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Physical Review A

Higher-order squeezing and photon statistics for squeezed thermal states

Paulina Marian

Published Feb 1, 1992• 82 citations
Publisher

Abstract

By use of the squeezed-number-state basis, we study several features of the squeezed thermal states. Higher-order squeezing properties are found to be entirely determined by the second-order ones. The photon-number distribution is expressed in closed form in terms of a Legendre polynomial. We point out that at a critical value of the squeeze parameter, pairwise oscillations of the photon-number distribution set in. Finally, a compact analytical expression of the exact lth-order correlation function is derived and examined.

DOI
10.1103/physreva.45.2044

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By use of the squeezed-number-state basis, we study several features of the squeezed thermal states. Higher-order squeezing properties are found to be entirely determined by the second-order ones. The photon-number distribution is expressed in closed form in terms of a Legendre polynomial. We point out that at a critical value of the squeeze parameter, pairwise oscillations of the photon-number distribution set in. Finally, a compact analytical expression of the exact lth-order correlation function is derived and examined.
We investigate a free monochromatic electromagnetic field which is the superposition of a squeezed thermal radiation and a coherent one. The main tool in our analysis is the characteristic function that has a Gaussian form. We establish an analytic formula for an arbitrary correlation function, as well as its strong-squeezing limit. Besides the usual quasiprobability densities, the coherent-state, number-state, coordinate, and momentum representations of the density operator are derived. We point out the nonclassical oscillations of the photon-number distribution and find its generating function. Collaterally, displaced thermal states and squeezed thermal states are revisited as nontrivial particular cases. We examine finally the squeezing properties of the field using the distribution functions of the quadratures.
We examine the influence of thermal noise on several non-classical properties of squeezed number states. In order to evaluate arbitrary-order moments of both amplitude and quadrature operators of the superposition, we use a normal-ordering technique based on McCoy's theorem. Our analytical results are compact formulae involving Gauss hypergeometric functions. We find that the thermal mean occupancy sufficient to destroy squeezing to any order is less than . Other non-classical features of a squeezed number state, such as pairwise oscillations in the photon number distribution, sub-Poissonian statistics and amplitude-squared squeezing disappear completely above this threshold.
We investigate nonclassical properties of the field states generated by subtracting any number of photons from the squeezed thermal state (STS). It is found that the normalization factor of photon-subtracted STS (PSSTS) is a Legendre polynomial of squeezing parameter rrr and average photon number $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ of the thermal state. Expressions of several quasiprobability distributions of PSSTS are derived analytically. Furthermore, the nonclassicality is discussed in terms of the negativity of the Wigner function (WF). It is shown that the WF of single PSSTS always has negative values if $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}<\mathrm{sinh}{}^{2}r$ at the phase space center. The decoherence effect on PSSTS is then included by analytically deriving the time evolution of WF. The results show that the WF of single PSSTS has negative value if $2\ensuremath{\kappa}t<\mathrm{ln}{1\ensuremath{-}(2\mathrm{n\ifmmode \bar{}\else \={}\fi{}}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\ensuremath{-}\mathrm{sinh}{}^{2}r)/[(2\mathfrak{N}+1)(\mathrm{n\ifmmode \bar{}\else \={}\fi{}}\mathrm{cosh}2r+\mathrm{sinh}{}^{2}r)]}$, which is dependent not only on average number N\mathfrak{N}N of thermal photons in the environment, but also on $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ and rrr.
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.