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Chinese Physics B

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states: Non-classical and non-Gaussian properties

Xue-xiang Xu, Hong‐Chun Yuan, Yan Wang

Published Jul 1, 2014• 9 citations
Publisher

Abstract

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q -parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

DOI
10.1088/1674-1056/23/7/070301

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We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q -parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.
We study the nonclassical properties of arbitrary number photon creation-then-annihilation operation(CA) and annihilation-then-creation operation(AC) to the coherent states,and give the analytical expression.Because of the noncoummutativity of between annihilation operator and the creation operator,the states generated by AC operation and CA operation have different nonclassical properties.We firstly derive the analytical expressions of normalization factor for these states,and then study the statistics characteristics by some nonclassical properties,such as the Mandel Q parameters,the photon number distribution and the Wigner function.It is shown that these states have a very distinct nonclassical properties,and the nonclassical state generated by AC operation can present more clear nonclassicality than those generated by the CA operation.
We explore two observable nonclassical properties of quantum states generated by repeatedly operating annihilationthen-creation(AC) and creation-then-annihilation(CA) on the coherent state, respectively, such as higher-order subPoissonian statistics and higher-order squeezing-enhanced effect. The corresponding analytical expressions are derived in detail depending on m. By numerically comparing those quantum properties, it is found that these states above have very different nonclassical properties and nonclassicality is exhibited more strongly after AC operation than after CA operation.
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 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.
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.