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Journal of Physics A Mathematical and General

Photon-added squeezed vacuum (one-photon) state as an even (odd) nonlinear coherent state

Nai-Le Liu, Zhihu Sun, Hong-Yi Fan

Published Feb 28, 2000• 10 citations
Publisher

Abstract

We show that the photon-added squeezed vacuum a m S ( z )|0 and the photon-added squeezed one-photon state a m S ( z )|1 , where m is a non-negative integer, may be regarded as even and odd nonlinear coherent states, respectively. To achieve this, we derive an operator-valued function f ( N , m ) of the number operator N = a a such that a m S ( z )| i ( i = 0,1) are eigenstates of f ( N , m ) a 2 . Based on this, and using the unified method developed by Shanta et al , we find that a m S ( z )| i can be equivalently expressed in exponential forms. The eigenstates of f ( N ,- m ) a 2 are also constructed and their nonclassical features are studied in detail.

DOI
10.1088/0305-4470/33/9/315

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We show that the photon-added squeezed vacuum a m S ( z )|0 and the photon-added squeezed one-photon state a m S ( z )|1 , where m is a non-negative integer, may be regarded as even and odd nonlinear coherent states, respectively. To achieve this, we derive an operator-valued function f ( N , m ) of the number operator N = a a such that a m S ( z )| i ( i = 0,1) are eigenstates of f ( N , m ) a 2 . Based on this, and using the unified method developed by Shanta et al , we find that a m S ( z )| i can be equivalently expressed in exponential forms. The eigenstates of f ( N ,- m ) a 2 are also constructed and their nonclassical features are studied in detail.
The states | , m , defined as up to a normalization constant and where m is a non-negative integer, are shown to be the eigenstates of where is a nonlinear function of the number operator . The explicit form of is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of the state | , m . The eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states | m and |0 respectively.
From the photon-added one-photon nonlinear coherent states a†m|α, ƒ〉, we introduce a new type of nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states |m〉 and |0〉, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail. Finally, we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions. PACS Nos.: 42.50Dv, 03.65Fd
The photon-added nonlinear coherent states, defined as adaggerm∣alpha,f>{a}^{\\dagger m}|\\alpha, f>adaggerm∣alpha,f> up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N+1)]f(N-m)[1-m/(N+1)]f(N−m)[1−m/(N+1)]. Here % |\\alpha, f> is the nonlinear coherent state with the nonlinear function f(N)f(N)f(N), NNN is the number operator, adaggera^{\\dagger}adagger is the boson creation operator and mmm is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)] obtained from the photon-added nonlinear coherent states with negative values of m.m.m. The nonlinear coherent states corresponding to the positive and negative values of mmm are shown to be the result of nonunitarily deforming the number states ∣m>|m>∣m> and ∣0>|0>∣0>, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of mmm in detail.
In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f -deformed creation operator A = f ( n ) a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f -deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.
Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane [Formula: see text]-oscillator. We consider in details the role of noncommutativity parameter [Formula: see text] on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.