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New generalized binomial theorems involving two-variable Hermite polynomials via quantum optics approach and their applications

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Abstract

We extend the ordinary binomial theorem to the case which involves two-variable Hermite polynomials in the context of quantum optics, and analytically obtain several new generalized binomial theorems whose results exactly equal the single- or two-mode Hermite polynomials. As their applications in the field of quantum optics, we analytically prove that the multiple-photon-subtracted squeezed state ambnesa†b†+ra†+tb† |00⟩ is equivalent to the Hermite-polynomial-weighted quantum state serving as an easily produced non-Gaussian entangled information resource, and the Wigner functions of spin coherent states and their marginal distributions are respectively the Laguerre polynomials and the Hermite polynomials.

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Authors and Affiliations

  1. School of Physical Science and Information Engineering, Liaocheng University, Liaocheng, 252059, P.R. China

    Xiang-Guo Meng

  2. Shandong Provincial Key Laboratory of Optical Communication Science and Technology, Liaocheng University, Liaocheng, 252059, P.R. China

    Xiang-Guo Meng

  3. Department of Computer, Weifang Medical University, Weifang, 261000, P.R. China

    Jian-Ming Liu

  4. Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu, 273165, P.R. China

    Ji-Suo Wang

  5. Department of Material Science and Engineering, University of Science and Technology of China, Hefei, 230026, P.R. China

    Hong-Yi Fan

Authors
  1. Xiang-Guo Meng
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  2. Jian-Ming Liu
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  3. Ji-Suo Wang
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  4. Hong-Yi Fan
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Correspondence to Xiang-Guo Meng.

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Meng, XG., Liu, JM., Wang, JS. et al. New generalized binomial theorems involving two-variable Hermite polynomials via quantum optics approach and their applications. Eur. Phys. J. D 73, 32 (2019). https://doi.org/10.1140/epjd/e2018-90224-6

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  • DOI: https://doi.org/10.1140/epjd/e2018-90224-6

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