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Journal of Optics

Squeezed Hermite polynomial state: nonclassical features and decoherence behavior

Xiang‐Guo Meng, Ji‐Suo Wang, Zhenshan S. Yang, Xiaoyan Zhang, Zhentao Zhang, Bao‐Long Liang, Kai‐Cai Li

Published Nov 12, 2019• 14 citations
Publisher

Abstract

Abstract We theoretically investigate the nonclassicality of the squeezed Hermite polynomial state (SHPS) by examining the squeezing feature, the oscillation of photon-number distribution (PND) and the negativity of the Wigner function (WF). Our results indicate that the squeezing operation leads to a large squeezing degree and negative volume of the WF, but the Hermite polynomial creation operation has less impact on them, and the two operations have opposite modulations of the PND. In addition, we study the evolution law of the SHPS in the amplitude decay channel (ADC). It is found that the density-operator evolution is related to two conjugated operator Hermite polynomials within normal ordering, which brings about a new two-variable special function and its generating function. We also find that the analytical WF evolution is represented as the compact form of this new special function, and that the large squeezing is more robust against the decoherence of the SHPS in the ADC.

DOI
10.1088/2040-8986/ab5693

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Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function (WF) for the squeezed negative binomial state (SNBS) and the analytical evolution law of density operator in the amplitude decay channel. The results show that the analytical WF is related to the square of the module of single-variable Hermite polynomials, which leads to a new two-variable special function and its generating function, and the parameters s and γ play opposite roles in the WF distributions. Besides, after undergoing this channel, the initial pure SNBS evolves into a new mixed state related to two operator Hermite polynomials within normal ordering, and fully loses its nonclassicality and decays to vacuum at long decay time.
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We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that the normalized factor is related to the two-variable Hermite polynomials. We then investigate the nonclassical properties in terms of Mandel's Q parameter, quadrature squeezing, second correlation, and the negativity of Wigner function (WF). It is shown that all these properties are related to the amplitude of coherent state, catalysis number and unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced as catalysis number and keeps a constant for single-photon catalysis. In addition, we examine the effect of decoherence by Wigner function, which show that the negative region, characteristic time of decoherence and structure of WF are affected by catalysis number and unbalanced BS. Our work provides a general analysis about how to prepare theoretically polynomials quantum states.
Abstract In this work, we theoretically construct an orthogonal state of a coherent state where the orthogonalizer is based on the Hermite polynomial excited operation with H m ( x ) being a Hermite polynomial of order m and creation operator , called the Hermite-excite-orthogonalized coherent state (HEOCS). Then, in comparison with the Hermite polynomial excited coherent state (HPECS), we numerically investigate their different nonclassical properties by examining several measurable features, such as photon number distribution, sub-Poisson statistics, the antibunching effect, the quadrature squeezing effect, and the negative Wigner function. The results demonstrate that both HEOCS and HPECS are non-Gaussian quantum states with highly nonclassical characteristics by improving and modulating the order of the Hermite polynomial and coherent amplitude, which indicates that performing the Hermite-excited operation on given Gaussian states is an effective approach to generating non-Gaussian states.
Abstract We propose a theoretical protocol to generate a kind of non-Gaussian state—a Laguerre polynomial excited coherent state (LPECS) by exploiting a two-mode squeezing transformation and a conditional measurement with a coherent state input. Then we investigate the nonclassical features of the LPECS according to the Glauber–Sudarshan P ( α ) function, photon number distribution, Mandel’s Q parameter, second-order correlation function, and squeezing properties as well as negative Wigner distribution. Our results show that the generated output state presents obvious nonclassical properties which can be modulated by a coherent amplitude, a squeezing parameter and a conditional measurement. In particular, the squeezing and negative Wigner function are clear.
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.