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Chinese Physics B

Construction of Laguerre polynomial’s photon-added squeezing vacuum state and its quantum properties*

LU Dao-ming

Published Jan 10, 2020• 1 citation
Publisher

Abstract

Laguerre polynomial’s photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of 〈ala †〉. Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that, firstly, the squeezing effect of the 1-order Laguerre polynomial’s photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter; secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and sub-Poissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state can enhance its non-classical properties.

DOI
10.1088/1674-1056/ab69e8

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Laguerre polynomial’s photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of 〈ala †〉. Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that, firstly, the squeezing effect of the 1-order Laguerre polynomial’s photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter; secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and sub-Poissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state can enhance its non-classical properties.
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 investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$κt>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).
We investigate the statistical properties and inseparability of the field states generated by any order nonlocal coherent photon addition (CPA) to the two-mode squeezed vacuum (TMSV). It is shown that the normalization factor of the CPA-TMSV is a Legendre polynomial, a compact expression. The statistical properties are discussed according to the analytical expressions of cross-correlation function, antibunching effect, and the negativity of its Wigner function. The inseparability is presented by using Shchukin–Vogel criteria and the Einstein–Podolsky–Rosen correlation. It is found that the symmetrical CPA-TMSV may possess stronger correlation than the single-mode photon-addition case. The lower bound of entanglement of the CPA-TMSV is considered, which indicates the logarithmic negativity is invalid for verifying the entanglement when the squeezing parameter is less than a threshold value, a period function of π/2. In addition, quantum teleportation is examined, which shows that asymmetric photon-added TMSV may be more useful for teleportation than the symmetric case.
Based on the two-mode squeezing operator which is the quantum version of the symplectic transformation, we find that the corresponding squeezed two-mode number state is just a two-variable Hermite polynomial excited state, which possesses well-behaved features, e.g. its Wigner function is a direct product of two Laguerre polynomials; its Husimi function, a Gaussian broaden version of the Wigner function, is related to two-variable Hermite polynomials. Moreover, its quantum statistical features, such as squeezing properties and the inter-mode photon bunching, are discussed.
We construct a new type of photon-added squeezed coherent state generated by repeatedly operating the bosonic creation operator on a new type of squeezed coherent state [Fan H Y and Xiao M 1996 Phys. Lett. A 220 81]. We find that its normalization factor is related to single-variable Hermite polynomials. Furthermore, we investigate its statistical properties, such as Mandel’s Q parameter, photon-number distribution, and Wigner function. The nonclassicality is displayed in terms of the intense oscillation of photon-number distribution and the negativity of the Wigner function.