Abstract
We construct a new state via thermo excitation on the thermo vacuum state. It is interestingly found that partial tracing over thermo-freedom will lead to a negative-binomial state characteristic of l in the a-mode space and annihilating one a-mode photon results in increasing one $\tilde {a}$-mode photon, which exhibits quantum entanglement between system and environment. We employ the summation method within ordered product of operators to proceed our discussion.
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