.J. Mele Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett., Volume 95 (2005)

[394] J.E. Moore; L. Balents Topological invariants of time-reversal-invariant band structures, Phys. Rev. B, Volume 75 (2007)

[395] D.N. Sheng; Z.Y. Weng; L. Sheng; F.D.M. Haldane Quantum spin Hall effect and topologically invariant Chern numbers, Phys. Rev. Lett., Volume 97 (2006)

[396] Liang Fu; C.L. Kane Time reversal polarization and a Z2 adiabatic spin pump, Phys. Rev. B, Volume 74 (2006)

[397] M. König et al. Quantum spin Hall insulator state in HgTe quantum wells, Science, Volume 318 (2007), p. 766

[398] B.A. Bernevig; T.L. Hughes; S.-C. Zhang Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science, Volume 314 (2006), p. 1757

[399] S. Rachel; K. Le Hur Topological insulators and Mott physics from the Hubbard interaction, Phys. Rev. B, Volume 82 (2010)

[400] T. Liu; B. Douçot; K. Le Hur Anisotropic quantum spin Hall effect, spin-orbital textures and Mott transition, Phys. Rev. B, Volume 88 (2013)

[401] M. Hohenadler; F.F. Assaad Correlation effects in two-dimensional topological insulators, J. Phys. Condens. Matter, Volume 25 (2013), p. 143201

[402] W. Witczak-Krempa; G. Chen; Y. Baek Kim; L. Balents Correlated quantum phenomena in the strong spin–orbit regime, Annu. Rev. Condens. Matter Phys., Volume 5 (2014), pp. 57-82

[403] Serge Florens; Antoine Georges Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions, Phys. Rev. B, Volume 70 (2004)

[404] Charles-Edouard Bardyn; Torsten Karzig; Gil Refael; Timothy C.H. Liew Chiral bogoliubons in nonlinear bosonic systems | arXiv

[405] A.V. Nalitov; G. Malpuech; H. Terças; D.D. Solnyshkov Spin–orbit coupling and the optical spin Hall effect in photonic graphene, Phys. Rev. Lett., Volume 114 (2015)

[406] Torsten Karzig; Charles-Edouard Bardyn; Netanel Lindner; Gil Refael Topological polaritons, Phys. Rev. X, Volume 5 (2015)

[407] C. Xu; J.E. Moore Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z2 topology, Phys. Rev. B, Volume 73 (2006)

[408] V. Gurarie Single particle Green's functions and interacting topological insulators, Phys. Rev. B, Volume 83 (2011)

[409] M. Levin; A. Stern Fractional topological insulators, Phys. Rev. Lett., Volume 103 (2009)

[410] C.W. Groth; M. Wimmer; A.R. Akhmerov; J. Tworzydło; C.W.J. Beenakker Theory of the topological Anderson insulator, Phys. Rev. Lett., Volume 103 (2009)

[411] E. Prodan; T.L. Hughes; B.A. Bernevig Entanglement spectrum of a disordered topological Chern insulator, Phys. Rev. Lett., Volume 105 (2010)

[412] Z. Wang; X.-L. Qi; S.-C. Zhang Topological invariants for interacting topological insulators with inversion symmetry, Phys. Rev. B, Volume 85 (2012)

[413] A. Go; W. Witczak-Krempa; G. Sang Jeon; K. Park; Y. Baek Kim Correlation effects on 3D topological phases: from bulk to boundary, Phys. Rev. Lett., Volume 109 (2012)

[414] B. Jan Carl; R. Thomale; G. Li; M. Laubach; S.-C. Zhang Fluctuation-induced topological quantum phase transitions in quantum spin hall and quantum anomalous Hall insulators, Phys. Rev. B, Volume 86 (2012)

[415] T.C. Lang; A.M. Essin; V. Gurarie; S. Wessel Z2 topological invariants in two dimensions from quantum Monte Carlo, Phys. Rev. B, Volume 87 (2013)

[416] M. Atala; M. Aidelsburger; M. Lohse; J.T. Barreiro; B. Paredes; I. Bloch Observation of the Meissner effect with ultracold atoms in bosonic ladders, Nat. Phys., Volume 10 (2014), pp. 588-593

[417] T. Kock; M. Olschläger; A. Ewerbeck; W.-M. Huang; L. Mathey; A. Hemmerich Observing chiral superfluid order by matter-wave interference, Phys. Rev. Lett., Volume 114 (2015)

[418] M. Bukov; A. Polkovnikov Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper–Hofstadter Hamiltonian, Phys. Rev. A, Volume 90 (2014)

