Driven dissipative dynamics and topology of quantum impurity systems

Karyn Le Hur; Loïc Henriet; Loïc Herviou; Kirill Plekhanov; Alexandru Petrescu; Tal Goren; Marco Schiro; Christophe Mora; Peter P. Orth

doi:10.1016/j.crhy.2018.04.003

Driven dissipative dynamics and topology of quantum impurity systems

Karyn Le Hur ¹ ; Loïc Henriet ²; Loïc Herviou ^1,³; Kirill Plekhanov ^1,⁴; Alexandru Petrescu ⁵; Tal Goren ¹; Marco Schiro ⁶; Christophe Mora ³; Peter P. Orth ⁷

¹ Centre de physique théorique, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France
² ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
³ Laboratoire Pierre-Aigrin, École normale supérieure–PSL Research University, CNRS, Université Pierre-et-Marie-Curie, Sorbonne Universités, Université Paris-Sorbonne Paris Cité, 24, rue Lhomond, 75231 Paris cedex 05, France
⁴ LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
⁵ Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
⁶ Institut de physique théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
⁷ Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

Comptes Rendus. Physique, Volume 19 (2018) no. 6, pp. 451-483.

Abstract
Résumé

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_{z} (t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.

Dans cette revue, nous proposons une introduction et une vue d'ensemble de quelques progrès parmi les plus récents dans le domaine de la dynamique en temps réel des modèles d'impuretés quantiques et de leurs réalisations dans les dispositifs quantiques. Nous nous intéressons au modèle spin–boson avec dissipation ohmique et aux modèles associés, qui décrivent un seul spin 1/2 couplé à une collection infinie d'oscillateurs harmoniques. Les sujets abordés s'inspirent en grande partie de nos travaux de ces dernières années, mais nous présentons également quelques résultats nouveaux. Nous commençons la première partie de cette revue par une introduction pédagogique à la dynamique en temps réel d'un spin dissipatif à hautes et basses températures. Nous nous intéressons ensuite à la dynamique dirigée en régime quantique au-delà de la limite de faible couplage spin–bain. Dans ces situations, la méthode faisant appel à l'équation de Schroedinger stochastique non perturbative est idéale pour obtenir numériquement la dynamique de spin, car elle permet d'incorporer des champs de polarisation $h_{z} (t)$ de dépendance temporelle arbitraire dans le hamiltonien. Nous présentons différentes applications récentes de cette méthode : (i) comment les propriétés topologiques du spin telles que la courbure de Berry et le nombre de Chern peuvent être mesurées dynamiquement, et comment la dissipation affecte la topologie et le protocole de mesure ; (ii) comment les chaînes de spin quantiques suivent la dynamique de synchronisation par couplage avec un bain commun. Dans la deuxième partie de cette revue, nous discutons l'ingénierie quantique du modèle spin-boson et des modèles associés en électrodynamique quantique des circuits (cQED), des circuits électriques quantiques et des architectures d'atomes froids. Dans différentes réalisations, l'environnement ohmique peut être représenté par une longue ligne de transmission (micro-ondes), un liquide de Luttinger, un condensat de Bose–Einstein unidimensionnel, une chaîne de jonctions Josephson supraconductrices. Nous montrons que l'impureté quantique peut être utilisée comme un capteur quantique pour détecter les propriétés d'un bain au couplage minimal, et comment la dynamique de spin dissipative peut conduire à de nouvelles perspectives dans la transition Mott–superfluide.

Published online: 2018-05-28

DOI: 10.1016/j.crhy.2018.04.003

Keywords: Quantum impurity model dynamics, Synchronization and spin topology, Light–matter and hybrid systems, Majorana quantum impurity models, Quantum materials, Quantum state engineering
Mot clés : Dynamique du modèle d'impuretés quantiques, Synchronisation et topologie de spin, Systèmes lumière–matière et hybrides, Modèle d'impureté quantique de Majorana, Matériaux quantiques, Ingénierie de l'état solide

Author's affiliations:

Karyn Le Hur ¹; Loïc Henriet ²; Loïc Herviou ^{1, 3}; Kirill Plekhanov ^{1, 4}; Alexandru Petrescu ⁵; Tal Goren ¹; Marco Schiro ⁶; Christophe Mora ³; Peter P. Orth ⁷

¹ Centre de physique théorique, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France
² ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
³ Laboratoire Pierre-Aigrin, École normale supérieure–PSL Research University, CNRS, Université Pierre-et-Marie-Curie, Sorbonne Universités, Université Paris-Sorbonne Paris Cité, 24, rue Lhomond, 75231 Paris cedex 05, France
⁴ LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
⁵ Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
⁶ Institut de physique théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
⁷ Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

@article{CRPHYS_2018__19_6_451_0,
     author = {Karyn Le Hur and Lo{\"\i}c Henriet and Lo{\"\i}c Herviou and Kirill Plekhanov and Alexandru Petrescu and Tal Goren and Marco Schiro and Christophe Mora and Peter P. Orth},
     title = {Driven dissipative dynamics and topology of quantum impurity systems},
     journal = {Comptes Rendus. Physique},
     pages = {451--483},
     publisher = {Elsevier},
     volume = {19},
     number = {6},
     year = {2018},
     doi = {10.1016/j.crhy.2018.04.003},
     language = {en},
}

TY  - JOUR
AU  - Karyn Le Hur
AU  - Loïc Henriet
AU  - Loïc Herviou
AU  - Kirill Plekhanov
AU  - Alexandru Petrescu
AU  - Tal Goren
AU  - Marco Schiro
AU  - Christophe Mora
AU  - Peter P. Orth
TI  - Driven dissipative dynamics and topology of quantum impurity systems
JO  - Comptes Rendus. Physique
PY  - 2018
SP  - 451
EP  - 483
VL  - 19
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crhy.2018.04.003
LA  - en
ID  - CRPHYS_2018__19_6_451_0
ER  -

%0 Journal Article
%A Karyn Le Hur
%A Loïc Henriet
%A Loïc Herviou
%A Kirill Plekhanov
%A Alexandru Petrescu
%A Tal Goren
%A Marco Schiro
%A Christophe Mora
%A Peter P. Orth
%T Driven dissipative dynamics and topology of quantum impurity systems
%J Comptes Rendus. Physique
%D 2018
%P 451-483
%V 19
%N 6
%I Elsevier
%R 10.1016/j.crhy.2018.04.003
%G en
%F CRPHYS_2018__19_6_451_0

