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Cited by 568Strong Light-Matter InteractionsAdvanced Thermodynamics and Statistical MechanicsQuantum many-body systems

Keldysh field theory for driven open quantum systems

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Sieberer, L M, Buchhold, M, Diehl, S·2016·Reports on Progress in Physics
DOI 10.1088/0034-4885/79/9/096001
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Abstract

Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven–dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.

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  • Fluids of light in cavity configurations are typically driven-dissipative, with the state determined by a dynamical balance of pumping and losses rather than thermal equilibrium.

    “fluids of light in cavity configurations are typically characterized by a driven-dissipative nature, where the state of the fluid is not determined by a thermal equilibrium condition, but rather by a dynamical balance of pumping and losses [8,9].”

    From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [9]

  • For the intermediate two-dimensional case, the Berezinskii-Kosterlitz-Thouless transition typical of equilibrium systems may be replaced by Kardar-Parisi-Zhang physics.

    “Even more subtle features have been pointed out for the intermediate two-dimensional case where the Berezinskii-Kosterlitz-Thouless transition typical of equilibrium systems [128,129] may be replaced by a Kardar-Parisi-Zhang (KPZ) physics [130][131][132].”

    From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [131]

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  1. Hohenberg P and Halperin B 1977 Theory of dynamic critical phenomena Rev. Mod. Phys. 49 435-79 · DOI
  2. Halpin-Healy T and Zhang Y-C 1995 Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics Phys. Rep. 254 215-414 · DOI
  3. Jensen H J 1998 Self Organized Criticality (Cambridge: Cambridge University Press)
  4. Hinrichsen H 2000 Non-equilibrium critical phenomena and phase transitions into absorbing states Adv. Phys. 49 815-958 · DOI
  5. Täuber U C 2014 Critical Dynamics: a Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge: Cambridge University Press)
  6. Bloch I, Dalibard J and Zwerger W 2008 Many-body physics with ultracold gases Rev. Mod. Phys. 80 885-964 · DOI · Paper page
  7. Baumann K, Guerlin C, Brennecke F and Esslinger T 2010 Dicke quantum phase transition with a superfluid gas in an optical cavity Nature 464 1301-6 · DOI · Paper page
  8. Ritsch H, Domokos P, Brennecke F and Esslinger T 2013 Cold atoms in cavity-generated dynamical optical potentials Rev. Mod. Phys. 85 553-601 · DOI
  9. Schausz P, Cheneau M, Endres M, Fukuhara T, Hild S, Omran A, Pohl T, Gross C, Kuhr S and Bloch I 2012 Observation of spatially ordered structures in a two-dimensional Rydberg gas Nature 491 87-91 · DOI
  10. Kasprzak J et al 2006 Bose-Einstein condensation of exciton polaritons Nature 443 409-14 Rep. Prog. Phys. 79 (2016) 096001 · DOI
  11. Carusotto I and Ciuti C 2013 Quantum fluids of light Rev. Mod. Phys. 85 299-366 · DOI
  12. Underwood D L, Shanks W E, Koch J and Houck A A 2012 Low-disorder microwave cavity lattices for quantum simulation with photons Phys. Rev. A 86 023837 · DOI · Paper page
  13. Britton J W, Sawyer B C, Keith A C, Joseph Wang C-C, Freericks J K, Uys H, Biercuk M J and Bollinger J J 2012 Engineered two-dimensional Ising interactions in a trapped- ion quantum simulator with hundreds of spins Nature 484 489-92 · DOI · Paper page
  14. Lechner W and Zoller P 2013 From classical to quantum glasses with ultracold polar molecules Phys. Rev. Lett. 111 185306 · DOI
  15. Altman E, Sieberer L M, Chen L, Diehl S and Toner J 2015 Two-dimensional superfluidity of exciton polaritons requires strong anisotropy Phys. Rev. X 5 011017 · DOI · Paper page
  16. Piazza F and Strack P 2014 Umklapp superradiance with a collisionless quantum degenerate fermi gas Phys. Rev. Lett. 112 143003 · DOI
  17. Keeling J, Bhaseen M J and Simons B D 2014 Fermionic superradiance in a transversely pumped optical cavity Phys. Rev. Lett. 112 143002 · DOI
