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 (Proc R Soc A 469:20110290, 2013) and by Galve et al. (Phys Rev Lett 105:180501, 2010; Phys Rev Lett 81:062117, 2010) in order to consider the possibility of both quantum refrigeration in enzymes and entanglement in the high temperature limit. 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.