The combination of driving and dissipation guides a quantum system into a nonequilibrium steady state (NESS). It is an intriguing question, in how far this principle can be exploited for the robust preparation of interesting many-body target states beyond the strict constraints of thermal equilibrium. We consider an open system of ultracold bosonic atoms coupled to a heat bath and show that, counterintuitively, the interplay of bath-induced dissipation and controlled Floquet (i.e., driving-induced) heating can give rise to nonequilibrium Bose condensation in a quantum-scar-like mode protected from the drive. In particular, we use Floquet-Born-Markov theory to microscopically derive kinetic equations for a one-dimensional system of bosonic atoms in an optical lattice of finite extent coupled to a three-dimensional thermal bath of weakly interacting bosons treated in Bogoliubov theory. The bath temperature $T$ is assumed to lie well above the crossover temperature, below which the majority of the system's particles form a (finite-size) Bose condensate in the single-particle ground state in equilibrium. However, when a strong local potential modulation is switched on, which resonantly excites the system, a nonequilibrium Bose condensate is formed in an excited state that decouples from the drive. This strategy of engineering the NESS of an open quantum system via tailored Floquet heating is likely to find applications also for different systems and target states.

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• Bose gases
• Cold gases in optical lattices
• Mixtures of atomic and/or molecular quantum gases
• Open quantum systems & decoherence
• Quantum statistical mechanics
• Floquet systems
• Ultracold gases