  18. Kollath C, Sheikhan A, Wolff S and Brennecke F 2016 Ultracold fermions in a cavity-induced artificial magnetic field Phys. Rev. Lett. 116 060401 · DOI
  19. Raftery J, Sadri D, Schmidt S, Türeci H E and Houck A A 2014 Observation of a dissipation-induced classical to quantum transition Phys. Rev. X 4 031043 · DOI
  20. Hartmann M J, Brandão F G S L and Plenio M B 2008 Quantum many-body phenomena in coupled cavity arrays Laser Photonics Rev. 2 527-56 · DOI
  21. Dalla Torre E G, Demler E, Giamarchi T and Altman E 2010 Quantum critical states and phase transitions in the presence of non-equilibrium noise Nat. Phys. 6 806-10 · DOI
  22. Sieberer L M, Huber S D, Altman E and Diehl S 2013 Dynamical critical phenomena in driven-dissipative systems Phys. Rev. Lett. 110 195301 · DOI
  23. van Horssen M and Garrahan J P 2015 Open quantum reaction-diffusion dynamics: absorbing states and relaxation Phys. Rev. E 91 032132 · DOI
  24. Marino J and Diehl S 2016 Driven Markovian quantum criticality Phys. Rev. Lett. 116 070407 · DOI
  25. Hsiang J-T and Hu B L 2015 Nonequilibrium steady state in open quantum systems: influence action, stochastic equation and power balance Ann. Phys. 362 139-69 · DOI
  26. Rey A M, Hu B L, Calzetta E, Roura A and Clark C W 2004 Nonequilibrium dynamics of optical-lattice-loaded Bose-Einstein-condensate atoms: beyond the Hartree- Fock-Bogoliubov approximation Phys. Rev. A 69 033610 · DOI
  27. Berges J, Borsányi Sz and Wetterich C 2004 Prethermalization Phys. Rev. Lett. 93 142002 · DOI
  28. Calabrese P and Cardy J 2006 Time dependence of correlation functions following a quantum quench Phys. Rev. Lett. 96 136801 · DOI · Paper page
  29. Mitra A and Giamarchi T 2011 Mode-coupling-induced dissipative and thermal effects at long times after a quantum quench Phys. Rev. Lett. 107 150602 · DOI
  30. Koghee S and Wouters M 2014 Dynamical Casimir emission from polariton condensates Phys. Rev. Lett. 112 036406 · DOI
  31. Carusotto I, Balbinot R, Fabbri A and Recati A 2010 Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates Eur. Phys. J. D 56 391-404 · DOI
  32. Larré P-É and Carusotto I 2015 Propagation of a quantum fluid of light in a cavityless nonlinear optical medium: general theory and response to quantum quenches Phys. Rev. A 92 043802 · DOI
  33. Gring M, Kuhnert M, Langen T, Kitagawa T, Rauer B, Schreitl M, Mazets I, Adu Smith D, Demler E and Schmiedmayer J 2012 Relaxation and prethermalization in an isolated quantum system Science 337 1318-22 · DOI
  34. Trotzky S, Chen Y-A, Flesch A, McCulloch I P, Schollwöck U, Eisert J and Bloch I 2012 Probing the relaxation towards equilibrium in an isolated strongly correlated one- dimensional bose gas Nat. Phys. 8 325-30 · DOI · Paper page
  35. Meinert F, Mark M J, Kirilov E, Lauber K, Weinmann P, Daley A J and Nägerl H-C 2013 Quantum quench in an atomic one-dimensional ising chain Phys. Rev. Lett. 111 053003 · DOI
  36. Hung C-L, Gurarie V and Chin C 2013 From cosmology to cold atoms: observation of sakharov oscillations in a quenched atomic superfluid Science 341 1213-5 · DOI
  37. Jaskula J-C, Partridge G B, Bonneau M, Lopes R, Ruaudel J, Boiron D and Westbrook C I 2012 Acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate Phys. Rev. Lett. 109 220401 · DOI
  38. Nardin G, Lagoudakis K G, Wouters M, Richard M, Baas A, André R, Dang L S, Pietka B and Deveaud-Plédran B 2009 Dynamics of long-range ordering in an exciton-polariton condensate Phys. Rev. Lett. 103 256402 · DOI
  39. Buchhold M and Diehl S 2015 Nonequilibrium universality in the heating dynamics of interacting Luttinger liquids Phys. Rev. A 92 013603 · DOI
  40. Buchhold M and Diehl S 2015 Kinetic theory for interacting Luttinger liquids Eur. Phys. J. D 69 1-20 · DOI
  41. Poletti D, Barmettler P, Georges A and Kollath C 2013 Emergence of glasslike dynamics for dissipative and strongly interacting bosons Phys. Rev. Lett. 111 195301 · DOI
  42. Cai Z and Barthel T 2013 Algebraic versus exponential decoherence in dissipative many-particle systems Phys. Rev. Lett. 111 150403 · DOI
