Coherence of mechanical oscillators mediated by coupling to different baths
AbstractWe study the nonequilibrium dynamics of two mechanical oscillators with general linear couplings to two uncorrelated thermal baths at temperatures T1 and T2, respectively. We obtain the complete solution of the Heisenberg-Langevin equations, which reveal a coherent mixing among the normal modes of the oscillators as a consequence of their off-diagonal couplings to the baths. Unique renormalization aspects resulting from this mixing are discussed. Diagonal and off-diagonal (coherence) correlation functions are obtained analytically in the case of strictly Ohmic baths with different couplings in the strong- and weak-coupling regimes. An asymptotic nonequilibrium stationary state emerges for which we obtain the complete expressions for the correlations and coherence. Remarkably, the coherence survives in the high-temperature, classical limit for T1≠T2. This is a consequence of the coherence being determined by the difference of the bath correlation functions. In the case of vanishing detuning between the oscillator normal modes both coupling to one and the same bath, the coherence retains memory of the initial conditions at long times. An out-of-equilibrium setup with small detuning and large |T1−T2| produces nonvanishing steady-state coherence in the high-temperature limit of the baths.