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Journal of Physics A Mathematical and Theoretical

Statistical properties and decoherence in a thermal channel of photon-excited squeezed coherent states

Zhen Wang, Xiang‐Guo Meng, Hong-Yi Fan

Published Mar 14, 2013• 3 citations
Publisher

Abstract

In this paper, photon-excited squeezed coherent states (PESCS) are studied theoretically by adding a photon to the squeezed coherent states repeatedly. By taking advantage of the normally ordered form of the density operator for PESCS, the analytical expressions of the normalization constant, Mandel Q -parameter, photon-number distribution, quadrature squeezing and Wigner function are derived and discussed in detail, and from these the sub-Poissonian photon statistics, photon-number oscillations, negative value of quadrature squeezing, and partial negativity and non-Gaussian distribution of a Wigner function are demonstrated, respectively. These criteria well exhibit the highly nonclassical properties and non-Gaussianity of PESCS. In addition, by deriving the normally ordered form of the density operator and Wigner function for PESCS in a thermal channel, the decoherence process of PESCS is analyzed both analytically and numerically.

DOI
10.1088/1751-8113/46/13/135305

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In this paper, photon-excited squeezed coherent states (PESCS) are studied theoretically by adding a photon to the squeezed coherent states repeatedly. By taking advantage of the normally ordered form of the density operator for PESCS, the analytical expressions of the normalization constant, Mandel Q -parameter, photon-number distribution, quadrature squeezing and Wigner function are derived and discussed in detail, and from these the sub-Poissonian photon statistics, photon-number oscillations, negative value of quadrature squeezing, and partial negativity and non-Gaussian distribution of a Wigner function are demonstrated, respectively. These criteria well exhibit the highly nonclassical properties and non-Gaussianity of PESCS. In addition, by deriving the normally ordered form of the density operator and Wigner function for PESCS in a thermal channel, the decoherence process of PESCS is analyzed both analytically and numerically.
We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.
We introduce the photon-subtracted squeezed coherent state (PSSCS), which is theoretically constructed by repeatedly subtracting photons from the squeezed coherent state (SCS) with squeezing parameter r and displacement amplitude α=|α|eiφ. Employing the normal ordering form of density operator of the SCS, we study the nonclassicality of the PSSCS by analyzing Mandel’s Q-parameter, quadratures squeezing, photon-number distribution (PND), and Wigner function (WF). We find that the PND in a PSSCS is a periodic function of φ with a period π and exhibits more remarkable oscillations than that of a SCS in the case of strong squeezing. The partial negative region of the WF is sensitive to r and |α|. The fidelity between PSSCS and SCS is analyzed, which manifests that larger photon subtraction number may result in lower fidelity. By virtue of the thermal entangled state representation the decoherence of the PSSCS in thermal environment is studied through the time evolution of the WF. The negative volume of the WF gradually diminishes with the increase of evolution time and thermal photon number, respectively. The study of the PSSCS shows that generating new photon-number-controllable nonclassical states from a weak coherent light may be realized by subtracting suitable photons from a SCS.
We theoretically put forward the Hermite-excited squeezed thermal states (HESTS) by applying operator Hermite polynomials on squeezed thermal states. Starting from the normally ordered density operator of squeezed thermal states and operator Hermite polynomials, the normalization factor is obtained, which is related to the Legendre polynomials. Several phase-space distribution functions, i.e., the Q function, P function, Wigner function (WF), and R function, are analytically derived. And the non-Gaussianity and nonclassicality are mainly reflected by the negativity of non-Gaussian WF and the existence of nonclassical depth. In addition, by deriving the normally ordered density operator and WF of HESTS in the laser channel, the decoherence effect is studied and discussed. Finally, the quantity in measuring non-Gaussianity is calculated to further quantitatively measure the non-Gaussianity of the resulting states.
We studied the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of the Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.
We study nonclassical properties of the optical field when photon subtraction/addition coherent operation ta+ra† (|t|2+|r|2=1) acts on a squeezed thermal state (STS) by examining its quadrature squeezing, sub-Poissonian statistics, and negativity of the Wigner function. The degree of squeezing of the coherent operated squeezed thermal state (COSTS) becomes weaker. The Mandel Q parameter decreases with r and quickly becomes negative, which implies sub-Poissonian statistics. Both the negative dip and negative area of the Wigner function increase with r for small squeezing values of κ. Decoherence of the COSTS in an amplitude-damping channel is studied by the time evolution of the Wigner function. The length of time that this nonclassical field preserves its partial negativity of the Wigner function can be modulated by the coherent operation. All these results indicate that the nonclassicality of the STS is sensitive to the coherent operation.