Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases

Alexandre Le Boité (1) , Giuliano Orso (1) , Cristiano Ciuti (1)

1 MPQ (UMR_7162) - Laboratoire Matériaux et Phénomènes Quantiques

We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. 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 of 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 classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevski approach.

Domaines: Physique Quantique [quant-ph]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Alexandre Le Boité, Giuliano Orso, Cristiano Ciuti. Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases. 2014. ⟨hal-01054033⟩