We determine the quasistationary distribution of Floquet-state occupation probabilities for a parametrically driven harmonic oscillator coupled to a thermal bath. Since the system exhibits detailed balance, and the canonical representatives of its quasienergies are equidistant, these probabilities are given by a geometrical Boltzmann distribution, but its quasitemperature differs from the actual temperature of the bath, being affected by the functional form of the latter's spectral density. We provide two examples of quasithermal engineering, i.e., of deliberate manipulation of the quasistationary distribution by suitable design of the spectral density: We show that the driven system can effectively be made colder than the undriven one, and demonstrate that quasithermal instability can occur even when the system is mechanically stable.

We demonstrate that a periodically driven quantum system can adopt a quasistationary state which is effectively much colder than a thermal reservoir it is coupled to, in the sense that certain Floquet states of the driven-dissipative system can carry much higher population than the ground state of the corresponding undriven system in thermal equilibrium. This is made possible by a rich Fourier spectrum of the system’s Floquet transition matrix elements, the components of which are addressed individually by a suitably peaked reservoir density of states. The effect is expected to be important for driven solid-state systems interacting with a phonon bath predominantly at well-defined frequencies.

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A periodically driven, moderately anharmonic oscillator constitutes an ideal model system for investigating quantum resonances, which are amenable to a quantum pendulum approximation. In the present paper, I study the quasi-stationary Floquet-state occupation probabilities which emerge when such a resonantly driven system is coupled to a heat bath. It is demonstrated that the Floquet state which is associated with the ground state of the pendulum turns into an effective ground state, carrying the highest population in the strong-driving regime. Moreover, the population of this effective Floquet ground state can even exceed that of the undriven system’s true ground state at the same bath temperature. These effects can be optimized by suitably engineering the properties of the bath.