Karyn Le Hur; Loïc Henriet; Loïc Herviou; Kirill Plekhanov; Alexandru Petrescu; Tal Goren; Marco Schiro; Christophe Mora; Peter P. Orth. Driven dissipative dynamics and topology of quantum impurity systems. Comptes Rendus. Physique, Volume 19 (2018) no. 6, pp. 451-483. doi : 10.1016/j.crhy.2018.04.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.04.003/

References
Cited by

[1] M.A. Nielsen; I.L. Chuang Quantum Computation and Quantum Information, Cambridge University Press, 2010

[2] R.P. Feynman Int. J. Theor. Phys., 21 (1982), p. 467

[3] C.L. Degen; F. Reinhard; P. Cappellaro Rev. Mod. Phys., 89 (2017)

[4] J. Kondo Prog. Theor. Phys. Oxford J., 32 (1964) no. 1, pp. 37-49

[5] A.C. Hewson; B. Coqblin Croatia (1997)

[6] A.J. Schofield Non-Fermi liquids, Contemp. Phys., Volume 40 (1999) no. 2, pp. 95-115

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

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

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

[10] I. Bloch; J. Dalibard; W. Zwerger Rev. Mod. Phys., 80 (2008), p. 885

[11] R.P. Feynman; F.L. Vernon Ann. Phys. (N.Y.), 24 (1963), p. 118

[12] P. Hänggi; G.L. Ingold Fundamental aspects of quantum Brownian motion, Chaos, Volume 15 (2005) (ARTN 026105)

[13] A.O. Caldeira; A.J. Leggett Phys. Rev. Lett., 46 (1981), pp. 211-214

[14] P.W. Anderson J. Phys. C, Solid State Phys., 3 (1970), pp. 2436-2441

[15] K. Wilson Rev. Mod. Phys., 47 (1975), pp. 773-840

[16] P. Nozières J. Low Temp. Phys., 17 (1974), p. 31

[17] I. Affleck Acta Phys. Pol. B, 26 (1995), pp. 1869-1932

[18] P. Nozières; A. Blandin J. Phys., 41 (1980), p. 193

[19] M. Blume; V.J. Emery; A. Luther Phys. Rev. Lett., 25 (1970), pp. 450-453

[20] A.J. Leggett; S. Chakravarty; A.T. Dorsey; M.P.A. Fisher; A. Garg; W. Zwerger Rev. Mod. Phys., 59 (1987) no. 1

[21] U. Weiss Quantum Dissipative Systems, World Scientific, Singapore, 2002

[22] A.J. Bray; M.A. Moore Phys. Rev. Lett., 49 (1982), p. 1545

[23] P.W. Anderson; G. Yuval; D.R. Hamann Phys. Rev. B, 1 (1970), pp. 4464-4473

[24] P.W. Anderson; G. Yuval J. Phys. C, 4 (1971), pp. 607-620

[25] M. Keil; H. Schoeller Phys. Rev. B, 63 (2001)

[26] H. Schoeller Eur. Phys. J. Spec. Top., 168 (2009), p. 179

[27] W. Metzner; M. Salmhofer; C. Honerkamp; V. Meden; K. Schonhammer Rev. Mod. Phys., 84 (2012), p. 299

[28] H.-P. Breuer; F. Petruccione The Theory of Open Quantum Systems, Oxford University Press, Oxford, UK, 2002

[29] R. Silbey; R.A. Harris J. Chem. Phys., 80 (1984), p. 2615

[30] D.P.S. McCutcheon; A. Nazir; S. Bose; A.J. Fisher Phys. Rev. B, 81 (2010)

[31] S. Bera; S. Florens; H.U. Baranger; N. Roch; A. Nazir; A.W. Chin Phys. Rev. B, 89 (2014) 121108(R)

[32] T. Giamarchi Quantum Physics in One Dimension, Clarendon Press, Oxford, UK, 2004

[33] A. Tsvelick; P. Wiegmann Adv. Phys., 32 (1983) no. 4, pp. 453-713

[34] N. Andrei; H. Johannesson Phys. Lett. A, 100 (1984), pp. 108-112

[35] R. Bulla; T.A. Costi; T. Pruschke Rev. Mod. Phys., 80 (2008), p. 395

[36] W. Hofstetter Phys. Rev. Lett., 85 (2000), p. 1508

[37] M-R. Li; K. Le Hur; W. Hofstetter Phys. Rev. Lett., 95 (2005)

[38] M. Vojta; N.-H. Tong; R. Bulla Phys. Rev. Lett., 94 (2005)

[39] F.B. Anders; A. Schiller Phys. Rev. B, 74 (2006)

[40] K. Le Hur; P. Doucet-Beaupré; W. Hofstetter Phys. Rev. Lett., 99 (2007)

[41] P.P. Orth; D. Roosen; W. Hofstetter; K. Le Hur Phys. Rev. B, 82 (2010)

[42] H.T.M. Nghiem; T.A. Costi Phys. Rev. B, 90 (2014)

[43] U. Schollwöck Rev. Mod. Phys., 77 (2005), p. 259

[44] S.R. White; A.E. Feiguin Phys. Rev. Lett., 93 (2004)

[45] P. Schmitteckert Phys. Rev. B, 70 (2004)

[46] A. Winter; H. Rieger Phys. Rev. B, 90 (2014)

[47] M. Schirò; M. Fabrizio Phys. Rev. B, 79 (2009)

[48] T.L. Schmidt; P. Werner; L. Muehlbacher; A. Komnik Phys. Rev. B, 78 (2008)

[49] P. Werner; T. Oka; A.J. Millis Phys. Rev. B, 79 (2009)

[50] C. Xu; A. Poudel; M.G. Vavilov Phys. Rev. A, 89 (2014)

[51] M. Bauer; D. Bernard; A. Tilloy J. Stat. Mech., P09001 (2014)

[52] A. Weichselbaum; F. Verstraete; U. Schollwock; J.I. Cirac; J. von Delft Phys. Rev. B, 80 (2009)

[53] A. Strathearn; P. Kirton; D. Kilda; J. Keeling; B.W. Lovett, 2017 | arXiv

[54] C. Schoen; K. Hammerer; M.M. Wolf; J.I. Cirac; E. Solano Phys. Rev. A, 75 (2007)

[55] M. Marcuzzi; E. Levi; S. Diehl; J.P. Garrahan; I. Lesanovsky Phys. Rev. Lett., 113 (2014)

[56] M.L. Wall; A. Safavi-Naini; A.M. Rey Phys. Rev. A, 94 (2016)

[57] J. Jin; A. Biella; O. Viyuela; L. Mazza; J. Keeling; R. Fazio; D. Rossini Phys. Rev. X, 6 (2016)

