Regular Article

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

¹ School of Physical Science and Information Engineering, Liaocheng University, Liaocheng 252059, P.R. China
² Shandong Provincial Key Laboratory of Optical Communication Science and Technology, Liaocheng University, Liaocheng 252059, P.R. China
³ Department of Computer, Weifang Medical University, Weifang 261000, P.R. China
⁴ Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, College of Physics and Engineering, Qufu Normal University, Qufu 273165, P.R. China
⁵ Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, P.R. China

^a e-mail: mengxiangguo1978@sina.com

Received: 9 May 2018
Received in final form: 18 August 2018
Published online: 12 February 2019

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 a^mbⁿe^{sa†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.