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Chinese Optics Letters

New approach for normalization and photon-number distributions of photon-added （-subtracted） squeezed thermal states

胡利云, 张智明

Published Jan 1, 2012• 0 citations
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Abstract

Using the thermal field dynamics theory to convert the thermal state into a 'pure' state in doubled Fock space, we find that the average value of efa a under squeezed thermal state (STS) is just the generating function of Legendre polynomials. Based on this remarkable result, the normalization and photon-number distributions of m-photon added (or subtracted) STSs are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.

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Modern Physics Letters A•Jun 28, 2009•11 citations
Using the thermal field dynamics theory to convert the thermal state into a 'pure' state in doubled Fock space, we find that the average value of efa a under squeezed thermal state (STS) is just the generating function of Legendre polynomials. Based on this remarkable result, the normalization and photon-number distributions of m-photon added (or subtracted) STSs are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.
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.
Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single-photon–added STS (PASTS) always has negative values at the phase space center. The decoherence effect on PASTS is examined by the analytical expression of WF. It is found that a longer threshold value of decay time than in single-photon–subtraction STS is included in single PASTS.