  43. Schachenmayer J, Pollet L, Troyer M and Daley A J 2014 Spontaneous emission and thermalization of cold bosons in optical lattices Phys. Rev. A 89 011601 · DOI
  44. Daley A J 2014 Quantum trajectories and open many-body quantum systems Adv. Phys. 63 77-149 · DOI
  45. Olmos B, Lesanovsky I and Garrahan J P 2012 Facilitated spin models of dissipative quantum glasses Phys. Rev. Lett. 109 020403 · DOI
  46. Marcuzzi M, Levi E, Li W, Garrahan J P, Olmos B and Lesanovsky I 2014 Emergence of directed percolation in the dynamics of dissipative Rydberg gases arXiv:1411.7984 · arXiv
  47. Lang J and Piazza F 2016 Critical relaxation with overdamped quasi-particles in driven-dissipative systems arXiv:1602.05102 · arXiv
  48. Poyatos J F, Cirac J I and Zoller P 1996 Quantum reservoir engineering with laser cooled trapped ions Phys. Rev. Lett. 77 4728-31 · DOI
  49. Bose S, Knight P L, Plenio M B and Vedral V 1999 Proposal for teleportation of an atomic state via cavity decay Phys. Rev. Lett. 83 5158-61 · DOI · Paper page
  50. Diehl S, Micheli A, Kantian A, Kraus B, Büchler H P and Zoller P 2008 Quantum states and phases in driven open quantum systems with cold atoms Nat. Phys. 4 878-83 · DOI
  51. Verstraete F, Wolf M M and Ignacio J 2009 Quantum computation and quantum-state engineering driven by dissipation Nat. Phys. 5 633-6 · DOI · Paper page
  52. Weimer H, Müller M, Lesanovsky I, Zoller P and Büchler H P 2010 A Rydberg quantum simulator Nat. Phys. 6 382-8 · DOI · Paper page
  53. Krauter H, Muschik C A, Jensen K, Wasilewski W, Petersen J M, Ignacio Cirac J and Polzik E S 2011 Entanglement generated by dissipation and steady state entanglement of two macroscopic objects Phys. Rev. Lett. 107 080503 · DOI
  54. Barreiro J T, Müller M, Schindler P, Nigg D, Monz T, Chwalla M, Hennrich M, Roos C F, Zoller P and Blatt R 2011 An open-system quantum simulator with trapped ions Nature 470 486-91 · DOI · Paper page
  55. Schindler P, Muller M, Nigg D, Barreiro J T, Martinez E A, Hennrich M, Monz T, Diehl S, Zoller P and Blatt R 2013 Quantum simulation of dynamical maps with trapped ions Nat. Phys. 9 361-7 · DOI
  56. Eisert J and Prosen T 2010 Noise-driven quantum criticality arXiv:1012.5013 · arXiv
  57. Kastoryano M J, Reiter F and Sørensen A S 2011 Dissipative preparation of entanglement in optical cavities Phys. Rev. Lett. 106 090502 · DOI
  58. Horstmann B, Ignacio Cirac J and Giedke G 2013 Noise- driven dynamics and phase transitions in fermionic systems Phys. Rev. A 87 012108 · DOI
  59. Höning M, Moos M and Fleischhauer M 2012 Critical exponents of steady-state phase transitions in fermionic lattice models Phys. Rev. A 86 013606 · DOI
  60. Lang N and Büchler H P 2015 Exploring quantum phases by driven dissipation Phys. Rev. A 92 012128 · DOI
  61. Kitaev A 2006 Anyons in an exactly solved model and beyond Ann. Phys. 321 2-111 · DOI · Paper page
  62. Hasan M Z and Kane C L 2010 Colloquium: Topological insulators Rev. Mod. Phys. 82 3045-67 · DOI · Paper page
  63. Diehl S, Rico E, Baraand M A and Zoller P 2011 Topology by dissipation in atomic quantum wires Nat. Phys. 7 971-7 · DOI
  64. Bardyn C-E, Baranov M A, Rico E, Imamoglu A, Zoller P and Diehl S 2012 Majorana modes in driven-dissipative atomic superfluids with a zero Chern number Phys. Rev. Lett. 109 130402 · DOI
  65. Budich J C, Zoller P and Diehl S 2015 Dissipative preparation of Chern insulators Phys. Rev. A 91 042117 · DOI
  66. Kardar M, Parisi G and Zhang Y-C 1986 Dynamic scaling of growing interfaces Phys. Rev. Lett. 56 889-92 · DOI
  67. Poletti D, Bernier J-S, Georges A and Kollath C 2012 Interaction-induced impeding of decoherence and anomalous diffusion Phys. Rev. Lett. 109 045302 · DOI
  68. Lesanovsky I and Garrahan J P 2013 Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases Phys. Rev. Lett. 111 215305 · DOI
  69. Lesanovsky I and Garrahan J P 2014 Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation Phys. Rev. A 90 011603 · DOI
  70. Olmos B, Lesanovsky I and Garrahan J P 2014 Out-of- equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics Phys. Rev. E 90 042147 · DOI
