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Acta Physica Sinica (Overseas Edition)

Squeezed coherent thermal state and its photon number distribution

Yimin Li, H.-R. Xia, Zugeng Wang, Zai-Xin Xu

Published Sep 1, 1997• 4 citations
Publisher

Abstract

The squeezed coherent thermal state is considered. Its various coherent representations, including Q-, P-and Bargmann representations are introduced. The analytic formula for the photon number distribution of such a quantum state is obtained directly from the Bargmann representation. The effects of the squeezing and the thermal noise on the photon distribution are discussed.

DOI
10.1088/1004-423x/6/9/006

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The squeezed coherent thermal state is considered. Its various coherent representations, including Q-, P-and Bargmann representations are introduced. The analytic formula for the photon number distribution of such a quantum state is obtained directly from the Bargmann representation. The effects of the squeezing and the thermal noise on the photon distribution are discussed.
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Much attention has been given in the past to two classes of squeezed states: the squeezed vacuum and coherent states. Here we study the effects of squeezing on number states and on thermal field states. The statistical properties of these various squeezed states are discussed using the second-order correlation functions. The quasiprobabilities of the Wigner, Q, and positive P representations are calculated and compared for the squeezed states. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability. The photon number distributions of the squeezed number and squeezed thermal states are extensively discussed and new interference effects in phase space are shown to lead to highly structured number distributions.
We consider the equilibrium thermal state of photons and determine the mean number and number variance of squeezed coherent photons. We use an integral representation for electro-magnetic radiation applicable both to systems in equilibrium and to systems in nonequilibrium to determine the spectral function of the radiation. The system considered is in thermal equilibrium and we find that the squeezed coherent photons are at a higher temperature than the photons themselves. Also, as expected, the mean number of squeezed coherent photons is greater than that of photons.
We consider a single-mode radiation field initially in a displaced squeezed thermal state. The weak interaction of such a field with a heat bath of arbitrary temperature is shown to preserve the Gaussian form of the characteristic function. Accordingly, the study of the time development of the density operator reduces to our previous description [P. Marian and T. A. Marian, preceding paper, Phys. Rev. A 47, 4474 (1993)] of the initial quantum state. As examples, photon statistics and squeezing properties of the damped field are analyzed. Based on the close relation between field dissipation and photon detection, we derive simple analytic formulas for the counting distribution and its factorial moments. Nonclassical features of a displaced squeezed thermal state, such as oscillations of the photon-number distribution, survive in the counting process, provided that the quantum efficiency of the detector is high enough.
The quantum phase distributions and variances of strong coherent and phase-squeezed states mixed with thermal light are calculated. We find that the effect of thermal light on the coherent phase distribution becomes important only when the number of thermal photons is of order one-half. Its effect on the phase distribution of phase-squeezed states (for the case where the number of photons is very large compared to e2r){e}^{2r})e2r) becomes important when the number of thermal photons is of order $\frac{1}{2}{e}^{\ensuremath{-}2r}$, where rrr is the squeezing parameter.