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Journal of Physics A Mathematical and General

Destruction of higher-order squeezing by thermal noise

Paulina Marian, Tudor A. Marian

Published Oct 7, 1996• 14 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/29/19/009

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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.
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.
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Abstract The nonclassicality is the prerequisite for quantum states to be applied into quantum information, especially for quantum metrology. Here we theoretically investigate the non-classical properties of the non-Gaussian state generated by repeatedly operating a number-conserving generalized superposition of products (GSP), i.e., ( s 1 aa † + t 1 a † a ) m with s 1 2 + t 1 2 = 1 , on the squeezed thermal state (STS), in terms of second-order correlation function, Mandel’s Q parameter, quadrature squeezing and Wigner function (WF). It is shown that, compared to the cases of the STS, the GSP-STS with the high-order GSP operations ( m > 1) at the small-squeezing levels can be beneficial to the existence of the photon-antibunching effect, the sub-Poissonian distribution and the partial negativity of the WF, apart from the quadrature squeezing. In addition, for the case of m = 1, we also compare with the non-classical properties of several different non-Gaussian resources, involving the photon-subtracted-then-added (PSTA) STS, the GSP-STS and the photon-added-then-subtracted (PATS) STS. It is found that the PSTA-STS with respect to the sub-Poissonian distribution and the partial negativity of the WF has a better performance than others. Significantly, the generated GSP-STS has an obvious advantage of showing the photon-antibunching effects, compared to the PSTA-STS and the PATS-STS, which means that our scheme may have an excellent guidance for the practical implementations in quantum information.
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.