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The Property of Generalized Nonlinear Equal-power Sum in Unequalled-intensity Unsymmetrical Superposition State

Wang Ju-xia

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

In this paper it is constructed a new type of unequalled-intensity unsymmetric multi-mode superposition state light field│Ψ (ab) 〉 q ,which is made of the linear superposition of macro scopically distinct two quantum states named the multi-mode imaginary conjugate coherent state│iZ j(a)  〉 q and the contrary state of multi -mode imaginary conjugate coherent state│iZ j(a)  〉 q respectively.By using the general theory of multi-mode squeezed state,the property of generalized nonlinear equal-power N-th power H-squeezing of the state│Ψ (ab) 〉 q mentioned above is studied firstly in detail.It is found that:(1).In the case of if Z j(a) ≠Z j(b) ,whether the q·N,the products of the cavity-mode number q and the squeezed power number N,is an even or odd number,the state│Ψ (ab) 〉 q can always presents equal-power N-th power H-squeezing effect.(2).When Z j(a) =Z j(b) and q·N is an odd number,the state│Ψ (ab) 〉 q can present the phenomenon of equal-power N-th power H-squeezing degenerate.

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In this paper it is constructed a new type of unequalled-intensity unsymmetric multi-mode superposition state light field│Ψ (ab) 〉 q ,which is made of the linear superposition of macro scopically distinct two quantum states named the multi-mode imaginary conjugate coherent state│iZ j(a)  〉 q and the contrary state of multi -mode imaginary conjugate coherent state│iZ j(a)  〉 q respectively.By using the general theory of multi-mode squeezed state,the property of generalized nonlinear equal-power N-th power H-squeezing of the state│Ψ (ab) 〉 q mentioned above is studied firstly in detail.It is found that:(1).In the case of if Z j(a) ≠Z j(b) ,whether the q·N,the products of the cavity-mode number q and the squeezed power number N,is an even or odd number,the state│Ψ (ab) 〉 q can always presents equal-power N-th power H-squeezing effect.(2).When Z j(a) =Z j(b) and q·N is an odd number,the state│Ψ (ab) 〉 q can present the phenomenon of equal-power N-th power H-squeezing degenerate.
The State |Ψ (ab) q=C (aI) pq |{iZ (a) * j} q+C (bI) nq |{-iZ (b) * j} q is a new type of unsymmetrical multi-mode superposition state light field. By using the unequalled-order squeezing general theory of multi-mode ridiative light field, the property of generalized nonlinear unequalled-order N j-thpower H-squeezing of the state |Ψ (ab) q mentioned above is studied firstly in detail. It is found that the two perpendicular component of the state |Ψ (ab) q can presents respectively any unequalled-order N j-th power H-squeezing effect that changes periodically and unequalled-order N j-H minimum uncertainty state under the different some conditions. The results show that the state |Ψ (ab) q is a kind of typical nonclassical multi-mode light field.
A new type of multi-mode superposition state light field |Ψ (2) n qis constructed, which is made of the linear superposition of macroscopically distinct two quantum state named the contrary state |{-iz * j} q of multi-mode imaginary conjugate coherent state |{iz * j} q and multi-mode vacuum state |Ψ (2) n q in this paper. By using the theory of multi-mode squeezed state, the property of generalized nonlinear equal-order N-th power Y-squeezing of the state |Ψ (2) n q mentioned above is studied firstly in detail. A series of significative new squeezing phenomenons are displayed.
On the bases of the linear superposition principle of quantum state in quantum mechanics, |ψ (3) 3q -the third kind of the three state superposition multimode superposition state light field is constructed that is composed of linear superposition of multimode complex conjugation coherent state |{Z * j} q ?multimode complex conjugation imaginary coherent state |{iZ * j} q and multimode vaccum state |{0 j} q . By utilizing the theory of multimode squeezed states, the properties of generalized nonlinear unequal-power N j-th power H-squeezing in the state |ψ (3) 3q is studied in detail. It is found that when the sum of the squeezing power of each mode is even number only and certain conditions are satisfied, the first perpendicular phase component and the second one of the state |ψ (3) 3q can always display any power generalized nonlinear unequal-power N j-th power H-squeezing effects that change periodically, respectively.
According to the linear superposition principle of state in quantum mechanics,the three state superposi-tion multimode Schr dinger-Cat State light-field,namely,multimode SCS light-field) │ Ψ ,3) q is constructed,which is composed of multimode complex conjugation imaginary coherent state,the contrary state of multimode complex conjugation imaginary coherent state,and multimode complex conjugation coherent state.The multimode squeezed state theory established recently by pro fessor Yang Zhiyong and academician Hou Xun is utilized to study the char-acteristics of generalized nonlinear unequal-power higher-power sum squeezing of the generalized electric-field com-ponent in the multimode SCS light-field │ Ψ ,3) q mentioned above in detail.The results show that under the condi-tion of the sum of squeezing-power-number for every mode being an even number,while some other fixed conditions are respectively satisfied by the sum of the products between the squeezing-power-number of each mode and the ini-tial phase which is in accordance with each mode above,by the interstate initial phase difference,and by the mean photon-number of each multimode coherent state light-field,the generalized electric-field component of the multi-mode SCS light-field │ Ψ ,3) q can always display the effects of any N j -th power generalized nonlinear unequal-power higher-power sum squeezing that change periodically and alternatively.
The properties of generalized nonlinear unequalled-order N j-th power H-squeezing in the two kinds of multi-mode superposition state light fields Ψ (2) +,3 q and Ψ (2) -,4 q constructed in document are studied in detail. By a large number of calculation, it is found that the two kinds multi-mode superposition states mentioned above can display any unequalled-order N j-th power H-squeezing that changes periodically and that the significative new phenomena of similitude squeezing and degenerate squeezing exist between the two superposition states. These results mentioned above demonstrate that the document is only the specific example of this paper under the certain conditions.
The third of the three state superpositions multimode superposition state light field |ψ(3)3q was constructed by linear superposition of multimode complex conjugation coherent state,|{Zj}q multimode complex conjugation imaginary coherent state |{iZj}q and multimode vaecum state |{0j}q.By utilizing the theory of multimode squeezed states,the properties of generalized nonlinear unequalpower Njth power Ysqueezing (or amplitude squeezing) in the state |ψ(3)3q was discussed.It is found that when the squeezing power of each mode Nj is even number only,and some certain conditions are satisfied,the first or second perpendicular phase component in the state |ψ(3)3q can always display any even number power generialized nonlinear unequalpower Njth power Ysqueezing effeets respectively,which is comlementary,also changes periodically.