  71. Diehl S, Yi W, Daley A J and Zoller P 2010 Dissipation- induced d-wave pairing of fermionic atoms in an optical lattice Phys. Rev. Lett. 105 227001 · DOI
  72. Dalibard J, Castin Y and Mølmer K 1992 Wave-function approach to dissipative processes in quantum optics Phys. Rev. Lett. 68 580-3 · DOI
  73. Plenio M B and Knight P L 1998 The quantum-jump approach to dissipative dynamics in quantum optics Rev. Mod. Phys. 70 101-44 · DOI · Paper page
  74. Gardiner C W and Zoller P 2000 Quantum Noise (Springer Series in Synergetics vol 56) 2nd edn (Berlin: Springer)
  75. Breuer H-P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
  76. Carusotto I and Ciuti C 2005 Spontaneous microcavity- polariton coherence across the parametric threshold: quantum Monte Carlo studies Phys. Rev. B 72 125335 · DOI · Paper page
  77. Goldenfeld N 1992 Lectures on Phase Transitions and the Renormalization Group (Frontiers in Physics Perseus Books Reading) (Reading, MA: Addison-Wesley)
  78. Cardy J 1996 Scaling and Renormalization in Statistical Physics (Cambridge Lecture Notes in Physics) (Cambridge: Cambridge University Press)
  79. Zinn-Justin J 2002 Quantum Field Theory and Critical Phenomena (International Series of Monographs on Physics vol 113) 4th edn (Oxford: Oxford University Press)
  80. Daley A J, Taylor J M, Diehl S, Baraand M 2009 Atomic three-body loss as a dynamical three-body interaction Phys. Rev. Lett. 102 040402 · DOI
  81. Bernier J-S, Barmettler P, Poletti D and Kollath C 2013 Emergence of spatially extended pair coherence through incoherent local environmental coupling Phys. Rev. A 87 063608 · DOI
  82. Bonnes L, Charrier D and Läuchli A M 2014 Dynamical and steady-state properties of a Bose-Hubbard chain with bond dissipation: a study based on matrix product operators Phys. Rev. A 90 033612 · DOI
  83. Bonnes L and Läuchli A M 2014 Superoperators versus trajectories for matrix product state simulations of open quantum system: a case study (arXiv:1411.4831) · arXiv
  84. Schwinger J 1961 Brownian motion of a quantum oscillator J. Math. Phys. 2 407 · DOI
  85. Schwinger J 1960 Field theory of unstable particles Ann. Phys. 9 169-93 · DOI
  86. Mahanthappa K 1962 Multiple production of photons in quantum electrodynamics Phys. Rev. 126 329-40 · DOI
  87. Bakshi P M and Mahanthappa K T 1963 Expectation value formalism in quantum field theory. I J. Math. Phys. 4 1 · DOI
  88. Bakshi P M and Mahanthappa K T 1963 Expectation value formalism in quantum field theory. II J. Math. Phys. 4 12 · DOI
  89. Li A C Y, Petruccione F and Koch J 2015 Resummation for nonequilibrium perturbation theory and application to open quantum lattices arXiv:1511.01551 · arXiv
  90. Degenfeld-Schonburg P, Navarrete-Benlloch C and Hartmann M J 2015 Self-consistent projection operator theory in nonlinear quantum optical systems: a case study on degenerate optical parametric oscillators Phys. Rev. A 91 053850 · DOI
  91. Weimer H 2015 Variational principle for steady states of dissipative quantum many-body systems Phys. Rev. Lett. 114 040402 · DOI
  92. Finazzi S, Le Boit A, Storme F, Baksic A and Ciuti C 2015 Corner-space renormalization method for driven- dissipative two-dimensional correlated systems Phys. Rev. Lett. 115 080604 · DOI
  93. Kamenev A 2011 Field Theory of Non-Equilibrium Systems (Cambridge: Cambridge University Press)
  94. Calzetta E A and Hu B-L B 2008 Nonequilibrium Quantum Field Theory (Cambridge: Cambridge University Press)
  95. Jarzynski C 1997 Nonequilibrium equality for free energy differences Phys. Rev. Lett. 78 2690-3 · DOI
  96. Jarzynski C 1997 Equilibrium free-energy differences from nonequilibrium measurements: a master-equation approach Phys. Rev. E 56 5018-35 · DOI
  97. Crooks G E 1999 Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences Phys. Rev. E 60 2721-6 · DOI
  98. Cardy J 1996 Renormalisation group approach to reaction- diffusion problems arXiv:cond-mat/9607163 · arXiv
  99. Doi M 1976 Second quantization representation for classical many-particle system J. Phys. A. Math. Gen. 9 1465-77 · DOI
  100. Peliti L 1985 Path integral approach to birth-death processes on a lattice J. Phys. 46 1469-83 · DOI
  101. Diehl S, Tomadin A, Micheli A, Fazio R and Zoller P 2010 Dynamical phase transitions and instabilities in open atomic many-body systems Phys. Rev. Lett. 105 015702 · DOI
  102. Sachdev S 2011 Quantum Phase Transitions 2nd edn (Cambridge: Cambridge University Press)
  103. Dalla Torre E G, Diehl S, Lukin M, Sachdev S and Strack P 2013 Keldysh approach for nonequilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities Phys. Rev. A 87 023831 · DOI · Paper page
  104. Buchhold M, Strack P, Sachdev S and Diehl S 2013 Dicke- model quantum spin and photon glass in optical cavities: nonequilibrium theory and experimental signatures Phys. Rev. A 87 063622 · DOI
  105. Maghrebi M F and Gorshkov A V 2016 Nonequilibrium many-body steady states via Keldysh formalism Phys. Rev. B 93 014307 · DOI
  106. Piazza F and Strack P 2014 Quantum kinetics of ultracold fermions coupled to an optical resonator Phys. Rev. A 90 043823 · DOI
  107. Bernier J-S, Poletti D and Kollath C 2014 Dissipative quantum dynamics of fermions in optical lattices: a slave- spin approach Phys. Rev. B 90 205125 · DOI
  108. Mabuchi H and Doherty A C 2002 Cavity quantum electrodynamics: coherence in context Science 298 1372-7 · DOI
  109. Hood C J, Lynn T W, Doherty A C, Parkins A S and Kimble H J 2000 The atom-cavity microscope: single atoms bound in orbit by single photons Science 287 1447-53 · DOI
  110. Nagy D, Kónya G, Szirmai G and Domokos P 2010 Dicke- model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity Phys. Rev. Lett. 104 130401 · DOI
  111. Baumann K, Mottl R, Brennecke F and Esslinger T 2011 Exploring symmetry breaking at the dicke quantum phase transition Phys. Rev. Lett. 107 140402 · DOI
  112. Maschler C and Ritsch H 2005 Cold atom dynamics in a quantum optical lattice potential Phys. Rev. Lett. 95 260401 · DOI
  113. Öztop B, Bordyuh M, Müstecaplolu Ö E and Türeci H E 2012 Excitations of optically driven atomic condensate in a cavity: theory of photodetection measurements New J. Phys. 14 085011 · DOI
  114. Kulkarni M, Öztop B and Türeci H E 2013 Cavity-mediated near-critical dissipative dynamics of a driven condensate Phys. Rev. Lett. 111 220408 · DOI
  115. Landig R, Brennecke F, Mottl R, Donner T and Esslinger T 2015 Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition Nat. Commun. 6 7046 · DOI
  116. Brennecke F, Mottl R, Baumann K, Landig R, Donner T and Esslinger T 2013 Real-time observation of fluctuations at the driven-dissipative Dicke phase transition Proc. Natl Acad. Sci. USA 110 11763-7 · DOI
  117. Hepp K and Lieb E H 1973 On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model Ann. Phys. 76 360-404 · DOI
  118. Wang Y K and Hioe F T 1973 Phase transition in the Dicke model of superradiance Phys. Rev. A 7 831-6 · DOI
  119. Emary C and Brandes T 2003 Chaos and the quantum phase transition in the Dicke model Phys. Rev. E 67 066203 · DOI
  120. Dimer F, Estienne B, Parkins A S and Carmichael H J 2007 Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system Phys. Rev. A 75 013804 · DOI
  121. Murch K W, Moore K L, Gupta S and Stamper-Kurn D M 2008 Observation of quantum-measurement backaction with an ultracold atomic gas Nat. Phys. 4 561-4 · DOI
  122. Strack P and Sachdev S 2011 Dicke quantum spin glass of atoms and photons Phys. Rev. Lett. 107 277202 · DOI
  123. Angelakis D G, Santos M F and Bose S 2007 Photon- blockade-induced Mott transitions and XY spin models in coupled cavity arrays Phys. Rev. A 76 031805 · DOI · Paper page
  124. Hartmann M J, Brandao F G S L and Plenio M B 2006 Strongly interacting polaritons in coupled arrays of cavities Nat. Phys. 2 849-55 · DOI · Paper page
  125. Schmidt S and Koch J 2013 Circuit QED lattices: towards quantum simulation with superconducting circuits Ann. Phys. 525 395-412 · DOI
  126. Schiró M, Bordyuh M, Öztop B and Türeci H E 2013 Quantum phase transition of light in the Rabi-Hubbard model J. Phys. B: At. Mol. Opt. Phys. 46 224021 · DOI
