Keldysh Field Theory for Driven Open Quantum Systems

Enhancing optical nonlinearities so that they become appreciable on the single photon level and lead to nonclassical light fields has been a central objective in quantum optics for many years. After this has been achieved in individual micro-cavities representing an effectively zero-dimensional volume, this line of research has shifted its focus towards engineering devices where such strong optical nonlinearities simultaneously occur in extended volumes of multiple nodes of a network. Recent technological progress in several experimental platforms now opens the possibility to employ the systems of strongly interacting photons these give rise to as quantum simulators. Here we review the recent development and current status of this research direction for theory and experiment. Addressing both, optical photons interacting with atoms and microwave photons in networks of superconducting circuits, we focus on analogue quantum simulations in scenarios where effective photon-photon interactions exceed dissipative processes in the considered platforms.

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“…For further work on non-equilibrium photon condensation, see [144,236,3], as well as the reviews [39,235] and references therein.…”

Section: Regimes Of Incoherent Pumpingmentioning

confidence: 99%

Quantum simulation with interacting photons

Hartmann

2016

J. Opt.

239

210

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“…Characterized by excitations with a finite lifetime, when sustained by finite-amplitude optical drives they display steady-state phases that are generally far richer [5][6][7][8][9][10] than their equilibrium counterparts [11,12]. Critical phenomena in these open driven-dissipative systems often come with genuinely new properties and novel dynamic universality classes, even when an effective temperature can be identified [13][14][15][16][17], a statement that can be made robust in renormalization group calculations [18,19]. Coupled cavity QED systems [20][21][22] have emerged as natural platforms to study many-body physics of open quantum systems.…”

mentioning

confidence: 99%

Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model

et al. 2016

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We explore the phase diagram of the dissipative Rabi-Hubbard model, as could be realized by a Ramanpumping scheme applied to a coupled cavity array. There exist various exotic attractors, including ferroelectric, antiferroelectric, and incommensurate fixed points, as well as regions of persistent oscillations. Many of these features can be understood analytically by truncating to the two lowest lying states of the Rabi model on each site. We also show that these features survive beyond mean field, using matrix product operator simulations. DOI: 10.1103/PhysRevLett.116.143603 Introduction.-A number of recent experimental breakthroughs [1][2][3][4] have spurred the investigation of nonequilibrium properties of hybrid quantum many-body systems of interacting matter and light. Characterized by excitations with a finite lifetime, when sustained by finiteamplitude optical drives they display steady-state phases that are generally far richer [5][6][7][8][9][10] than their equilibrium counterparts [11,12]. Critical phenomena in these open driven-dissipative systems often come with genuinely new properties and novel dynamic universality classes, even when an effective temperature can be identified [13][14][15][16][17], a statement that can be made robust in renormalization group calculations [18,19]. Coupled cavity QED systems [20][21][22] have emerged as natural platforms to study many-body physics of open quantum systems. The current fabrication and control capabilities in solid-state quantum optics allows us to probe lattice systems [23][24][25][26][27][28][29][30][31] in the mesoscopic regime, providing a first glimpse into how macroscopic quantum behavior may arise far from equilibrium. It is therefore of interest to identify a physical system where a nonequilibrium phase transition (i) can be studied-at least in principle-in the thermodynamic limit, (ii) can be compared to an equilibrium analogue through a proper limiting procedure, and (iii) can be easily realized in an architecture that is currently available.The Rabi-Hubbard (RH) model [32] represents the minimal description of coupled cavity QED systems, explicitly containing terms which do not conserve the particle number. These terms are relevant for the lowfrequency behavior of the coupled system and their inclusion lead, in equilibrium, to a Z 2 -symmetry breaking phase transition between a quantum disordered paraelectric phase and an Ising ferroelectric [32,33]. The equilibrium RH transition requires a sizable intercavity hopping or light-matter interaction, of the order of the transition

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“…Ignoring the self-energy in the left hand side of Eq. ( 11) (i.e., the quasi-particle approximation [31]), we have that…”

Section: Discussionmentioning

confidence: 99%

“…Making the Wigner transformation f (t, ω) = d∆te i∆t f (t, ∆t), where t = t 1 + t 2 and ∆t = t 2 − t 1 are the forward and relative time, and under the gradient approximation [31], Eq. ( 17) yields that…”

Section: Discussionmentioning

confidence: 99%

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Artificial electromagnetic field with cold atoms in two-dimensional optical lattice

Guo,

Chen,

Liu

2019

Preprint

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We propose that an artificial electromagnetic field can be engineered in the context of cold fermionic atoms that are coupled to a cavity mode via two-photon processes in a two-dimensional optical lattice. There is a standing-wave pump laser inducing the electric effect in one spatial direction, and a second running-wave laser beam generates the magnetic flux perpendicular to the lattice plane. In the static scenario, the bulk spectrum resembles the fractal structure of the Hofstadter butterfly and the edge mode spectrum indicates the occurrence of the quantum Hall phase. The Keldysh formulism is utilized to capture the time evolution. The back action between atoms and cavity field gives a picture of the time-dependent non-equilibrium dynamics. We find that the spontaneous emergence of the artificial electromagnetic field stimulates the Hall current, and the superradiant cavity field emerges without pump threshold. Moreover, the magnetic flux not only modify the bulk topology, but also drives a series of dynamical phase transitions.

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Keldysh Field Theory for Driven Open Quantum Systems

Cited by 30 publications

References 218 publications

Quantum simulation with interacting photons

Quantum simulation with interacting photons

Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model

Artificial electromagnetic field with cold atoms in two-dimensional optical lattice

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