Generalized Thermo Vacuum State Derived by the Partial Trace Method

H. Matsumoto

Liyun Hu, Fan Hong‐Yi

By virtue of the technique of integration within an ordered product of operators, we present a new approach for deriving the generalized thermo vacuum state which is simpler in form than that obtained from the Takahashi—Umezawa method. using this new approach, the thermo field dynamics can be developed. Applications of the new state are discussed.

Weifeng Wu, Hong-Yi Fan

In nature, there exists superposition of Gaussian light and chaotic light, so we introduce the density operator for describing the Gaussian-enhanced chaotic light (GECL). By virtue of the method of integration within ordered product (IWOP) of operators, we derive its normalization constant. Then, by virtue of the partial trace method, we derive its thermo vacuum state and this may greatly simplify the calculation of photon number average and quantum fluctuation in GECL. It is demonstrated that the second-order degree of coherence of GECL is larger than 2.

博臣 梅沢, 紘 松本, 昌 立木

Heng-Mei Li, Xue-xiang Xu, Hong-Yun Huang +1 more

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.

Hiroomi Umezawa, H. Matsumoto, M. Tachiki