Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model

Abstract

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

Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems

“…In the subsection B, we investigate Landau-Zener sweeps for the array and interpret the results with a Kibble-Zurek type argument. Recent developments linked non non-equilibrium physics in these lattice systems involve Matrix Product States [94][95][96] ; stochastic mean-field methods also allow to describe non-equilibrium light-matter systems 97 .…”

Quantum Monte Carlo study of the Rabi-Hubbard model

“…The out of equilibrium behavior of the RH model has been recently studied in Ref. [23]. The related Dicke model and the nature of its transition are also the subject of intense research [22,[24][25][26].…”

Keldysh field theory for driven open quantum systems

“…In cirquit QED, strong non-linearities can be generated, e.g., by coupling to adjacent qubits made of Cooper pair boxes [132,133]. This gives rise to many-body variants of the Rabi model [134], whose phase diagrams have been studied recently [135][136][137]. Furthermore, for the implementation of lattice Dicke models with large collective spins, the use of hybrid quantum systems consisting of superconducting cavity arrays coupled to solid-state spin ensembles have been proposed [138].…”