Applying the theory of multi-mode squeezing state, the properties of the generalized nonlinear equal-power difference squeezing of the multi-mode complex conjugation odd- and even-coherent state light field are further studied in detail. The findings demonstrate that if, at least one mode n_j (j = 1, 2, 3,..., 2q) of the photon number is less than squeezing power N and q·N, the products of cavity modes number q and squeezing-power number N, no matter an even-number or odd-number, the generalized both magnetic field and electrical field perpendicular phase component of multi-mode complex conjugation odd- and even-coherent state light field present equal-power difference squeezing conditions at the same time. This phenomenon is called generalized nonlinear equal-power N-th Power X-Strange-Squeezing effect. The result is completely different from what has been reported recently and is not identical with the law of the uncertainty relation. Therefore, the above mentioned illustrates that the multi-mode complex conjugation odd- and even-coherent state light fields are really two types of multi-mode non-classical light field.
Applying the theory of multi-mode squeezing state, the properties of the generalized nonlinear equal-power difference squeezing of the multi-mode complex conjugation odd- and even-coherent state light field are further studied in detail. The findings demonstrate that if, at least one mode n_j (j = 1, 2, 3,..., 2q) of the photon number is less than squeezing power N and q·N, the products of cavity modes number q and squeezing-power number N, no matter an even-number or odd-number, the generalized both magnetic field and electrical field perpendicular phase component of multi-mode complex conjugation odd- and even-coherent state light field present equal-power difference squeezing conditions at the same time. This phenomenon is called generalized nonlinear equal-power N-th Power X-Strange-Squeezing effect. The result is completely different from what has been reported recently and is not identical with the law of the uncertainty relation. Therefore, the above mentioned illustrates that the multi-mode complex conjugation odd- and even-coherent state light fields are really two types of multi-mode non-classical light field.
The properties of equalpower Nth power X squeezing of the first enen number mode fourstate superimposition multimode superimposition state,which is composed of the linear super positions of the multimode even and odd coherent state that they have as same as even number mode,was studied based on the theory of multimode squeezed states.The results show when the qN(q,cavity mode number) is even number,and the photon numbers nj of any mode is less than N,two quadrature phase components of the state appear as equalorder Nth X squeezing in same time;when qN is odd number,njN, and also other necessary conditions the two quadrature phase components of the state present the equal power Nth power Xsqueezing effect.
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.
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.
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.
By utilizing the multi-mode squeezing state theory,the properties of the equal-order N-th power Y squeezing of stateare studied.According to the linear superposition principle of quantum mechanics,the fourth kind of four-state superposition multi-mode superposition states light field |Ψ~((4))_0,Ⅳ〉_qis constructed with multi-mode complex conjugate-odd coherent state(|Ψ~((2))_0,Ⅳ〉_q) and imaginary-odd coherent state(|Ψ~((2))_i,O〉_q).The new properties of the equal-order N-th power Y squeezing of state |Ψ~((4))_0,Ⅳ〉_qare found.When squeezing order Nis an even number,initial phase φ_j and initial phase difference θ_1-θ_2 indifferent conditions,1) When N=4m(m=1,2,3,…) the first orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents the equal-order N-th power Y squeezing;2).When N=4m′-2(m′=1,2,3,…),the second orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents N-th power Y squeezing effects.
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.