Two coupled nonlinear cavities in a driven-dissipative environment

Abstract

We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.

The driven-dissipative Bose–Hubbard dimer: phase diagram and chaos

“…The considerable amount of multistability of the Bose-Hubbard model(2) is represented by the overlap between the different shaded region of figure 2. For even lower negative values of δ than shown in figure 2, one can find up to nine equilibria, as pointed out in [31].…”

Mapping repulsive to attractive interaction in driven–dissipative quantum systems

“…We then 2. Driven-dissipative Bose-Hubbard dimer: mapping positive to negative U We consider a driven-dissipative Bose-Hubbard dimer [29][30][31][32] with either repulsive or attractive onsite interaction, > U 0 or < U 0, respectively. By inspection of the equations of motion, we will reveal an exact mapping between the cases of positive and negative U, i.e., between dimers with repulsive and attractive onsite interaction.…”

Localization and self-trapping in driven-dissipative polariton condensates

“…These include states where the density is symmetrical in the two wells, as well as states where the condensate becomes trapped in the pumped well. The appearance of asymmetrical states is similar to the phenomenon of macroscopic quantum self-trapping, as previously analyzed for polaritons without gain and loss [26], and for resonant pumping [27,28]. In these cases, however, the asymmetry is caused by strong interactions, which prevent a complete transfer of population between the wells.…”