[58] Z. Blunden-Codd; S. Bera; B. Bruognolo; N.-O. Linden; A.W. Chin; J. von Delft; A. Nazir; S. Florens Phys. Rev. B, 95 (2017)

[59] J. Dalibard; Y. Castin; K. Molmer Phys. Rev. Lett., 68 (1992), p. 580

[60] C.W. Gardiner; A.S. Parkins; P. Zoller Phys. Rev. A, 46 (1992), p. 4363

[61] N. Gisin; I.C. Percival J. Phys. A, 25 (1992), p. 5677

[62] H.-P. Breuer; B. Kappler; F. Petruccione Phys. Rev. A, 59 (1999), p. 1633

[63] G.B. Lesovik; A.O. Lebedev; A.O. Imambekov JETP Lett., 75 (2002), p. 474

[64] J. Cao; L.W. Ungar; G.A. Voth J. Chem. Phys., 104 (1996), p. 4189

[65] W.T. Strunz; L. Diosi; N. Gisin Phys. Rev. Lett., 82 (1999), p. 1801

[66] J.T. Stockburger; C.H. Mac J. Chem. Phys., 110 (1999), p. 4983

[67] J.T. Stockburger; H. Grabert Phys. Rev. Lett., 88 (2002)

[68] Y. Zhou; J. Shao J. Chem. Phys., 128 (2008)

[69] A. Imambekov; V. Gritsev; E. Demler Varenna, Italy (2006)

[70] P.P. Orth; A. Imambekov; K. Le Hur Phys. Rev. A, 82 (2010)

[71] P.P. Orth; A. Imambekov; K. Le Hur Phys. Rev. B, 87 (2013)

[72] L. Henriet; K. Le Hur Phys. Rev. B, 93 (2016)

[73] L. Henriet; Z. Ristivojevic; P.P. Orth; K. Le Hur Phys. Rev. A, 90 (2014)

[74] L. Henriet; A. Sclocchi; P.P. Orth; K. Le Hur Phys. Rev. B, 95 (2017)

[75] L. Henriet Non-equilibrium Dynamics of Many Body Quantum Systems, 2016 https://hal.archives-ouvertes.fr/tel-01525432v1 (PhD thesis) | arXiv

[76] A. Georges; G. Kotliar; W. Krauth; M. Rozenberg Rev. Mod. Phys., 68 (1996), pp. 13-125

[77] P. Werner; K. Volker; M. Troyer; S. Chakravarty Phys. Rev. Lett., 94 (2005)

[78] P. Werner; M. Troyer; S. Sachdev J. Phys. Soc. Jpn., Suppl., 74 (2005), p. 67

[79] S. Sachdev; P. Werner; M. Troyer Phys. Rev. Lett., 92 (2004)

[80] S. Pankov; S. Florens; A. Georges; G. Kotliar; S. Sachdev Phys. Rev. B, 69 (2004)

[81] A. Georges; O. Parcollet; S. Sachdev Phys. Rev. Lett., 85 (2000), pp. 840-843

[82] H. Weber; M. Vojta Eur. Phys. J. B, 53 (2006), p. 185

[83] W. Wu; M. Ferrero; A. Georges; E. Kozik Phys. Rev. B, 96 (2017)

[84] U. Bissbort; R. Thomale; W. Hofstetter Phys. Rev. A, 81 (2010)

[85] G. Kulaitis; F. Krüger; F. Nissen; J. Keeling Phys. Rev. A, 87 (2013)

[86] A. Le Boité; G. Orso; C. Ciuti Phys. Rev. Lett., 110 (2013)

[87] M.V. Berry Proc. R. Soc. A, 392 (1984) no. 1802, pp. 45-57

[88] A. Polkovnikov; V. Gritsev Proc. Natl. Acad. Sci. USA, 109 (2012), p. 6457

[89] M. Kolodrubetz; P. Mehta; A. Polkovnikov | arXiv

[90] Y. Liu; F. Piechon; J.N. Fuchs Europhys. Lett., 103 (2013)

[91] M. Delehaye; S. Laurent; I. Ferrier-Barbut; S. Jin; F. Chevy; C. Salomon Phys. Rev. Lett., 115 (2015)

[92] P. Cedraschi; M. Büttiker Ann. Phys. (N.Y.), 289 (2001), pp. 1-23

[93] A. Recati; P.O. Fedichev; W. Zwerger; J. von Delft; P. Zoller Phys. Rev. Lett., 94 (2005)

[94] P.P. Orth; I. Stanic; K. Le Hur Phys. Rev. A, 77 (2008) 051601(R)

[95] K. Le Hur Phys. Rev. Lett., 92 (2004)

[96] A.A. Houck; H. Türeci; J. Koch Nat. Phys., 8 (2012), pp. 292-299

[97] K. Le Hur; L. Henriet; A. Petrescu; K. Plekhanov; G. Roux; M. Schiro C. R. Physique, 17 (2016), pp. 808-835

[98] M. Goldstein; M.H. Devoret; M. Houzet; L.I. Glazman Phys. Rev. Lett., 110 (2013)

[99] A. Clerk; M.-H. Devoret; S.M. Girvin; F. Marquardt; R. Schoelkopf Rev. Mod. Phys., 82 (2010), p. 1155

[100] F. Verstraete; M.M. Wolf; I. Cirac Nat. Phys., 5 (2009), pp. 633-636

[101] S. Diehl; A. Micheli; A. Kantian; B. Kraus; H.P. Büchler; P. Zoller Nat. Phys., 4 (2008), pp. 878-883

[102] E.G. Dalla Torre; E. Demler; T. Giamarchi; E. Altman Nat. Phys., 6 (2010), pp. 806-810

[103] C.-E. Bardyn; M.A. Baranov; C.V. Kraus; E. Rico; A. Imamoglu; P. Zoller; S. Diehl New J. Phys., 15 (2013) no. 8

[104] F. Grusdt; N.Y. Yao; D.A. Abanin; M. Fleischhauer; E.A. Demler Nat. Commun., 7 (2016)

[105] E. Flurin; V.V. Ramasesh; S. Hacohen-Gourgy; L.S. Martin; N.Y. Yao; I. Siddiqi Phys. Rev. X, 7 (2017)

[106] V.L. Berezinskii; V.L. Berezinskii Sov. Phys. JETP, 32 (1971) no. 3, pp. 493-500

[107] J.M. Kosterlitz; D. Thouless J. Phys. C, Solid State Phys., 6 (1973) no. 7, pp. 1181-1203

[108] K. Le Hur Understanding Quantum Phase Transitions (L.D. Carr, ed.), Taylor and Francis, Boca Raton, 2010 | arXiv

