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

Recently, model systems with quadratic Hamiltonians and time-dependent interactions were studied by Briegel and Popescu and by Galve et al. in order to 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 this line of research, we studied a model comprising two quantum harmonic oscillators driven by a time-dependent harmonic coupling. Such a system was embedded in a thermal bath represented in two different ways. In one case, the bath was composed of a finite but great number of independent harmonic oscillators with an Ohmic spectral density. In the other case, the bath was more efficiently defined in terms of a single oscillator coupled to a non-Hamiltonian thermostat. In both cases, we simulated the effect of the thermal disorder on the generation of the squeezed states in the two-oscillators relevant system. We found that, in our model, the thermal disorder of the bath determines the presence of a threshold temperature, for the generation of squeezed states, equal to T=311.13 K. Such a threshold is estimated to be within temperatures where chemical reactions and biological activity comfortably take place.