  127. Schiró M, Bordyuh M, Oztop B and Türeci H E 2012 Phase transition of light in cavity QED lattices Phys. Rev. Lett. 109 053601 · DOI
  128. Schiró M, Joshi C, Bordyuh M, Fazio R, Keeling J and Türeci H E 2016 Exotic attractors of the non-equilibrium Rabi-Hubbard model Phys. Rev. Lett. 116 143603 · DOI
  129. Zou L J, Marcos D, Diehl S, Putz S, Schmiedmayer J, Majer J and Rabl P 2014 Implementation of the Dicke lattice model in hybrid quantum system arrays Phys. Rev. Lett. 113 023603 · DOI
  130. Ruiz-Rivas J, del Valle E, Gies C, Gartner P and Hartmann M J 2014 Spontaneous collective coherence in driven dissipative cavity arrays Phys. Rev. A 90 033808 · DOI
  131. Marcos D, Tomadin A, Diehl S and Rabl P 2012 Photon condensation in circuit quantum electrodynamics by engineered dissipation New J. Phys. 14 055005 · DOI
  132. Tomadin A and Fazio R 2010 Many-body phenomena in QED-cavity arrays J. Opt. Soc. Am. B 27 A130-6 · DOI
  133. Kepesidis K V and Hartmann M J 2012 Bose-Hubbard model with localized particle losses Phys. Rev. A 85 063620 · DOI
  134. Le Boité A, Orso G and Ciuti C 2013 Steady-state phases and tunneling-induced instabilities in the driven dissipative Bose-Hubbard model Phys. Rev. Lett. 110 233601 · DOI
  135. Jin J, Rossini D, Leib M, Hartmann M J and Fazio R 2014 Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities Phys. Rev. A 90 023827 · DOI
  136. Le Boité A, Orso G and Ciuti C 2014 Bose-Hubbard model: relation between driven-dissipative steady states and equilibrium quantum phases Phys. Rev. A 90 063821 · DOI
  137. Biella A, Mazza L, Carusotto I, Rossini D and Fazio R 2015 Photon transport in a dissipative chain of nonlinear cavities Phys. Rev. A 91 053815 · DOI
  138. Deng H, Haug H and Yamamoto Y 2010 Exciton-polariton Bose-Einstein condensation Rev. Mod. Phys. 82 1489-537 · DOI
  139. Byrnes T, Kim N Y and Yamamoto Y 2014 Exciton-polariton condensates Nat. Phys. 10 803-13 · DOI
  140. Keeling J, Szymańska M H and Littlewood P B 2010 Keldysh Green's function approach to coherence in a non-equilibrium steady state: connecting Bose-Einstein condensation and lasing Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures (NanoScience and Technology ed G Slavcheva and P Roussignol) (Berlin: Springer)
  141. Szymańska M H, Keeling J and Littlewood P B 2012 Non- equilibrium Bose-Einstein condensation in a dissipative environment (arXiv:1206.1784) · arXiv
  142. Klaers J, Schmitt J, Vewinger F and Weitz M 2010 Bose- Einstein condensation of photons in an optical microcavity Nature 468 545-8 · DOI
  143. Demokritov S O, Demidov V E, Dzyapko O, Melkov G A, Serga A A, Hillebrands B and Slavin A N 2006 Bose- Einstein condensation of quasi-equilibrium magnons at room temperature under pumping Nature 443 430-3 · DOI
  144. Alloing M, Beian M, Lewenstein M, Fuster D, González Y, González L, Combescot R, Combescot M and Dubin F 2014 Evidence for a bose-einstein condensate of excitons Europhys. Lett. 107 10012 · DOI
  145. Falkenau M, Volchkov V V, Rührig J, Griesmaier A and Pfau T 2011 Continuous loading of a conservative potential trap from an atomic beam Phys. Rev. Lett. 106 163002 · DOI
  146. Mewes M-O, Andrews M R, Kurn D M, Durfee D S, Townsend C G and Ketterle W 1997 Output coupler for Bose-Einstein condensed atoms Phys. Rev. Lett. 78 582-5 · DOI
  147. Robins N P, Figl C, Jeppesen M, Dennis G R and Close J D 2008 A pumped atom laser Nat. Phys. 4 731-6 · DOI
  148. Robins N P, Altin P A, Debs J E and Close J D 2013 Atom lasers: production, properties and prospects for precision inertial measurement Phys. Rep. 529 265-96 · DOI
  149. Imamoglu A, Ram R J, Pau S and Yamamoto Y 1996 Nonequilibrium condensates and lasers without inversion: exciton-polariton lasers Phys. Rev. A 53 4250-3 · DOI
  150. Wouters M and Carusotto I 2007 Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons Phys. Rev. Lett. 99 140402 · DOI
  151. Wouters M and Carusotto I 2010 Superfluidity and critical velocities in nonequilibrium Bose-Einstein condensates Phys. Rev. Lett. 105 020602 · DOI
