Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Reports on Mathematical Physics Pub Date : 2024-08-01 DOI:10.1016/S0034-4877(24)00056-9
Pankaj Kumar, Rakesh Kumar
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Abstract

We study the Hong–Mandel higher-order squeezing of both quadrature components for an arbitrary 2nth-order (n ≠1) considering the most general Hermitian operator, Xθ = X1 cos θ + iX2 sin θ, in the superposed state, |Ψ〉 = K [|Ψ0) + reiϕ |0〉] of the orthogonal even coherent state and vacuum state. Here | Ψ0〉 = K[|α, +〉 + |iα, +〉] is the orthogonal coherent state, |α, +〉 = K′[|α) + | – α〉] and |iα, +〉 = K [|iα, +〉 + | – iα, +〉] are even coherent states, operators X1,2 are defined by X1 + iX2 = a, a is the annihilation operator, α, θ, r and ϕ are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |Ψ〉. We find that maximum simultaneous 2nth-order Hong–Mandel squeezing of both quadrature components Xθ and Xθ+π/2 exhibited by the orthogonal even coherent state enhances in its superposition with vacuum state. We conclude that the values of higher-order momenta in the superposed state become much closer to the best minimum values of the corresponding values of higher-order momenta explored numerically so far than that obtained in orthogonal even coherent state. Variations of 2nth-order squeezing for n = 2,3 and 4, i.e. fourth, sixth and eighth-order squeezing with different parameters have also been discussed.
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正交偶相干态和真空态叠加时两个正交分量的高阶挤压
我们研究了在正交偶相干态和真空态的叠加态,|Ψ〉 = K [|Ψ0) + reiϕ |0〉]中,任意 2n 阶(n≠1)的两个正交分量的 Hong-Mandel 高阶挤压。这里 |Ψ0〉 = K[|α, +〉 + |iα, +〉]是正交相干态,|α, +〉 = K′[|α) + | - α〉]和 |iα, +〉 = K″ [|iα, +〉 + | - iα, +〉]是偶相干态,算子 X1、2由X1 + iX2 = a定义,a是湮没算子,α、θ、r和j是任意参数,唯一的限制是叠加态|Ψ〉的归一化条件。我们发现,在正交偶相干态与真空态的叠加中,正交偶相干态的正交分量 Xθ 和 Xθ+π/2 同时表现出的最大 2n 阶 Hong-Mandel 压缩会增强。我们的结论是,与正交偶相干态相比,叠加态中的高阶矩值更接近于迄今为止数值探索的相应高阶矩值的最佳最小值。此外,还讨论了 n = 2、3 和 4 的二阶挤压变化,即不同参数下的四阶、六阶和八阶挤压。
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来源期刊
Reports on Mathematical Physics
Reports on Mathematical Physics 物理-物理:数学物理
CiteScore
1.80
自引率
0.00%
发文量
40
审稿时长
6 months
期刊介绍: Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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