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Photon-added coherent states as nonlinear coherent states

S. Sivakumar

Published Jan 1, 1999• 82 citations
OpenAlex

Abstract

The states |α,m〉, defined as â †m|α 〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(ˆn,m)â where f(ˆn,m) is a nonlinear function of the number operator ˆn. The explicit form of f(ˆn,m) 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 |α,m〉.

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Photon-added coherent states as nonlinear coherent states

S Sivakumar

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.

arXiv:quant-ph/9806061•Journal of Physics A Mathematical and General•Jan 1, 1999•102 citations

Photon-added nonlinear coherent states

Xiao-guang Wang, P. O. Box, Typeset Using Revtex

The photon-added nonlinear coherent states, defined as ${a}^{\\dagger m}|\\alpha, f>$ up to a normalization constant, are still nonlinear coherent states with the nonlinear function $f(N-m)[1-m/(N+1)]$. Here $% |\\alpha, f>$ is the nonlinear coherent state with the nonlinear function $f(N)$, $N$ is the number operator, $a^{\\dagger}$ is the boson creation operator and $m$ is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function $f(N+m)[1+m/(N+1)]$ obtained from the photon-added 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.

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

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

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.

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Squeezing Character of Squeezed Photon-added Coherent States

Jia Xin-juan

This paper introduces the squeezed photon-added coherent states defined by |α,m,ξ〉=S(ξ)a+m|α〉up to a normalization constant,where |α〉is a coherent state,m an integer and S(ξ) a squeezing operator.It studies the mathematical and physical properties of such states.Phase squeezing character of the fields in such states is demonstrated.The conclusion shows that the more field quadrature x is squeezed,the larger squeezing parameter becomes.

Journal of Hebei Polytechnic University•Jan 1, 2009•0 citations

Photon-added one-photon and two-photon nonlinear coherent states

Xiaoguang Wang

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

arXiv:quant-ph/0001003•Canadian Journal of Physics•Jan 1, 2001•8 citations

Boson inverse operators and associated coherent states

Anil Roy, C. L. Mehta

Making use of the recently introduced inverses of boson creation and annihilation operators, the authors show that the 'photon-added coherent states' are eigenstates of the operator (a Dagger m aa Dagger -m ) and also of the operator (a-ma Dagger -1 ) with eigenvalue alpha . The authors discuss completeness of these states. They obtain another family of photon-added coherent states which are proportional to a -m mod alpha ), where m is a positive integer and mod alpha ) is a coherent state. They show that these are the eigenstates of the operator (a -m a m+1 ) with eigenvalue alpha . Analogously, the authors introduce 'photon-depleted coherent states', a Dagger -m mod alpha ), and show that these are the eigenstates of the operator (a+ma Dagger -1 ) with eigenvalue alpha . The conditions for squeezing and antibunching of photons have also been discussed.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Oct 1, 1995•12 citations
The states |α,m〉, defined as â †m|α 〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(ˆn,m)â where f(ˆn,m) is a nonlinear function of the number operator ˆn. The explicit form of f(ˆn,m) 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 |α,m〉.
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.
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.
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.
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
Making use of the recently introduced inverses of boson creation and annihilation operators, the authors show that the 'photon-added coherent states' are eigenstates of the operator (a Dagger m aa Dagger -m ) and also of the operator (a-ma Dagger -1 ) with eigenvalue alpha . The authors discuss completeness of these states. They obtain another family of photon-added coherent states which are proportional to a -m mod alpha ), where m is a positive integer and mod alpha ) is a coherent state. They show that these are the eigenstates of the operator (a -m a m+1 ) with eigenvalue alpha . Analogously, the authors introduce 'photon-depleted coherent states', a Dagger -m mod alpha ), and show that these are the eigenstates of the operator (a+ma Dagger -1 ) with eigenvalue alpha . The conditions for squeezing and antibunching of photons have also been discussed.