  152. Ciuti C and Carusotto I 2006 Input-output theory of cavities in the ultrastrong coupling regime: the case of time- independent cavity parameters Phys. Rev. A 74 033811 · DOI
  153. Chiocchetta A and Carusotto I 2014 Quantum Langevin model for nonequilibrium condensation Phys. Rev. A 90 023633 · DOI
  154. Hackermüller L, Schneider U, Moreno-Cardoner M, Kitagawa T, Best T, Will S, Demler E, Altman E, Bloch I and Paredes B 2010 Anomalous expansion of attractively interacting fermionic atoms in an optical lattice Science 327 1621-4 · DOI
  155. Meinert F, Mark M J, Kirilov E, Lauber K, Weinmann P, Gröbner M, Daley A J and Nägerl H-C 2014 Observation of many-body dynamics in long-range tunneling after a quantum quench Science 344 1259-62 · DOI
  156. Preiss P M, Ma R, Eric Tai M, Lukin A, Rispoli M, Zupancic P, Lahini Y, Islam R and Greiner M 2015 Strongly correlated quantum walks in optical lattices Science 347 1229-33 · DOI
  157. Pichler H, Daley A J and Zoller P 2010 Nonequilibrium dynamics of bosonic atoms in optical lattices: decoherence of many-body states due to spontaneous emission Phys. Rev. A 82 063605 · DOI
  158. Pichler H, Schachenmayer J, Daley A J and Zoller P 2013 Heating dynamics of bosonic atoms in a noisy optical lattice Phys. Rev. A 87 033606 · DOI
  159. Fisher M P A, Weichman P B, Grinstein G and Fisher D S 1989 Boson localization and the superfluid-insulator transition Phys. Rev. B 40 546-70 · DOI · Paper page
  160. Jaksch D, Bruder C, Cirac J I, Gardiner C W and Zoller P 1998 Cold bosonic atoms in optical lattices Phys. Rev. Lett. 81 3108-11 · DOI · Paper page
  161. Barnett S M and Radmore P M 1997 Methods in Theoretical Quantum Optics (Oxford: Oxford University Press)
  162. Leibfried D, Blatt R, Monroe C and Wineland D 2003 Quantum dynamics of single trapped ions Rev. Mod. Phys. 75 281-324 · DOI · Paper page
  163. Marcuzzi M, Levi E, Diehl S, Garrahan J P and Lesanovsky I 2014 Universal nonequilibrium properties of dissipative Rydberg gases Phys. Rev. Lett. 113 210401 · DOI
  164. Marquardt F and Girvin S M 2009 Optomechanics Physics 2 40 · DOI
  165. Kossakowski A 1972 On quantum statistical mechanics of non-hamiltonian systems Rep. Math. Phys. 3 247-74 · DOI · Paper page
  166. Bacon D, Childs A M, Chuang I L, Kempe J, Leung D W and Zhou X 2001 Universal simulation of Markovian quantum dynamics Phys. Rev. A 64 062302 · DOI
  167. Altland A and Simons B 2010 Condensed Matter Field Theory 2nd edn (Cambridge: Cambridge University Press)
  168. Feynman R 1948 Space-time approach to non-relativistic quantum mechanics Rev. Mod. Phys. 20 367-87 · DOI
  169. Negele J W and Orland H 1998 Quantum Many-Particle Systems (Boulder, CO: Westview Press)
  170. Sieberer L M, Huber S D, Altman E and Diehl S 2014 Nonequilibrium functional renormalization for driven- dissipative Bose-Einstein condensation Phys. Rev. B 89 134310 · DOI
  171. Amit D J and Martin-Mayor V 2005 Field Theory, the Renormalization Group and Critical Phenomena 3rd edn (Singapore: World Scientific)
  172. Calzetta E and Hu B L 1988 Nonequilibrium quantum fields: closed-time-path effective action, Wigner function and Boltzmann equation Phys. Rev. D 37 2878-900 · DOI
  173. Zwerger W 2004 Anomalous fluctuations in phases with a broken continuous symmetry Phys. Rev. Lett. 92 027203 · DOI
  174. Walls D F and Milburn G J 2008 Quantum Optics 2nd edn (Berlin: Springer)
  175. Talkner P 1986 The failure of the quantum regression hypothesis Ann. Phys. 167 390-436 · DOI
  176. Ford G and O'Connell R 1996 There is no quantum regression theorem Phys. Rev. Lett. 77 798-801 · DOI
  177. Sieberer L M, Chiocchetta A, Gambassi A, Täuber U C and Diehl S 2015 Thermodynamic equilibrium as a symmetry of the Schwinger-Keldysh action Phys. Rev. B 92 134307 · DOI
  178. Wouters M and Carusotto I 2006 Absence of long-range coherence in the parametric emission of photonic wires Phys. Rev. B 74 245316 · DOI · Paper page
  179. Szymańska M, Keeling J and Littlewood P 2006 Nonequilibrium quantum condensation in an incoherently pumped dissipative system Phys. Rev. Lett. 96 230602 · DOI
