Strongly correlated photons in arrays of nonlinear cavities (A. Le Boité)

I will present recent theoretical results on strongly correlated photons in arrays of nonlinear cavities, described by a driven-dissipative Bose-Hubbard model [2,3]. I will describe a general method for computing the mean-field phase diagram of the driven-dissipative model, based on an exact quantum solution of the single-site problem [2,3]. We will see that the intrinsic nonequilibrium nature of the system gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling [2]. Moreover, the study of collective excitations in the steady-state phases reveals that modulational instabilities can be triggered by purely imaginary excitation branches, giving rise to inhomogeneous patterns in the system. In the limit of weak dissipation and driving, I will show analytical results describing generalized Mott insulating phases [3]. Instead of pure Mott-insulator states, we find statistical mixtures with the same second-order coherence as a Fock state with n photons, but a mean photon number equal to n/2. These mixed states occur when n pump photons have the same energy as n interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to a classical coherent state takes place.

References:
[1] I. Carusotto and C. Ciuti, Rev. Mod. Phys. 85, 299 (2013)
[2] A. Le Boité, G. Orso, C. Ciuti, Phys. Rev. Lett. 110, 233601 (2013)
[3] A. Le Boité, G. Orso, C. Ciuti, Phys. Rev. A 90, 063821 (2014)