Spontaneous collective coherence in driven dissipative cavity arrays

Abstract

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay exponentially with distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous build-up of collective coherence in the system. Arrays of optical or microwave cavities, each interacting strongly with quantum emitters and mutually coupled via the exchange of photons, have been introduced as prototype setups for the study of quantum manybody physics of light [1][2][3]. Even though ground or thermal equilibrium states of the corresponding quantum many-body systems are challenging to generate in experiments, much of the initial attention has focussed on this regime [4][5][6][7]. In any realistic experiment with cavity arrays, however, photons are dissipated due to the imperfect confinement of the light, and emitter excitations have finite lifetimes. It is thus crucial and useful to explore the driven-dissipative regime of these structures, where photon losses are continuously compensated by pumping new photons into the cavities. A special role is here taken by the stationary states where photon pumping and losses balance each other in a dynamical equilibrium. This regime has thus received considerable attention in recent years, where coherent and strongly correlated phases have been discovered [8][9][10], but also analogies to quantum Hall physics [11] and topologically protected quantum states [12] have been discussed.In previous investigations of coupled cavity arrays in driven-dissipative regimes, the pump mechanism that injects photons into the array has been assumed to be a coherent drive at each cavity [8][9][10][11][12]. Therefore any phase-coherence between light fields in distant cavities that was seen in these studies can at least in part be attributed to the fixed phase relation between their coherent input drives. Here, in contrast, we show that such a coherence between distant cavities can build up spontaneously, triggered only by physical processes within the array. In this way we address the question of whether a non-equilibrium superfluid can develop in these structures. To this end, we consider a cavity array that is only driven by an incoherent pump which explicitly avoids any external source for a preferred phase relation between photons in different cavities.In our model, each cavity strongly interacts with a twolevel emitter. Whereas both, emitters and cavity photons, are subject to dissipation processes, the cavities are excited via the emitters only, whi...

Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

“…Some care with the definition of superfluidity in photonic systems has to be taken in the (more realistic) case where leakage is present. A discussion of this issue has just been started for the case of cavity arrays [20], see also Refs. [21,22] for an analysis in related systems.…”

Photon transport in a dissipative chain of nonlinear cavities

“…[12][13][14][15][16][17][18][19][20]-and several different properties both of the transient and steady-state regimes were highlighted. These include the spectroscopy of many-body photon states [12,[15][16][17]20], crystallisation of photons [14], instabilities induced by pulsed driving [13], steady state critical phenomena [18,19]. There is by now a compelling evidence that cavity arrays are naturally designed to become open-system quantum simulators.…”

Linked cluster expansions for open quantum systems on a lattice

“…Recently, a large body of theoretical works has been devoted to the investigation of the collective behavior emerging in dynamical response 12 , many-body spectroscopy [13][14][15] , transport [16][17][18][19][20] , as well as stationary properties. In the latter context, a careful engineering of the coupling between the system and the environment can stabilize interesting many-body phases in the steady state 21,22 .…”