Entanglement of quantum oscillators coupled to different heat baths

Abstract

We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature $T_1$ and $T_2$ with bilinear couplings between them. We particularly focus on the entanglement or inseparability property of their quantum states. The critical temperatures of two respective oscillators, $T_{1c}$ and $T_{2c}$, higher than which the entanglement disappears, can be determined. It is found that when two damping parameters are largely different, say ${\gamma }_1\ll {\gamma }_2$, the critical temperature $T_{1c}$ with respect to the frequency ${\Omega }_{+}$, the higher frequency among two normal modes frequencies, can be very large, $T_{1c}\gg {\Omega }_{+}$, while $T_{2c}\propto {\Omega }_{+}$ with the possibility of hot entanglement. The entanglement of two oscillators with the temperature-dependent damping parameters ${\gamma }_{1;2,T}$ from heat baths is also discussed.

17 pages, 3 figures