[419] E. Orignac; T. Giamarchi Meissner effect in a bosonic ladder, Phys. Rev. B, Volume 64 (2001)

[420] François Crépin; Nicolas Laflorencie; Guillaume Roux; Pascal Simon Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator–Luttinger liquid–Bose glass, Phys. Rev. B, Volume 84 (2011)

[421] T. Giamarchi Quantum Physics in One Dimension, Oxford University Press, 2003

[422] A. Petrescu; K. Le Hur Bosonic Mott insulator with Meissner currents, Phys. Rev. Lett., Volume 111 (2013)

[423] A. Petrescu; K. Le Hur Chiral Mott insulators, Meissner effect, and Laughlin states in quantum ladders, Phys. Rev. B, Volume 91 (2015)

[424] M. Piraud; F. Heidrich-Meisner; I.P. McCulloch; S. Greschner; T. Vekua; U. Schollwöck Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder, Phys. Rev. B, Volume 91 (2015)

[425] S. Greschner; M. Piraud; F. Heidrich-Meisner; I.P. McCulloch; U. Schollwöck; T. Vekua Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: swimming against the tide, Phys. Rev. Lett., Volume 115 (2015)

[426] M. Di Dio; S. De Palo; E. Orignac; R. Citro; M. Luisa Chiofalo Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux, Phys. Rev. B, Volume 92 (2015)

[427] A. Dhar; M. Maji; T. Mishra; R.V. Pai; S. Mukerjee; A. Paramekanti Bose Hubbard model in a strong effective magnetic field: emergence of a chiral Mott insulator ground state, Phys. Rev. A, Volume 85 (2012), p. 041602(R)

[428] Ran Wei; Erich J. Mueller Theory of Bosons in two-leg ladders with large magnetic fields, Phys. Rev. A, Volume 89 (2014)

[429] A. Tokuno; A. Georges Ground states of a Bose–Hubbard ladder in an artificial magnetic field: field-theoretical approach, New J. Phys., Volume 16 (2014)

[430] J.C.Y. Teo; C.L. Kane From Luttinger liquid to non-Abelian quantum Hall states, Phys. Rev. B, Volume 89 (2014)

[431] C.L. Kane; R. Mukhopadhyay; T.C. Lubensky The fractional quantum Hall effect in an array of quantum wires, Phys. Rev. Lett., Volume 88 (2002)

[432] Eran Sagi; Yuval Oreg; Ady Stern; Bertrand I. Halperin Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states, Phys. Rev. B, Volume 91 (2015)

[433] B.K. Stuhl; H.-I. Lu; L.M. Aycock; D. Genkina; I.B. Spielman Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science, Volume 349 (2015), pp. 1514-1518

[434] M. Mancini; G. Pagano; G. Cappellini; L. Livi; M. Rider; J. Catani; C. Sias; P. Zoller; M. Inguscio; M. Dalmonte; L. Fallani Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science, Volume 349 ( 25 September 2015 ) no. 6255, pp. 1510-1513

[435] I. Vasic; A. Petrescu; K. Le Hur; W. Hofstetter Chiral bosonic phases on the Haldane Honeycomb lattice, Phys. Rev. B, Volume 91 (2015)

[436] Lih-King Lim; C. Morais Smith; Andreas Hemmerich Staggered-vortex superfluid of ultracold Bosons in an optical lattice, Phys. Rev. Lett., Volume 100 (2008)

[437] I. Affleck; J.B. Marston The large-N Limit of the Hubbard model: implications for High-T superconductors, Phys. Rev. B, Volume 37 (1988), p. 3774

[438] S. Chakravarty; R.B. Laughlin; D.K. Morr; C. Nayak Hidden order in the cuprates, Phys. Rev. B, Volume 63 (2001)

[439] B. Fauque; Y. Sidis; V. Hinkov; S. Pailhes; C.T. Lin; X. Chaud; Ph. Bourges Magnetic order in the pseudogap phase of high-TC superconductors, Phys. Rev. Lett., Volume 96 (2006)

[440] J.O. Fjaerestad; J.B. Marston; U. Schollwoeck Orbital currents and charge density waves in a generalized Hubbard ladder, Ann. Phys. (N.Y.), Volume 321 (2006), p. 894

[441] G. Roux; E. Orignac; S.R. White; D. Poilblanc Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases, Phys. Rev. B, Volume 76 (2007)

[442] S.T. Carr; B.N. Narozhny; A.A. Nersesyan Spinless Fermionic ladders in a magnetic field: phase diagram, Phys. Rev. B, Volume 73 (2006)

