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A many-body Wannier-Stark system coupled to an effective reservoir is studiedwithin a non-Hermitian approach in the presence of a periodic driving. We showhow the interplay of dissipation and driving dynamically induces a subspace ofstates which are very robust against dissipation. We numerically probe thestructure of these asymptotic states and their robustness to imperfections inthe initial-state preparation and to the size of the system. Moreover, theasymptotic states are found to be strongly entangled making them interestingfor further applications.

Generation of robust entangled states in a non-hermitian periodically driven two-band Bose-Hubbard system