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arXiv:0904.4297 · Chinese Physics Letters

Generalized Thermo Vacuum State Derived by the Partial Trace Method

Liyun Hu, Fan Hong‐Yi

Published Sep 1, 2009• 9 citations
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Abstract

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.

DOI
10.1088/0256-307x/26/9/090307

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Generalized Thermo Vacuum State Derived by the Partial Trace Method

胡利云, 范洪义

Chinese Physics Letters•Jan 1, 2009•0 citations
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.
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann—Feynman theorem and the entroy variation in the context of the TVS.
The core of optical field theory at finite temperature is how to introduce the thermo-vacuum state which is the basis of comprehensive investigation of electromagnetic field by virtue of quantum statistic method. Based on the spirit of thermo-field dynamics initiated by Takahashi and Umezawa, we first employ the integration method within the ordered product of operators to search for thermo-vacuum state for the optical negative binomial state (NBS)s=s+1(1-)n|n,+,+,which takes the form of pure negative binomial state. The newly found thermo-vacuum state brings convenience for evaluating the Wigner function of NBS and the fluctuation of photon numbers in NBS.
According to the thermo field dynamics proposed by Takahashi–Umezawa, the Hamiltonian h = a†a - ã†ã and h|n, ñ〉 = 0 of the original optical field excitation state |n〉 and its tilde state |ñ〉 in the Hilbert space cannot embody the eigenvalue spectrum of h. To avoid the weakness, new thermo excitation states are successfully constructed by introducing appropriate thermo excitation operators. It is noted that they are entangled states. Applications of the new thermo excitation state in constructing new thermo squeezed state and phase state are also presented.