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Floquet engineering is an important tool for realizing topologicallynontrivial band structures for charge-neutral atoms in optical lattices.However, the preparation of a topological-band-insulator-type state offermions, with one nontrivial quasi-energy band filled completely and theothers empty, is challenging as a result of both driving induced heating aswell as imperfect adiabatic state preparation (with the latter induced by theunavoidable gap closing when passing the topological transition). Analternative procedure that has been proposed is to prepare such statesdissipatively, i.e. as a steady state that emerges when coupling the system toreservoirs. Here we discuss a concrete scheme that couples the system to aweakly interacting Bose-condensate given by second atomic species acting as aheat bath. Our strategy relies on the engineering of the potential for the bathparticles, so that they occupy weakly coupled tubes perpendicular to thetwo-dimensional system. Using Floquet-Born-Markov theory, we show that theresulting nonequilibrium steady state of the driven-dissipative systemapproximates a topological insulator. We even find indications for theapproximate stabilization of an anomalous Floquet topological insulator, astate that is impossible to realize in equilibrium.

Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering