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)ρs =∞∑n=0 ( n+s n )γs+1(1−γ)n|n⟩⟨n|.We find that the thermo-vacuum state we search for is just the fictitious-mode excitation in the thermo vacuum state for chaotic state or expressed as∞∑n=0 v u u t ( n+s n )γs+1 (1−γ)n|n, s˜+˜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.
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