[443] H.P. Büchler; M. Hermele; S.D. Huber; Matthew P.A. Fisher; P. Zoller Atomic quantum simulator for lattice gauge theories and ring exchange models, Phys. Rev. Lett., Volume 95 (2005)

[444] B. Douçot; L.B. Ioffe Physical implementation of protected qubits, Rep. Prog. Phys., Volume 75 (2012)

[445] B.M. Terhal Quantum error correction for quantum memories, Rev. Mod. Phys., Volume 87 (2015), p. 307

[446] R. Barends et al. Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature, Volume 508 (2014), pp. 500-503

[447] S. Vijay; L. Fu Physical implementation of a Majorana fermion surface code for fault–tolerant quantum computation | arXiv

[448] L.A. Landau; S. Plugge; E. Sela; A. Altland; S.M. Albrecht; R. Egger | arXiv

[449] D. Marcos; P. Widmer; E. Rico; M. Hafezi; P. Rabl; U.-J. Wiese; P. Zoller Two-dimensional lattice gauge theories with superconducting quantum circuits, Ann. Phys., Volume 351 (2014), p. 634

[450] D.S. Rokhsar; S.A. Kivelson Superconductivity and the quantum hard-core dimer gas, Phys. Rev. Lett., Volume 61 (1988), p. 2376

[451] Moessner; S.L. Sondhi; E. Fradkin Short-ranged RVB physics, quantum dimer models and Ising gauge theories, Phys. Rev. B, Volume 65 (2002)

[452] S. Chandrasekharan; U.-J. Wiese Quantum link models: a discrete approach to gauge theories, Nucl. Phys. B, Volume 492 (1997), pp. 455-474

[453] A. Kitaev Anyons in an exactly solved model and beyond, Ann. Phys., Volume 321 (2006), p. 2

[454] M.Y. Azbel Energy spectrum of a conduction electron in a magnetic field, JETP, Volume 19 (1964), p. 634

[455] N. Goldman; I. Satija; P. Nikolic; A. Bermudez; M.A. Martin-Delgado; M. Lewenstein; I.B. Spielman Engineering time-reversal invariant topological insulators with ultra-cold atoms, Phys. Rev. Lett., Volume 105 (2010)

[456] Daniel Cocks; Peter P. Orth; Stephan Rachel; Michael Buchhold; Karyn Le Hur; Walter Hofstetter Time-reversal-invariant Hofstadter–Hubbard model with ultracold fermions, Phys. Rev. Lett., Volume 109 (2012)

[457] Peter P. Orth; Daniel Cocks; Stephan Rachel; Michael Buchhold; Karyn Le Hur; Walter Hofstetter Correlated topological phases and exotic magnetism with ultracold fermions, J. Phys. B, At. Mol. Opt. Phys., Volume 46 (2013), p. 134004

[458] Mathias S. Scheurer; Stephan Rachel; Peter P. Orth Dimensional crossover and cold-atom realization of topological Mott insulators, Sci. Rep., Volume 5 (2015), p. 8386

[459] Marie Piraud; Zi Cai; Ian P. McCulloch; Ulrich Schollwöck Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: a density matrix renormalization group study, Phys. Rev. A, Volume 89 (2014)

[460] Y. Pomeau; S. Rica Diffraction Non-Linéaire, C. R. Acad. Sci. Paris, Volume 317 (1993) no. II, p. 1287

[461] Roman Süsstrunk; Sebastian D. Huber Observation of phononic helical edge states in a mechanical topological insulator, Science, Volume 349 (2015), p. 47

[462] C.-E. Bardyn; M.A. Baranov; C.V. Kraus; E. Rico; A. Imamoglu; P. Zoller; S. Diehl Topology by dissipation | arXiv

[463] Alexandru Petrescu; H. Francis Song; Stephan Rachel; Zoran Ristivojevic; Christian Flindt; Nicolas Laflorencie; Israel Klich; Nicolas Regnault; Karyn Le Hur Fluctuations and entanglement spectrum in quantum Hall states, J. Stat. Mech. (2014)

[464] L. Saminadayar; D.C. Glattli; Y. Jin; B. Etienne Observation of the e/3 fractionally charged Laughlin quasiparticle, Phys. Rev. Lett., Volume 79 (1997), p. 2526

[465] R. de-Picciotto; M. Reznikov; M. Heiblum; V. Umansky; G. Bunin; D. Mahalu Direct observation of a fractional charge, Nature, Volume 389 (1997), pp. 162-164

Cited by Sources:

Comments - Policy