Thermal purification and thermal entanglement of the two-resonant-coupled-oscillator system at finite temperature
Heng-Mei Li, Xue-xiang Xu, Hong-Yun Huang, Ye‐Jun Xu · Journal of Physics A Mathematical and Theoretical · 2014
Following the spirit of thermo field dynamics, we adopt the partial trace method to explicitly derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-resonant-coupled-oscillator system coupled to the thermal equilibrium environment. The TVS is a pure state in the four-dimensional extended Hilbert space. Based on the TVS, the Wigner function of this quantum system is derived conveniently. From the known Gaussian Wigner function, we obtain the covariance matrix of the quadrature component and quantify the degree of thermal entanglement for the TVS by using logarithmic negativity. It is found that entanglement takes place only at low temperature.