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Journal of Optoelectronics·laser

The Properties of Unequal-power N_j-th Power Y-squeezing in the Third Kind of Multimode Superposition State Light Field with the Superposition of Three Quantum States

Sun Zhong

Published Jan 1, 2003• 1 citation
OpenAlex

Abstract

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.

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The first kind of the three state superposition multimode superposition state light field ψ(3)1q is constructed that is composed of multimode coherent state light field {Zj}q, multimode vacuum state light field {0j}q and contrary state {-Zj}q of multimode coherent state light field {Zj}q and that is based on the linear superposition principle of quantum state in quantum mechanics. Then the multimode squeezed state theory is utilized to study the effects of equalpower higherpower sum squeezing of generalized electric field component in the state ψ(3)1q . It is found that under certain and fixed conditions, the generalized electric field component (or the second perpendicular phase component) of the state ψ(3)1q can always display generalized nonlinear equalpower oddnumbermode with evennumberpower, evennumbermode with oddnumberpower, evennumbermode with evennumberpower, or oddnumbermode with oddnumberpower higherpower sum squeezing effects respectively and periodically.

Journal of Shaanxi Normal University•Jan 1, 2003•0 citations
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.
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.
It was constructed firstly that the three-states superposition multimode functional superposition state light-field|ψ~((3))_f_q was made up of the two different multimode complex conjugate functional coherent state |{f~(((a))~*)_j(x,y,z)}_q and |{f~(((b))~*)_j(x,y,z)}_q which had rather different spatial intensity distribution characteristics and the multimode vacuum state |{0_j}_q according to the linear superposition principle of quantum state in quantum mechanics. And then the multimode squeezed state theory was utilized to study the effects of generalized nonlinear unequal-power higher-power Y-squeezing of generalized magnetic-field component in the state|ψ~((3))_f_q. It was shown that under a series of fixed conditions,the generalized magnetic-field component of the state|ψ~((3))_f_q can always display the effects of generalized nonlinear unequal-power higher-power Y-squeezing which changes periodically and alternatively; the any asymmetrical spatial distribution profile of the classical intensity and the classical amplitude,and the any spatial distribution features of the initial classical phase of the quantum light-field state|ψ~((3))_f_q would have a direct influence upon the squeezed degree and squeezed depth of generalized nonlinear unequal-power higher-power Y-squeezing present by the generalized magnetic-field component in the state |ψ~((3))_f_q.
In this paper,the multimode squeezed state theory is utilized to study the characteristics of generalized nonlinear-unequal-power N j -th power H-squeezing of generalized electric-field component in the state |Ψ (2) (f) g, made up of the linear superposition of multimode functional coherent state |{f j (x,y,z) } g and its contrary state |{-f j( x,y,z )} g according to the superposition principle of quantum state in quantum mechanics.It shows the results:under the condition of the sum of squeezing-power-number being an any odd-number,while some other fixed conditions are satisfied by the suate |Ψ (2) (f) g the state |Ψ (2) (f) g can display the effects of any generalized nonlinear unequal-power N j -th power H-squeezing that changes periodically and alternatively.
The first kind of the three state superposition multimode superposition state light field ψ(3)1q is constructed that is composed of multimode coherent state light field {Zj}q, multimode vacuum state light field {0j}q and contrary state {-Zj}q of multimode coherent state light field {Zj}q and that is based on the linear superposition principle of quantum state in quantum mechanics. Then the multimode squeezed state theory is utilized to study the effects of equalpower higherpower sum squeezing of generalized electric field component in the state ψ(3)1q . It is found that under certain and fixed conditions, the generalized electric field component (or the second perpendicular phase component) of the state ψ(3)1q can always display generalized nonlinear equalpower oddnumbermode with evennumberpower, evennumbermode with oddnumberpower, evennumbermode with evennumberpower, or oddnumbermode with oddnumberpower higherpower sum squeezing effects respectively and periodically.