[109] K. Le Hur Ann. Phys. (N.Y.), 323 (2008), pp. 2208-2240 | arXiv

[110] D.J. Bishop; J.D. Reppy Phys. Rev. Lett., 40 (1978), p. 1727

[111] Z. Hadzibabic; P. Krüger; M. Cheneau; B. Battelier; J.-B. Dalibard Nature, 441 (2006) no. 1118

[112] D.J. Thouless Phys. Rev., 187 (1969), pp. 732-733

[113] A. Kopp; K. Le Hur Phys. Rev. Lett., 98 (2007)

[114] M. Haeberlein et al. | arXiv

[115] P. Forn-Díaz; J.J. Garcia-Ripoll; B. Peropadre; M.A. Yurtalan; J.-L. Orgiazzi; R. Belyansky; C.M. Wilson; A. Lupascu Nat. Phys., 13 (2017), p. 39

[116] J. Puertas Martinez; S. Leger; N. Gheereart; R. Dassonneville; L. Planat; F. Foroughi; Y. Krupko; O. Buisson; C. Naud; W. Guichard; S. Florens; I. Snyman; N. Roch | arXiv

[117] A. Kapitulnik; N. Mason; S.A. Kivelson; S. Chakravarty Phys. Rev. B, 63 (2001)

[118] M. Fitzpatrick; N.M. Sundaresan; A.C.Y. Li; J. Koch; A.A. Houck Phys. Rev. X, 7 (2017)

[119] S. Jezouin; M. Albert; F.D. Parmentier; A. Anthore; U. Gennser; A. Cavanna; I. Safi; F. Pierre Nat. Commun., 4 (2013), p. 1802

[120] H.T. Mebrahtu; I.V. Borzenets; D.E. Liu; H. Zheng; Y.V. Bomze; A.I. Smirnov; H.U. Baranger; G. Finkelstein Nature, 488 (2012), p. 61

[121] S.F. Huelga; M.B. Plenio Contemp. Phys., 54 (2013), pp. 181-207

[122] S. Schmidt; J. Koch Ann. Phys., 525 (2013), pp. 395-412

[123] M.J. Hartmann J. Opt., 18 (2016)

[124] C. Noh; D.G. Angelakis Rep. Prog. Phys., 80 (2016)

[125] I. Carusotto; C. Ciuti Rev. Mod. Phys., 85 (2013), p. 299

[126] G. Toulouse C. R. Acad. Sci., 268 (1969), p. 1200

[127] F. Guinea; V. Hakim; A. Muramatsu Phys. Rev. B, 32 (1985), p. 4410

[128] O. Kashuba; D.M. Kennes; M. Pletyukhov; V. Meden; H. Schoeller Phys. Rev. B, 88 (2013)

[129] Z. Ristivojevic; A. Petkovic; P. Le Doussal; T. Giamarchi Phys. Rev. Lett., 109 (2012)

[130] S.J. Weber; A. Chantasri; J. Dressel; A.N. Jordan; K.W. Murch; I. Siddiqi Nature, 511 (2014), pp. 570-573

[131] N. Roch; M.E. Schwartz; F. Motzoi; C. Macklin; R. Vijay; A.W. Eddins; A.N. Korotkov; K.B. Whaley; M. Sarovar; I. Siddiqi Phys. Rev. Lett., 112 (2014) no. 17

[132] N. Fläschner; B.S. Rem; M. Tarnowski; D. Vogel; D.-S. Lühmann; K. Sengstock; C. Weitenberg Science, 352 (2016), p. 1091

[133] S. Sugawa; F. Salces-Carcoba; A.R. Perry; Y. Yue; I.B. Spielman | arXiv

[134] O. Parlavecchio; C. Altimiras; J.-R. Souquet; P. Simon; I. Safi; P. Joyez; D. Vion; P. Roche; D. Esteve; F. Portier Phys. Rev. Lett., 114 (2015) no. 12

[135] G.-L. Ingold; Yu.V. Nazarov Single Charge Tunneling (H. Grabert; M.H. Devoret, eds.), NATO ASI Ser. B, vol. 294, Plenum Press, New York, 1992, pp. 21-107 | arXiv

[136] C.L. Kane; M.P.A. Fisher Phys. Rev. Lett., 68 (1992), p. 1220

[137] I. Safi; H. Saleur Phys. Rev. Lett., 93 (2004)

[138] T. Giamarchi; H.J. Schulz Phys. Rev. B, 37 (1988), p. 325

[139] F.D.M. Haldane J. Phys. C, 14 (1981), p. 2585

[140] J. Dubois; T. Jullien; F. Portier; P. Roche; A. Cavanna; Y. Jin; W. Wegscheider; P. Roulleau; D.C. Glattli Nature, 502 (2013) no. 7473, pp. 659-663

[141] 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 Ann. Phys., 526 (2014), p. 1

[142] J. Gabelli; B. Reulet Phys. Rev. B, 87 (2013)

[143] T. Goren; K. Le Hur; E. Akkermans | arXiv

[144] E. Akkermans; G.V. Dunne Phys. Rev. Lett., 108 (2012)

[145] M. Knap; A. Kantian; T. Giamarchi; I. Bloch; M.D. Lukin; E. Demler Phys. Rev. Lett., 111 (2013)

[146] M. Atala; M. Aidelsburger; J.T. Barreiro; D. Abanin; T. Kitagawa; E. Demler; I. Bloch Nat. Phys., 9 (2013), p. 795

[147] M. Schiró; A. Mitra Phys. Rev. Lett., 112 (2014)

[148] M. Schiró; A. Mitra Phys. Rev. B, 91 (2015)

[149] A. Furusaki; K.A. Matveev Phys. Rev. Lett., 88 (2002)

[150] K. Le Hur; M.-R. Li Phys. Rev. B, 72 (2005)

[151] T. Weißl; B. König; E. Dumur; A.K. Feofanov; I. Matei; C. Naud; O. Buisson; F.W.J. Hekking; W. Guichard Phys. Rev. B, 92 (2015)

[152] I.M. Pop; I. Protopopov; F. Lecocq; Z. Peng; B. Pannetier; O. Buisson; W. Guichard Nat. Phys., 6 (2010), p. 589

[153] V.E. Manucharyan; J. Koch; L. Glazman; M. Devoret Science, 326 (2009), pp. 113-116

[154] C. Sabin; A. White; L. Hackermuller; I. Fuentes Nat. Sci. Rep., 4 (2014) (id. 6436)

[155] A. Lamacraft Phys. Rev. B, 79 (2009) 241105(R)

[156] P.O. Fedichev; U.R. Fischer Phys. Rev. Lett., 91 (2003)

