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Journal of Shangluo University

The Effects of Equal-Power 2p-Th Power Y-Squrrzing of Generalize Magnetic Field Component in the State |Ψ_6~(3)>q

Chen Yong-zhuang

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

It is constructed that the sixth kind of multimode superposition light field statel(3)3, which is made of the linear superpositions of macroscopically distinct three quantum state named multimode complex conjugation coherent state 1(Z),the contrary state l{-Zj}, of multimode complex conjugation coherent l{Zj}, and multimode coherent state 1{Z}),.By using the theory of multitmode squeezed states,the generalized nonlinear equal-order 2p-th power Y-squeezing effects of generalizde magnetic field component in the state 6 ), mentioned is studied firstly in detail.lt is found that:if the squeezed rcumber N=2p, certain conditions are satisfied respectively by the initial phase (here, j=1,2,3,……,q)of each mode in the state , by the initial phase difference (θ3-θ1), (θ3-θ2) between any two components in the , and by the sum of mean photon-numbers of all the single-mode coherent state light field which is modulated by the intial phase cpj of each mode,the generalized magnetic field component in the state can always display the effects of even-number generalized nonlinear equal-order 2p-th power y-squeezing.

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Journal of Northwest University•Jan 1, 2003•0 citations
It is constructed that the sixth kind of multimode superposition light field statel(3)3, which is made of the linear superpositions of macroscopically distinct three quantum state named multimode complex conjugation coherent state 1(Z),the contrary state l{-Zj}, of multimode complex conjugation coherent l{Zj}, and multimode coherent state 1{Z}),.By using the theory of multitmode squeezed states,the generalized nonlinear equal-order 2p-th power Y-squeezing effects of generalizde
magnetic field component in the state 6 ), mentioned is studied firstly in detail.lt is found that:if the squeezed rcumber N=2p, certain conditions are satisfied respectively by the initial phase (here, j=1,2,3,……,q)of each mode in the state , by the initial phase difference (θ3-θ1), (θ3-θ2)
between any two components in the , and by the sum of mean photon-numbers of all the single-mode coherent state light field which is modulated by the intial phase cpj of each mode,the generalized magnetic field component in the state can always display the effects of even-number generalized nonlinear equal-order 2p-th power y-squeezing.
By utilizing the theory of multimode squeezed states established recently, the generalized nonlinear even number power equal-power N-th power Y-squeezing effects of generalized magnetic-field component in the new kind of multimode quantum light-field state (｜Ψ~((3))〉_q) is studied firstly in detail, which is composed of the linear superposition of macroscopically distinct three quantum states named multimode complex conjugation imaginary coherent state, the contrary state of multimode complex conjugation imaginary coherent state and multimode complex conjugation coherent state. It is found that under certain and fixed conditions, the generalized magnetic-field component in the state ｜Ψ~((3))〉_q can always display the effects of even number power generalized nonlinear equal-power N-th power Y-squeezing.
Three-state superposition multimode superposition state lightfield is constructed by the linear superposition of multimode coherent state,multimode complex conjugate coherent state and its contrary state.Through multimode squeezing theory,the characteristics of generalized magnetic field equal power N-th power H-squeezing are studied.It is found that,when the squeezed power number is even,and when the initial phases of each mode,the initial phase differences between states,and the sum of the average number for initial phase modulation of each state change continuously between certain closed intervals,then the generalized magnetic field component can always present the effect of periodically changing and generalized non-linear equal-power even-number-power H-squeezing.
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 is constructed in this paper that the three-states superposition multimode functional superposition state light field ｜ψ~((3))_f〉_q is made up of the multimode vacuum state ｜{0_j}〉_q, and the two different multimode complex functional coherent states ｜{f~~((a)*)_f(x,y,z)}〉_q and ｜{f~~((b)*)_f(x,y,z)}〉_q which have rather different spatial intensity distribution characteristic according to the superposition principle of quantum state in quantum mechanics. The properties of equal-power higher-power amplitude-squeezing (Y-squeezing) of generalized magnetic field component of the state ｜ψ~((3))_f〉_q is studied firstly by utilizing the multimode squeezed state theory. It is shown that under a series of fixed conditions, the generalized magnetic-field component of the state ｜ψ~((3))_f〉_q can display the effect of generalized nonlinear equal-power higher-power Y-squeezing which changes periodically and alternatively; and the asymmetrical spatial distribution of the classical intensity and the classical amplitude, and the spatial distribution features of the initial classical phase of light-field in the state ｜ψ~((3))_f〉_q would have a direct influence upon the squeezed degree of equal-power higher-power Y-squeezing present by the generalized magnetic-field component in the state ｜ψ~((3))_f〉_q.
Based on the superposition of state in the quantum mechanics,the multi-mode superposition |Ψn(2), is mode of the multi-mode complex conjugate coherent state | {z^ } , and the contrary state | { - zj(b)}q of multi-mode complex conjugate coherent state | { - zj(b)* }q (here j = 1, 2, 3,…, q). By using the multi-mode squeezed state theory,the equal-power Nth Power Y-Squeezing properties in the | Ψn(2)q is studied. It is found that under the conditions of the amplitudes orresponding modes are unequal but the initial phases of corresponding modes are equal,scilicet Rj(a)≠Rj(b) and ψj(a)=ψj(b)=ψj,the two quardrature phase components of state |Ψn(2)q can always display respectively the equal-power Nth power Y-squeezing effects which changes periodically while some conditions are satisfied respectively by the initial phase pj of each mode and initial phase difference θpq(R) -θnq(R) =Δθ between the two components of the state | Ψn(2)q whether squeezing-order-number N is odd number or even number, but squeezing-intensity under N is odd number, bigger than squeezing-intensity under N being even number.