  180. Zhou G-Z, Su Z-B, Hao B-L and Yu L 1980 Closed time path Green's functions and critical dynamics Phys. Rev. B 22 3385-407 · DOI
  181. Chou K-C, Su Z-B, Hao B-L and Yu L 1985 Equilibrium and nonequilibrium formalisms made unified Phys. Rep. 118 1-131 · DOI
  182. Martin P, Siggia E and Rose H 1973 Statistical dynamics of classical systems Phys. Rev. A 8 423-37 · DOI
  183. Janssen H-K 1976 On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties Z. Phys. B: Condens. Matter Quanta 23 377-80 · DOI
  184. Bausch R, Janssen H K and Wagner H 1976 Renormalized field theory of critical dynamics Z. Phys. B: Condens. Matter Quanta 24 113-27 · DOI
  185. Chaikin P M and Lubensky T C 1995 Principles of condensed matter physics (Cambridge: Cambridge University Press)
  186. Kubo R 1966 The fluctuation-dissipation theorem Rep. Prog. Phys. 29 255-84 · DOI
  187. Chiocchetta A, Gambassi A and Carusotto I 2015 Laser operation and Bose-Einstein condensation: analogies and differences arXiv:1503.02816 · arXiv
  188. Kubo R 1957 Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems J. Phys. Soc. Japan 12 570-86 · DOI · Paper page
  189. Martin P and Schwinger J 1959 Theory of many-particle systems. I Phys. Rev. 115 1342-73 · DOI · Paper page
  190. Jakobs S G, Pletyukhov M and Schoeller H 2010 Properties of multi-particle Green's and vertex functions within Keldysh formalism J. Phys. A: Math. Theor. 43 103001 · DOI
  191. Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Boulder, CO: Westview Press)
  192. Janssen H K 1979 Field-theoretic method applied to critical dynamics Dynamical Critical Phenomena and Related Topics (Lecture Notes in Physics vol 104) ed C P Enz (Berlin: Springer) pp 25-47
  193. Aron C, Biroli G and Cugliandolo L F 2010 Symmetries of generating functionals of Langevin processes with colored multiplicative noise J. Stat. Mech P11018 [208 · DOI
  194. Aron C, Barci D G, Cugliandolo L F, Arenas Z G and Lozano G S 2014 Dynamical symmetries of Markov processes with multiplicative white noise arXiv:1412.7564 · arXiv
  195. Altland A, De Martino A, Egger R and Narozhny B 2010 Transient fluctuation relations for time-dependent particle transport Phys. Rev. B 82 115323 · DOI
  196. Hafezi M, Adhikari P and Taylor J M 2014 Engineering three-body interaction and Pfaffian states in circuit QED systems Phys. Rev. B 90 060503 · DOI
  197. Graham R and Tél T 1990 Steady-state ensemble for the complex Ginzburg-Landau equation with weak noise Phys. Rev. A 42 4661-77 · DOI
  198. Mitra A, Takei S, Kim Y B and Millis A J 2006 Nonequilibrium quantum criticality in open electronic systems Phys. Rev. Lett. 97 236808 · DOI
  199. Mitra A and Giamarchi T 2012 Thermalization and dissipation in out-of-equilibrium quantum systems: a perturbative renormalization group approach Phys. Rev. B 85 075117 · DOI
  200. Gebauer R and Car R 2004 Current in open quantum systems Phys. Rev. Lett. 93 160404 · DOI

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Authors
Sieberer, L. M., Buchhold, M., & Diehl, S.
Affiliations
  • Weizmann Institute of Science (IL)
  • Institute of Theoretical Physics
  • University of Cologne (DE)
Corresponding author
Sieberer, L M
Venue
Reports on Progress in Physics
Publisher
IOP Publishing
Published
2016-08-02
Volume
79
Issue
9
Pages
096001
ISSN
  • 0034-4885 (ISSN-L)
  • 1361-6633
DOI
10.1088/0034-4885/79/9/096001
OpenAlex
W2188987909
Cited by
568
References
11
Citations by year
2026: 72 · 2025: 79 · 2024: 78 · 2023: 55 · 2022: 68 · 2021: 54 · 2020: 47 · 2019: 45 · 2018: 31 · 2017: 25 · 2016: 14
FWCI
18.13
Type
journal article
Language
en
Open access
Licence
Locations
  • Reports on Progress in Physics (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Division of Physics (NSF PHY11-25915)
  • European Research Council (UQUAM)
  • Deutsche Forschungsgemeinschaft (ZUK 64)
  • Austrian Science Fund (START grant Y 581-N16)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
nonequilibrium quantum dynamics, driven-dissipative systems, cold atoms, microcavity arrays

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