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Communications in Theoretical Physics

A Kind of Atomic Coherent State as a Two-Mode Squeezed State

Ma Shan-Jun, Wang Shu-Jing

Published Sep 1, 2009• 0 citations
Publisher

Abstract

We find that a kind of atomic coherent state, formed as exp[ξJ + – ξ*J − ] |00〉, when the SU(2) generators J± are taken as Fan's form, J + = (1/2)(a 1 – a 2 † )(a 1 † – a 2 ), J − = (1/2)(a † 1 + a 2 ) (a 1 + a 2 † ), and J 0 = (1/2)(a 1 † a 2 † – a 1 a 2 ), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.

DOI
10.1088/0253-6102/52/3/25

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We find that a kind of atomic coherent state, formed as exp[ξJ + – ξ*J − ] |00〉, when the SU(2) generators J± are taken as Fan's form, J + = (1/2)(a 1 – a 2 † )(a 1 † – a 2 ), J − = (1/2)(a † 1 + a 2 ) (a 1 + a 2 † ), and J 0 = (1/2)(a 1 † a 2 † – a 1 a 2 ), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.
我们发现一个新κ-参数挤压了协调州的| p ， q > _κ 表示，它拥有行为优良特征，即，它的 Wigner 功能“ s 边缘的分发在”q方向“并且在里面”p方向“是 Gaussian 形式 exp {-κ(q''- q )~ 2 }，并且 exp {( p ”-p)~2/κ},分别地。基于这， | p 的 Husimi 功能， q > _ κ也被获得，它是 Gaussian 拓宽 Wigner 功能的版本。| p， q > _ κ状态为学习 Husimi 操作员的各种各样的性质提供一个好代表性的空格。
A new class of non-classical state of the radiation field,called as two-mode squeezed superposed coherent state,is described in this paper.It is defined as ｜φ〉=CS(ξ)(｜α_1,α_2〉+e~(iφ)｜α~*_1,α~*_2〉).Calculating its normalized constant,its non-classical nature is discussed,including squeezed effect,sub-Poissonian distributing,anti-bunching effect,and the second-order cross correlation function between the two-mode.Numerical results demonstrate that the two-mode squeezed superposed coherent state possesses more obvious non-classical properties.Selecting suitable parameters α_1,α_2,φ,θandξ,the two-mode squeezed superposed coherent state can be reduced to the two-mode squeezed superposed vacuum state and the two-mode superposed coherent state.Therefore it is a kind of more generalized non-classical quantum state.
We have investigated the properties of two-mode squeezed states of various kinds: squeezed coherent states, squeezed number states, squeezed thermal states, and squeezed number-thermal states. The properties studied include characteristic functions, photon number distributions, and high-order moments. We show that a two-mode squeezed coherent state appears in either of its modes as a Glauber-Lachs superposition of a coherent signal with thermal noise; this generalizes the well-known thermofield result that a two-mode squeezed vacuum state behaves like a pure thermal state in either of its modes. We investigate the higher-order squeezing (in the sense of Hong and Mandel) of squeezed coherent-thermal and squeezed number-thermal states. Although the squeezing is found to increase with order in both cases, there are nevertheless interesting differences that can be traced to the fact that the Wigner function has a Gaussian form for the former but not for the latter.
We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.