[157] A. Posazhennikova; W. Belzig Europhys. Lett., 87 (2009)

[158] S.M. Girvin Quantum machines: measurement and control of engineered quantum systems, Oxford, UK, July 2011 (2014)

[159] Y. Makhlin; G. Schön; A. Shnirman New Directions in Mesoscopic Physics (Towards Nanoscience) (R. Fazio; V.F. Gantmakher; Y. Imry, eds.), Kluwer, Dordrecht, 2003, pp. 197-224 | arXiv

[160] Y.A. Pashkin; T. Yamamoto; O. Astafiev; Y. Nakamura; D.V. Averin; J.S. Tsai Nature, 421 (2003), p. 823

[161] W.G. van der Wiel; S. De Franceschi; J.M. Elzerman; T. Fujisawa; S. Tarucha; L.P. Kouwenhoven Rev. Mod. Phys., 75 (2003) no. 1, pp. 1-22

[162] Y.R.P. Sortais; H. Marion; C. Tuchendler; A.M. Lance; M. Lamare; P. Fournet; C. Armellin; R. Mercier; G. Messin; A. Browaeys; P. Grangier Phys. Rev. A, 75 (2007)

[163] L. Borda; G. Zarand; P. Simon Phys. Rev. B, 72 (2005)

[164] J. Koch; et al.; A.A. Houck et al. Quantum Inf. Process., 76 (2007), p. 105

[165] R. Barends et al. Phys. Rev. Lett., 111 (2013)

[166] H.T. Mebrahtu; I.V. Borzenets; H. Zheng; Y.V. Bomze; A.I. Smirnov; S. Florens; H.U. Baranger; G. Finkelstein Nat. Phys., 9 (2013), p. 732

[167] C.-H. Chung; K. Le Hur; G. Finkelstein; M. Vojta; P. Woelfle Phys. Rev. B, 87 (2013)

[168] K. Le Hur Phys. Rev. B, 85 (2012) 140506(R)

[169] S. Camalet; P. Degiovanni; J. Schriefl; F. Delduc Europhys. Lett., 68 (2004) no. 37

[170] A. Dousse; L. Lanco; J. Suffczynski; E. Semenova; A. Miard; A. Lemaitre; I. Sagnes; C. Roblin; J. Bloch; P. Senellart Phys. Rev. Lett., 101 (2008)

[171] N.S. Williams; K. Le Hur; A.N. Jordan J. Phys. A, Math. Theor., 44 (2011)

[172] S. Braun; P. Ronzheimer; M. Schreiber; S.S. Hodgman; T. Rom; I. Bloch; U. Schneider Science, 339 (2013), pp. 52-55

[173] M. Schroer; M. Kolodrubetz; W. Kindel; M. Sandberg; J. Gao; M. Vissers; D. Pappas; A. Polkovnikov; K. Lehnert Phys. Rev. Lett., 113 (2014)

[174] P. Roushan; C. Neill; Y. Chen; M. Kolodrubetz; C. Quintana; N. Leung; M. Fang; R. Barends; B. Campbell; Z. Chen; B. Chiaro; A. Dunsworth; E. Jeffrey; J. Kelly; A. Megrant; J. Mutus; P.J.J. OMalley; D. Sank; A. Vainsencher; J. Wenner; T. White; A. Polkovnikov; A.N. Cleland; J.M. Martinis Nature, 515 (2014), pp. 241-244

[175] 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 Science, 318 (2007), p. 1889

[176] M. Aidelsburger; M. Lohse; C. Schweizer; M. Atala; J.T. Barreiro; S. Nascimbène; N.R. Cooper; I. Bloch; N. Goldman Nat. Phys., 11 (2015), pp. 162-166

[177] G. Jotzu; M. Messer; R. Desbuquois; M. Lebrat; T. Uehlinger; D. Greif; T. Esslinger Nature, 515 (2014), pp. 237-240

[178] N. Doiron-Leyraud; T. Szkopek; T. Pereg-Barnea; C. Proust; G. Gervais Phys. Rev. B, 91 (2015)

[179] K. Bennaceur; J. Guillemette; P.L. Lévesque; N. Cottenye; F. Mahvash; N. Hemsworth; A. Kumar; Y. Murata; S. Heun; M.O. Goerbig; C. Proust; M. Siaj; R. Martel; G. Gervais; T. Szkopek Phys. Rev. B, 92 (2015)

[180] Y. Zhang; Y.-W. Tan; H.L. Stormer; P. Kim Nature, 438 (2005), pp. 201-204

[181] C. Emary; T. Brandes Phys. Rev. E, 67 (2003)

[182] O. Scarlatella; M. Schiró | arXiv

[183] P. Xu; A. Holm Kiilerich; R. Blattmann; Y. Yu; S.-L. Zhu; K. Molmer Phys. Rev. A, 96 (2017)

[184] G. Goldstein; C. Aron; C. Chamon Phys. Rev. B, 92 (2015)

[185] P. Nalbach; S. Vishveshwara; A.A. Clerk Phys. Rev. B, 92 (2015)

[186] O. Viehmann; J. von Delft; F. Marquardt New J. Phys., 15 (2013)

[187] B. Neyenhuis; J. Smith; A.C. Lee; J. Zhang; P. Richerme; P.W. Hess; Z.-X. Gong; A.V. Gorshkov; C. Monroe | arXiv

[188] B. Yan; S.A. Moses; B. Gadway; J.P. Covey; K.R.A. Hazzard; A. Maria Rey; D.S. Jin; J. Ye Nature, 501 (2013), p. 521

[189] R. Barends et al. Nature, 534 (2016), p. 222

[190] H. Labuhn; D. Barredo; S. Ravets; S. de Léséleuc; T. Macrì; T. Lahaye; A. Browaeys Nature, 534 (2016), p. 667

[191] T.L. Nguyen, J.-M. Raimond, C. Sayrin, R. Cortinas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, T. Jolicoeur, M. Brune, Towards quantum simulation with circular Rydberg atoms, ArXiv e-prints, July 2017.

