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Recently, model systems with quadratic Hamiltonians and time-dependentinteractions were studied by Briegel and Popescu and by Galve et al. in orderto consider the possibility of both quantum refrigeration in enzymes [Proc. R.Soc. 469 20110290 (2013)] and entanglement in the high temperature limit [Phys.Rev. Lett. 105 180501 (2010); Phys. Rev. A 81 062117 (2010)]. Following thisline of research, we studied a model comprising two quantum harmonicoscillators driven by a time-dependent harmonic coupling. Such a system wasembedded in a thermal bath represented in two different ways. In one case, thebath was composed of a finite but great number of independent harmonicoscillators with an Ohmic spectral density. In the other case, the bath wasmore efficiently defined in terms of a single oscillator coupled to anon-Hamiltonian thermostat. In both cases, we simulated the effect of thethermal disorder on the generation of the squeezed states in thetwo-oscillators relevant system. We found that, in our model, the thermaldisorder of the bath determines the presence of a threshold temperature, forthe generation of squeezed states, equal to T=311.13 K. Such a threshold isestimated to be within temperatures where chemical reactions and biologicalactivity comfortably take place.

Non-Hamiltonian modeling of squeezing and thermal disorder in driven oscillators