Robust entangled states in a non-hermitian periodically driven two-band Bose-Hubbard Hamiltonian

The steady state properties of a many-body Wannier-Stark system coupled to an effective reservoir is studied within the non-Hermitian approach in the presence of periodic time-dependent driving. We show how the interplay between dissipation and shaking dynamics reveals a hidden symmetries yielding the occurrence of a (quasi-) loss- and interaction-free subspace. We numerically probe the geometric structure of the asymptotic state and its robustness to imperfections in the preparation of the initial conditions, dissipation and the size of system.