Time Dynamics and Green’s Functions of a Driven-Dissipative Bose-Hubbard Dimer

The fast advances in the QED quantum simulators^1,2,3,4 call for the development of theoretical tools to study out of equilibrium nonlinear cavities. In this work⁵ we report a numerical study of the building block of these systems, a dimer made by two driven-dissipative coupled cavities, provided with a Kerr nonlinearity. Despite its simplicity, this is a completely non-trivial system which sheds light on larger lattices. While under a semiclassical analysis the system experiences a phase transition from a localized to a delocalized regime even in the open case, the numerically exact solution of the quantum system shows no sharp transition. We also show that while the open nature of the system does not allow to gain insights on the Hamiltonian from a long-time analysis of quantum mechanical observables unless an effective loss imbalance is realized, a rich information about the quantum spectra is encoded in the single-particle Green’s function.


References

1. Knap et al, PRA. 83, 023821.
2. Schmidt et al, PRB. 82, 100507.
3. Rafteri et al, PRX. 4, 031043.
4. Rodriguez et al, Nat. Commun. 7, 11887.
5. Seclì et al, in preparation.