{"title":"Higher-order squeezing of both quadrature components in superposition of orthogonal even coherent state and vacuum state","authors":"Pankaj Kumar, Rakesh Kumar","doi":"10.1016/S0034-4877(24)00056-9","DOIUrl":null,"url":null,"abstract":"<div><div>We study the Hong–Mandel higher-order squeezing of both quadrature components for an arbitrary 2<em>n</em><sup>th</sup>-order (<em>n</em> ≠1) considering the most general Hermitian operator, <em>X<sub>θ</sub> = X</em><sub>1</sub> cos <em>θ + iX</em><sub>2</sub> sin <em>θ</em>, in the superposed state, |<em>Ψ</em>〉 = <em><strong>K</strong></em> [|Ψ<sub>0</sub>) + <em>re</em><sup><em>i</em>ϕ</sup> |0〉] of the orthogonal even coherent state and vacuum state. Here | Ψ<sub>0</sub>〉 = <strong><em>K</em></strong>[|α, +〉 + |iα, +〉] is the orthogonal coherent state, |α, +〉 = <strong><em>K</em></strong>′[|α) + | – α〉] and |<em>i</em>α, +〉 = <strong><em>K</em></strong><em>″</em> [|<em>i</em>α, +〉 + | – <em>i</em>α, +〉] are even coherent states, operators <em>X</em><sub>1,2</sub> are defined by <em>X</em><sub>1</sub> + <em>iX</em><sub>2</sub> = <em>a, a</em> is the annihilation operator, α, <em>θ</em>, <em>r</em> and ϕ are arbitrary parameters and the only restriction on these is the normalization condition of the superposed state |<em>Ψ</em>〉. We find that maximum simultaneous 2<em>n</em><sup>th</sup>-order Hong–Mandel squeezing of both quadrature components <em>X<sub>θ</sub></em> and <em>X<sub>θ+π</sub></em>/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 2<em>n</em><sup>th</sup>-order squeezing for <em>n</em> = 2,3 and 4, i.e. fourth, sixth and eighth-order squeezing with different parameters have also been discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 1","pages":"Pages 73-82"},"PeriodicalIF":1.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000569","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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.
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.