Abstract
Phase space analysis of quantum states is a newly developed topic in quantum optics. In this work we present Wigner phase space distributions for the two-mode binomial state produced by quantum entanglement between a vacuum state and a number state in a beamsplitter. By using two new binomial formulas involving two-variable Hermite polynomials and the so-called entangled Wigner operator, we find that the analytical Wigner function for the binomial state |ξ〉q ≡ D(ξ) |q, 0〉 is related to a Laguerre polynomial, i.e.,
and its marginal distributions are proportional to the module-square of a single-variable Hermite polynomial. Also, the numerical results show that the larger number sum q of two modes lead to the stronger interference effect and the nonclassicality of the states |ξ〉q is stronger for odd q than for even q.
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Project supported by the National Natural Science Foundation of China (Grant No.11347026), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2016AM03 and ZR2017MA011)
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Li, KC., Meng, XG. & Wang, JS. Phase Space Analysis of the Two-mode Binomial State Produced by Quantum Entanglement in a Beamsplitter. Int J Theor Phys 58, 2521–2530 (2019). https://doi.org/10.1007/s10773-019-04142-3
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DOI: https://doi.org/10.1007/s10773-019-04142-3