[192] J.A. Acebrón; L.L. Bonilla; C.J.P. Vicente; F. Ritort; R. Spigler Rev. Mod. Phys., 77 (2005), p. 137

[193] V. Flovik; F. Macia; E. Wahlström Sci. Rep., 6 (2016)

[194] F. Lesage; H. Saleur Phys. Rev. Lett., 80 (1998), p. 4370

[195] K. Saito; M. Wubs; S. Kohler; Y. Kayanuma; P. Hanggi Phys. Rev. B, 75 (2007)

[196] B. Damski Phys. Rev. Lett., 95 (2005)

[197] S. Hershfield Phys. Rev. Lett., 70 (1993), p. 2134

[198] P. Mehta; N. Andrei Phys. Rev. Lett., 96 (2006)

[199] B. Doyon Phys. Rev. Lett., 99 (2007)

[200] P. Dutt; J. Koch; J.E. Han; K. Le Hur Ann. Phys., 326 (2011), pp. 2963-2999

[201] L. Foini; L.F. Cugliandolo; A. Gambassi J. Stat. Mech. (2012)

[202] L. Foini; A. Gambassi; R. Konik; L.F. Cugliandolo | arXiv

[203] C. Monthus J. Stat. Mech. (2017)

[204] H. Li; F.D.M. Haldane Phys. Rev. Lett., 101 (2008)

[205] R. Thomale; A. Sterdyniak; N. Regnault; B.A. Bernevig Phys. Rev. Lett., 104 (2010)

[206] N. Lanatà; H.U.R. Strand; Y. Yao; G. Kotliar Phys. Rev. Lett., 113 (2014)

[207] R. Singh; J.H. Bardarson; F. Pollmann New J. Phys., 18 (2016)

[208] D.J. Luitz; N. Laflorencie; F. Alet Phys. Rev. B, 91 (2015)

[209] J.C. Budich; S. Diehl Phys. Rev. B, 91 (2015)

[210] A. Uhlmann Rep. Math. Phys., 24 (1986), p. 229

[211] J. Zhu; M. Shi; V. Vedral; X. Peng; D. Suter; J. Du EPL, 94 (2011)

[212] R.S. Whitney; Y. Gefen Phys. Rev. Lett., 90 (2003)

[213] N. Flüschner; D. Vogel; M. Tarnowski; B.S. Rem; D.S. Lühmann; M. Heyl; J.C. Budich; L. Mathey; K. Sengstock; C. Weitenberg | arXiv

[214] S.F. Caballero-Benitez; G. Mazzucchi; I.B. Mekhov Phys. Rev. A, 93 (2016)

[215] P. Strack; S. Sachdev Phys. Rev. Lett., 107 (2011)

[216] P. Nataf; M. Dogan; K. Le Hur Phys. Rev. A, 86 (2012)

[217] L. Perfetti; B. Sciolla; G. Biroli; C.J. van der Beek; C. Piovera; M. Wolf; T. Kampfrath Phys. Rev. Lett., 114 (2015)

[218] M. Sassetti; U. Weiss Phys. Rev. Lett., 65 (1990), p. 2262

[219] H. Shiba Prog. Theor. Phys., 54 (1975), p. 967

[220] R.A. Barankov; L.S. Levitov Phys. Rev. Lett., 96 (2006)

[221] G. Carleo; M. Troyer Science, 355 (2017), p. 602

[222] T. Fukuhara; A. Kantian; M. Endres; M. Cheneau; P. Schauss; S. Hild; D. Bellem; U. Schollwöck; T. Giamarchi; C. Gross; I. Bloch; S. Kuhr Nat. Phys., 9 (2013), p. 235

[223] M.P.A. Fisher; G. Grinstein; D.S. Fisher Phys. Rev. B, 40 (1989), pp. 546-570

[224] D. Jaksch; C. Bruder; J.I. Cirac; C.W. Gardiner; P. Zoller Phys. Rev. Lett., 81 (1998), p. 3108

[225] M. Greiner; O. Mandel; T. Esslinger; T.W. Hänsch; I. Bloch Nature, 415 (2002), pp. 39-44

[226] K. Le Hur; T.M. Rice Ann. Phys., 324 (2009), p. 1452

[227] J. Bauer; C. Salomon; E. Demler Phys. Rev. Lett., 111 (2013)

[228] T. Giamarchi; A.J. Millis Phys. Rev. B, 46 (1992), p. 9325

[229] G. Boéris; L. Gori; M.D. Hoogerland; A. Kumar; E. Lucioni; L. Tanzi; M. Inguscio; T. Giamarchi; C. D'Errico; G. Carleo; G. Modugno; L. Sanchez-Palencia Phys. Rev. A, 93 (2016) (Rapid Comm.)

[230] S. Rachel; N. Laflorencie; H.F. Song; K. Le Hur Phys. Rev. Lett., 108 (2012)

[231] H.F. Song; S. Rachel; C. Flindt; I. Klich; N. Laflorencie; K. Le Hur Phys. Rev. B, 85 (2012) (Editors' Suggestion)

[232] A. Petrescu; H.F. Song; S. Rachel; Z. Ristivojevic; C. Flindt; N. Laflorencie; I. Klich; N. Regnault; K. Le Hur J. Stat. Mech. (2014)

[233] N. Laflorencie Phys. Rep., 643 (2016), pp. 1-59

[234] J.F. Sherson; C. Weitenberg; M. Endres; M. Cheneau; I. Bloch; S. Kuhr Nature, 467 (2010), p. 68

[235] W.S. Bakr; J.I. Gillen; A. Peng; S. Fölling; M. Greiner Nature, 462 (2009), pp. 74-77

[236] B. Gadway; D. Pertot; J. Reeves; M. Vogt; D. Schneble Phys. Rev. Lett., 107 (2011)

[237] J. Billy; V. Josse; Z. Zuo; A. Bernard; B. Hambrecht; P. Lugan; D. Clément; L. Sanchez-Palencia; P. Bouyer; A. Aspect Nature, 453 (2008) no. 7197, pp. 891-894

[238] J-y. Choi; S. Hild; J. Zeiher; P. Schauss; A. Rubio-Abadal; T. Yefsah; V. Khemani; D.A. Huse; I. Bloch; C. Gross Science, 352 (2016), p. 1547

[239] S. Restrepo; J. Cerrillo; V.M. Bastidas; D.G. Angelakis; T. Brandes Phys. Rev. Lett., 117 (2016)

[240] E. Orignac; T. Giamarchi Phys. Rev. B, 64 (2001)

[241] A. Petrescu; K. Le Hur Phys. Rev. B, 91 (2015)

[242] M. Mancini; G. Pagano; G. Cappellini; L. Livi; M. Rider; J. Catani; C. Sias; P. Zoller; M. Inguscio; M. Dalmonte; L. Fallani, 2015 (ArXiv e-prints) | arXiv

[243] M. Atala; M. Aidelsburger; M. Lohse; J.T. Barreiro; B. Paredes; I. Bloch Nat. Phys., 10 (2014), pp. 588-593

[244] M. Lacki; H. Pichler; A. Sterdyniak; A. Lyras; V.E. Lembessis; O. Al-Dossary; J.C. Budich; P. Zoller Phys. Rev. A, 93 (2016)

