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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Deformed photon-added nonlinear coherent states and their non-classical properties
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Deformed photon-added nonlinear coherent states and their non-classical properties

机译：形变加光子的非线性相干态及其非经典性质

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摘要

In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f, m〉, which in a special case lead to the well-known photon-added coherent state (PACS) |α, m〉. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that the introduced states can also be classified in the f-deformed coherent states, with a special nonlinearity function. Next, we will show that these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m, i.e. |α, f, -m〉, is then presented. Our approach has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, non-degenerate spectrum. Finally, after applying the formalism to a particular physical system known as the P?schl-Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function f(n) = √n, some of the non-classical properties, such as the Mandel parameter, second-order correlation function, in addition to first- and second-order squeezing of the corresponding states, will be investigated numerically.
机译：在本文中，我们将尝试为构造变形的加有光子的非线性相干态（DPANCSs）|α，f，m〉提出一个一般形式，这在特殊情况下会导致众所周知的加有光子的相干态（PACS）|α，m〉。研究了引入的DPANCS的一些代数结构，尤其研究了作为广义相干态最重要性质的恒等式的解析。同时，将证明引入的状态还可以被分类为具有特定的非线性函数的f变形相干态。接下来，我们将说明可以通过简单的理论方案来产生这些状态。然后，对具有负值m的DPANCS进行讨论，即|α，f，-m>。我们的方法有潜力用于构建各种新型DPANCS，它们对应于具有已知非线性函数的任何非线性振荡器，以及具有已知离散，非简并光谱的任意可解量子系统。最后，在将形式主义应用于称为P？schl-Teller（PT）势的特定物​​理系统和对应于特定非线性函数f（n）=√n的非线性相干态之后，一些非经典性质除了相关状态的一阶和二阶压缩外，还将对诸如Mandel参数之类的二阶相关函数进行研究。

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