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Laser Physics Letters

Nonclassical properties of coherent state orthogonalization via Hermite polynomial excited operation

Hong‐Chun Yuan, Xue-xiang Xu, Jianwen Cai, Ye‐Jun Xu

Published Apr 11, 2019• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ab0c86

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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.
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 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.
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.
An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text]. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.
Abstract We propose a scheme to generate a new kind of non-Gaussian state—the Laguerre polynomial excited coherent state (LPECS)—by using multiphoton catalysis with coherent state input. The nonclassical properties of the LPECS are studied in terms of nonclassical depth, Mandel’s parameter, second-order correlation, quadrature squeezing, and the negativity of the Wigner function (WF). It is found that the LPECS is highly nonclassical and its nonclassicality depends on the amplitude of the coherent state, the catalysis photon number, and the parameters of the unbalanced beam splitter (BS). In particular, the maximum degree of squeezing can be enhanced by increasing the catalysis photon number. In addition, we examine the effect of decoherence using the WF, which shows that the negative region, the characteristic time of decoherence, and the structure of the WF are affected by catalysis photon number and the parameters of the unbalanced BS. Our work provides general analysis on how to prepare polynomial quantum states, which may be useful in the fields of quantum information and quantum computation.
A scheme for conditional generating Hermite polynomial excited squeezed vacuum states (HPESVS) is proposed. Injecting a two-mode squeezed vacuum state (TMSVS) into a beam splitter (BS) and counting the photons in one of the output channels, the conditional state in the other output channel is just a HPESVS. To exhibit a number of nonclassical effects and non-Gaussianity, we mainly investigate the photon number distribution, sub-Poissonian distribution, quadrature component distribution, and Wigner function of the conditional HPESVS. We find that its nonclassicality closely relates to the control parameter of the BS, the squeezed parameter of TMSVS, and the photon number of conditional measurement. These further demonstrate that performing the conditional measurement on a BS is an effective approach to generate non-Gaussian state.