Quantum temperature of a modulated oscillator: spectral signatures

Relaxation of a quantum system is usually due to emission of excitations of a thermal reservoir. The emission events happen at random. For periodically modulated systems, the corresponding noise leads to a finite-width distribution over the quasi-energy (Floquet) states. It can be characterized by an effective nonzero quantum temperature even where the temperature of the reservoir is zero. We show that, as a result, the spectra of fluctuations and response of a parametrically modulated underdamped nonlinear oscillator can display a fine structure. The form of the spectra sensitively depends on the temperature of the reservoir.