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Journal of Physics A Mathematical and Theoretical

Statistical properties of a generalized photon-modulated thermal state

Xue-xiang Xu, Hong‐Chun Yuan, Liyun Hu, Hong-Yi Fan

Published Oct 14, 2011• 11 citations
Publisher

Abstract

In this paper, we introduce a new kind of quantum state, generalized photon-modulated thermal states (GPMTS), which are obtained by repeatedly acting the superposed operation (a coherent superposition of photon subtraction and addition) on the thermal state. It is found that the normalization factor of GPMTS is a Legendre polynomial. Moreover, we present the analytical expressions of several quasi-probability distributions for GPMTS and calculate the corresponding tomogram and photocount distribution as well.

DOI
10.1088/1751-8113/44/44/445306

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In this paper, we introduce a new kind of quantum state, generalized photon-modulated thermal states (GPMTS), which are obtained by repeatedly acting the superposed operation (a coherent superposition of photon subtraction and addition) on the thermal state. It is found that the normalization factor of GPMTS is a Legendre polynomial. Moreover, we present the analytical expressions of several quasi-probability distributions for GPMTS and calculate the corresponding tomogram and photocount distribution as well.
In this paper, we propose a class of the generalized photon-added coherent states (GPACSs) obtained by repeatedly operating the combination of Bosonic creation and annihilation operatoes on the coherent state. The normalization factor of GPACS is related to Hermite polynomial. We also derive the explicit expressions of its statistical properties such as photocount distribution, Wigner function and tomogram and investigate their behaviour as the photon-added number varies graphically. It is found that GPACS is a kind of nonclassical state since Wigner function exhibits the negativity by increasing the photon-added number.
In this paper, we present the generalized photon-modulated coherent state (GPMCS) generated by repeatedly operating the combination of Bosonic creation and annihilation operators on the coherent state. It is found that the GPMCS is a Hermite-excited coherent state and its normalization factor is related to single-variable Hermite polynomials. Furthermore, some significant quantum statistical properties of the GPMCS are investigated, such as photon-number distribution (PND) and the Wigner function (WF). We find that the WF of the GPMCS has negative values when the generalized photon-modulation exists, which implies the nonclassical properties of the GPMCS.
Abstract Two new photon‐modulated states are introduced by operating a more general coherent superposition on two classical states (coherent and thermal) and their nonclassicality caused by the operation is investigated via examining the squeezing, sub‐Poissonian statistics, nonclassical depth, and negativity of Wigner distribution. Their density‐operator and Wigner‐distribution evolutions in the thermal channel are also explored. It is found that the high‐order operation has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon‐modulated states for thermal noise. For convenience, a new three‐variable special polynomial and its generating function are introduced via the normal ordering of operators.
Using the normally ordered form of thermal state characteristic of average photon number nc, we introduce the photon-added thermal state (PATS) and investigate its statistical properties, such as Mandel's Q-parameter, photon number distribution (PND), and Wigner function (WF). We then study its decoherence in a thermal environment with average thermal photon number [Formula: see text] and dissipative coefficient κ by deriving analytical expressions of the WF. The nonclassicality is discussed in terms of the negativity of the WF. It is found that the WF is always positive when [Formula: see text] for any number PATS. The expression for time evolution of the PND and the tomogram of PATS are also derived analytically, which are related to hypergeometric function and single variable Hermite polynomials.