[245] P. Roushan et al. Nat. Phys., 13 (2017), pp. 146-151

[246] J. Koch; A.A. Houck; K. Le Hur; S.M. Girvin Phys. Rev. A, 82 (2010)

[247] A. Petrescu; A.A. Houck; K. Le Hur Phys. Rev. A, 86 (2012)

[248] N. Goldman; J. Dalibard Phys. Rev. X, 4 (2014)

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

[250] S.M. Cronenwett; T.H. Oosterkamp; L.P. Kouwenhoven Science, 281 (1998), p. 540

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

[252] L.I. Glazman; M. Pustilnik New Directions in Mesoscopic Physics (Towards Nanoscience) (R. Fazio; V.F. Gantmakher; Y. Imry, eds.), Kluwer, Dordrecht, 2003, pp. 93-115

[253] O. Astafiev; A.M. Zagoskin; A.A. Abdumalikov; Yu.A. Pashkin; T. Yamamoto; K. Inomata; Y. Nakamura; J.S. Tsai Science, 327 (2010), pp. 840-843

[254] I.-C. Hoi; C.M. Wilson; G. Johansson; J. Lindkvist; B. Peropadre; T. Palomaki; P. Delsing New J. Phys., 15 (2013)

[255] T.A. Costi Phys. Rev. Lett., 80 (1998), p. 1038

[256] B. Sbierski; M. Hanl; A. Weichselbaum; H.E. Türeci; M. Goldstein; L.I. Glazman; J. von Delft; A. Imamoglu Phys. Rev. Lett., 111 (2013)

[257] A. Leclair; F. Lesage; S. Lukyanov; H. Saleur Phys. Lett. A, 235 (1997), pp. 203-208

[258] J.-T. Shen; S. Fan Phys. Rev. Lett., 98 (2007)

[259] P. Longo; P. Schmitteckert; K. Busch Phys. Rev. Lett., 104 (2010)

[260] V.I. Yudson; P. Reineker Phys. Rev. A, 78 (2008)

[261] M. Malekakhlagh; A. Petrescu; H.E. Türeci Phys. Rev. A, 94 (2016)

[262] R.M. Potok; I.G. Rau; H. Shtrikman; Y. Oreg; D. Goldhaber-Gordon; A.J. Keller; L. Peeters; C.P. Moca; I. Weymann; D. Mahalu; V. Umansky; G. Zaránd; D. Goldhaber-Gordon Nature, 446 (2007), pp. 237-240 (167–171)

[263] Z. Iftikhar; S. Jezouin; A. Anthore; U. Gennser; F.D. Parmentier; A. Cavanna; F. Pierre Nature, 526 (2015), p. 233

[264] M. Schiró; K. Le Hur Phys. Rev. B, 89 (2014)

[265] O. Dmytruk; M. Trif; C. Mora; P. Simon Phys. Rev. B, 93 (2016)

[266] A. Cottet; T. Kontos; B. Douçot Phys. Rev. B, 91 (2015)

[267] M.R. Delbecq; V. Schmitt; F.D. Parmentier; N. Roch; J.J. Viennot; G. Fève; B. Huard; C. Mora; A. Cottet; T. Kontos Phys. Rev. Lett., 107 (2011)

[268] 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 | arXiv

[269] M. Büttiker; A. Prêtre; H. Thomas Phys. Rev. Lett., 70 (1993), p. 4114

[270] J. Gabelli; G. Fève; J.-M. Berroir; B. Plaçais Rep. Prog. Phys., 75 (2012)

[271] S.E. Nigg; R. Lopez; M. Büttiker Phys. Rev. Lett., 97 (2006)

[272] C. Mora; K. Le Hur Nat. Phys., 6 (2010), p. 697

[273] K.A. Matveev Sov. Phys. JETP, 98 (1990), p. 1598

[274] K.A. Matveev Phys. Rev. B, 51 (1995), p. 1743

[275] K. Le Hur; G. Seelig Phys. Rev. B, 65 (2002)

[276] Y. Hamamoto; T. Jonckheere; T. Kato; T. Martin Phys. Rev. B, 81 (2010)

[277] Y. Etzioni; B. Horovitz; P. Le Doussal Phys. Rev. Lett., 106 (2011)

[278] M. Filippone; K. Le Hur; C. Mora Phys. Rev. Lett., 107 (2011)

[279] M. Filippone; K. Le Hur; C. Mora Phys. Rev. B, 88 (2013)

[280] P. Dutt; T.L. Schmidt; C. Mora; K. Le Hur Phys. Rev. B, 87 (2013)

[281] M. Filippone; C. Mora Phys. Rev. B, 86 (2012)

[282] P. Coleman; L. Ioffe; A.M. Tsvelik Phys. Rev. B, 52 (1995), p. 6611

[283] C. Mora; K. Le Hur Phys. Rev. B, 88 (2013)

[284] A. Golub; E. Grosfeld Phys. Rev. B, 86 (2012) 241105(R)

[285] T. Müller; R. Thomale; B. Trauzettel; E. Bocquillon; O. Kashuba | arXiv

[286] D. Litinski; P.W. Brouwer; M. Filippone | arXiv

[287] H. Yi; C.L. Kane; H. Yi Phys. Rev. B, 57 (1998)

[288] Y. Oreg; G. Refael; F. von Oppen Phys. Rev. Lett., 105 (2010)

[289] R.M. Lutchyn; J.D. Sau; S. Das Sarma Phys. Rev. Lett., 105 (2010)

[290] L. Herviou; K. Le Hur; C. Mora Phys. Rev. B (2016) (Editor's Suggestion)

[291] B. Béri Phys. Rev. Lett., 110 (2013)

[292] K. Michaeli; L. Aviad Landau; E. Sela; L. Fu | arXiv

[293] B. Beri; N.R. Cooper Phys. Rev. Lett., 109 (2012)

[294] A. Altland; R. Egger Phys. Rev. Lett., 110 (2013)

[295] E. Eriksson; C. Mora; A. Zazunov; R. Egger Phys. Rev. Lett., 113 (2014)

[296] J. Dalibard; F. Gerbier; G. Juzeliünas; P. Öhberg Rev. Mod. Phys., 83 (2011), p. 1523

[297] X.-Y. Feng; G.-M. Zhang; T. Xiang Phys. Rev. Lett., 98 (2007)

[298] K. Le Hur; A. Soret; F. Yang (to be published in Phys. Rev. B) | arXiv

[299] T.A. Sedrakyan; L.I. Glazman; A. Kamenev Phys. Rev. Lett., 114 (2015)

