Generating a Nonclassical Thermal State Via Number Operators
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Generating a Nonclassical Thermal State Via Number Operators Gang Ren1 · Jian‑ming Du1 · Hai‑jun Yu1 · Wen‑hai Zhang1 Received: 18 February 2020 / Accepted: 25 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We study a nonclassical thermal state by repeatedly operating the number operator on normal thermal state. Then, we investigate the nonclassical features of this state according to the P-function, photon-number distribution, Mandel’s Q-parameter, second-order correlation function and negative Wigner distribution as well as squeezing properties. Our results show that this state presents nonclassical properties, such as sub-Poissonian statistics, anti-bunching effects and negative Wigner distribution, at low temperature with small parameter m, which is the number of times for the number operator operates on normal thermal state. However, the squeezing effect of this state is not found. Keywords Thermal state · Number operator · Low temperature · Sub-Poissonian statistics · Squeezing effect
1 Introduction In quantum information, non-Gaussian thermal state has been an important resource for its nonclassical properties such as photon anti-bunching and squeezing [1–3]. Non-Gaussian thermal state shows its efficiency in some quantum protocols for quantum information processing [4, 5]. It has been shown that the generation of nonclassical states may be related to photon operations such as photon addition and subtraction [6, 7]. Such states have some enhanced nonclassical properties, such as sub-Poissonian statistics, higher-order squeezing and negativity of Wigner function. The photon-added and photon-subtracted operations have been realized in the experiment by using nonlinear processes in the optical cavity [8, 9]. In recent years, theoretical and experimental effort has been focused on the sequential combination operations, such as annihilation-then-creation (ATC) aa† and creation-then-annihilation (CTA) a† a [10, 11]. In experiment, recent studies * Gang Ren [email protected] 1
School of Electronic Engineering, Huainan Normal University, Huainan 232001, China
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Vol.:(0123456789)
Journal of Low Temperature Physics
have been designed to manipulate electromagnetic modes by effectively controlling their phase space. Operation of CTA has been realized by preventing access to a single energy level, corresponding to a number of photons N, confined the dynamics of the field to levels 0 to N − 1 [12]. Thus, this study set out to investigate the effect of CTA on thermal states. It is hoped that this research will contribute to a deeper understanding of the non-Gaussian operation on thermal states. This paper begins by introducing the CTA thermal state, and its normalization constant is also derived in Sect. 2. It will then go on to physical properties of this state via some quantum criterion, such as P-function, photon-number distribution, Mandel’s Q-parameter, second-order correlation function and negative Wigner distribution as well as the degree of squeezin
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