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arXiv:0901.1424 · Modern Physics Letters A

WIGNER FUNCTIONS OF THERMO NUMBER STATE, PHOTON SUBTRACTED AND ADDED THERMO VACUUM STATE AT FINITE TEMPERATURE

LI-YUN HU, HONG-YI FAN

Published Sep 14, 2009• 24 citations
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Abstract

Based on Takahashi–Umezawa thermo field dynamics and the order-invariance of Weyl ordered operators under similar transformations, we present a new approach to derive the exact Wigner functions of thermo number state, photon subtracted and added thermo vacuum state. We find that these Wigner functions are related to the Gaussian–Laguerre type functions of temperature, whose statistical properties are then analyzed.

DOI
10.1142/s0217732309030953

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Based on Takahashi–Umezawa thermo field dynamics and the order-invariance of Weyl ordered operators under similar transformations, we present a new approach to derive the exact Wigner functions of thermo number state, photon subtracted and added thermo vacuum state. We find that these Wigner functions are related to the Gaussian–Laguerre type functions of temperature, whose statistical properties are then analyzed.
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.