[300] S.M. Albrecht; A.P. Higginbotham; M. Madsen; F. Kuemmeth; T.S. Jespersen; J. Nygard; P. Krogstrup; C.M. Marcus Nature, 531 (2016), p. 206

[301] L.A. Landau; E. Sela | arXiv

[302] A. Zazunov; F. Buccheri; P. Sodano; R. Egger | arXiv

[303] J.J. Viennot; M.R. Delbecq; L.E. Bruhat; M.C. Dartiailh; M. Desjardins; M. Baillergeau; A. Cottet; T. Kontos C. R. Physique, 17 (2016) no. 7, pp. 705-717

[304] B. Sothmann; R. Sánchez; A.N. Jordan Nanotechnology, 26 (2015)

[305] L. Henriet; A.N. Jordan; K. Le Hur Phys. Rev. B, 92 (2015)

[306] U.C. Mendes; C. Mora Phys. Rev. B, 93 (2016)

[307] G.-W. Deng et al. Phys. Rev. Lett., 115 (2015)

[308] G.-W. Deng et al. Nano Lett., 15 (2015), p. 6620

[309] L. Borda; G. Zarand; W. Hofstetter; B.I. Halperin; J. von Delft Phys. Rev. Lett., 90 (2003)

[310] A.J. Keller et al. Nat. Phys., 10 (2014), pp. 145-150

[311] C. Mora; P. Vitushinsky; X. Leyronas; A.A. Clerk; K. Le Hur Phys. Rev. B, 80 (2009) (Editors' Suggestion)

[312] A. Rosch; J. Kroha; P. Wölfle Phys. Rev. Lett., 87 (2001)

[313] K. Le Hur; P. Simon; D. Loss Phys. Rev. B, 75 (2007)

[314] H.-P. Breuer; F. Petruccione The Theory of Open Quantum Systems, 2002

[315] P. Donohue; T. Giamarchi Phys. Rev. B, 63 (2001)

[316] A. Tokuno; A. Georges New J. Phys., 16 (2014)

[317] F. Crépin; N. Laflorencie; G. Roux; P. Simon Phys. Rev. B, 84 (2011)

[318] M. Piraud; F. Heidrich-Meisner; I.P. McCulloch; S. Greschner; T. Vekua; U. Schollwock Phys. Rev. B, 91 (2015)

[319] S. Greschner; M. Piraud; F. Heidrich-Meisner; I.P. McCulloch; U. Schollwock; T. Vekua Phys. Rev. Lett., 115 (2015)

[320] S. Greschner, M. Piraud, F. Heidrich-Meisner, I.P. McCulloch, U. Schollwock, T. Vekua, 2016, ArXiv e-prints.

[321] A. Petrescu; M. Piraud; G. Roux; I.P. McCulloch; K. Le Hur Phys. Rev. B, 96 (2017)

[322] R.B. Laughlin Phys. Rev. Lett., 50 (1983), p. 1395

[323] F. Grusdt; M. Honing Phys. Rev. A, 90 (2014)

[324] T. Matsubara; H. Matsuda Prog. Theor. Phys., 16 (1956), p. 569

[325] E.G. Batyev; L.S. Braginskii Sov. Phys. JETP, 60 (1984)

[326] A.B. Kuklov; B.V. Svistunov Phys. Rev. Lett., 90 (2003)

[327] E. Altman; W. Hofstetter; E. Demler; M.D. Lukin New J. Phys., 5 (2003), p. 113

[328] L.-M. Duan; E. Demler; M.D. Lukin Phys. Rev. Lett., 91 (2003)

[329] A. Isacsson; M.-C. Cha; K. Sengupta; S.M. Girvin Phys. Rev. B, 72 (2005)

[330] A. Dhar; M. Maji; T. Mishra; R.V. Pai; S. Mukerjee; A. Paramekanti; A. Dhar; T. Mishra; M. Maji; R.V. Pai; S. Mukerjee; A. Paramekanti Phys. Rev. B, 85 (2012)

[331] M. Calvanese Strinati; E. Cornfeld; D. Rossini; S. Barbarino; M. Dalmonte; R. Fazio; E. Sela; L. Mazza | arXiv

[332] R.N. Palmer; D. Jaksch Phys. Rev. Lett., 96 (2003)

[333] A.S. Sorensen; E. Demler; M.D. Lukin Phys. Rev. Lett., 94 (2005)

[334] M. Hafezi; A.S. Sorensen; E. Demler; M.D. Lukin Phys. Rev. A, 76 (2007)

[335] L. Hormozi; G. Moller; S.H. Simon Phys. Rev. Lett., 108 (2012)

[336] N.R. Cooper; J. Dalibard Phys. Rev. Lett., 110 (2013)

[337] N.Y. Yao; A.V. Gorshkov; C.R. Laumann; A.M. Läuchli; J. Ye; M.D. Lukin Phys. Rev. Lett., 110 (2013)

[338] A. Sterdyniak; B.A. Bernevig; N.R. Cooper; N. Regnault Phys. Rev. B, 91 (2015)

[339] M. Hafezi; M.D. Lukin; J.M. Taylor New J. Phys., 15 (2013)

[340] E. Kapit; M. Hafezi; S.H. Simon Phys. Rev. X, 4 (2014)

[341] J. Cho; D.G. Angelakis; S. Bose Phys. Rev. Lett., 101 (2008)

[342] A.L.C. Hayward; A.M. Martin; A.D. Greentree Phys. Rev. Lett., 108 (2012)

[343] C. Noh; D.G. Angelakis Rep. Prog. Phys., 80 (2017) | arXiv

[344] B.M. Anderson; R. Ma; C. Owens; D.I. Schuster; J. Simon Phys. Rev. X, 6 (2016)

[345] C.L. Kane; R. Mukhopadhyay; T.C. Lubensky Phys. Rev. Lett., 88 (2002)

[346] J.C.Y. Teo; C.L. Kane Phys. Rev. B, 89 (2014)

[347] T. Neupert; C. Chamon; C. Mudry; R. Thomale Phys. Rev. B, 90 (2014)

[348] M. Lohse; C. Schweizer; O. Zilberberg; M. Aidelsburger; I. Bloch Nat. Phys., 12 (2016), p. 350

[349] S. Nakajima; T. Tomita; S. Taie; T. Ichinose; H. Ozawa; L. Wang; M. Troyer; Y. Takahashi Nat. Phys., 12 (2016), pp. 296-300

[350] J. Tangpanitanon; V.M. Bastidas; S. Al-Assam; P. Roushan; D. Jaksch; D.G. Angelakis Phys. Rev. Lett., 117 (2016)

Cited by Sources:

Comments - Policy