The multi-mode squeezed state theory is utilized to study the effects of higher order unequal-order N_jth power H-squeezing on the multi-mode quantum superposition state |ψ〉_q that is made of the linear superpositinos of the two nonsymmetry multi-mode coherent states |{z~((a)~*)_j}〉_q and |-{z~((b)~*)_j}〉_q, it is found that two quardrature phase components in state |ψ〉_q can always display respectively the generalized nonliear higher-order unequal -order N_jth power Y-squeezing effects which changes periodically while some conditions are satisfied respectively by the sum ∑qj=1N_jφ_j of the multiplication N_jφ_j of the initial phase φ_j of each mode and squeezing order number N_j of each mode(here j=1,2,3,…,q), and by the initial phase difference θ~((R))_(pq)-θ~((R))_(nq) between the two components of state |ψ〉_q. The squeezing intensity is bigger when sum ∑qj=1N_j of squeezing order number N_j of each mode is odd number.
The multi-mode squeezed state theory is utilized to study the effects of higher order unequal-order N_jth power H-squeezing on the multi-mode quantum superposition state |ψ〉_q that is made of the linear superpositinos of the two nonsymmetry multi-mode coherent states |{z~((a)~)_j}〉_q and |-{z~((b)~)_j}〉q, it is found that two quardrature phase components in state |ψ〉q can always display respectively the generalized nonliear higher-order unequal -order N_jth power Y-squeezing effects which changes periodically while some conditions are satisfied respectively by the sum ∑qj=1N_jφ_j of the multiplication N_jφ_j of the initial phase φ_j of each mode and squeezing order number N_j of each mode(here j=1,2,3,…,q), and by the initial phase difference θ~((R))(pq)-θ~((R))(nq) between the two components of state |ψ〉_q. The squeezing intensity is bigger when sum ∑qj=1N_j of squeezing order number N_j of each mode is odd number.
The multi-mode squeezed state theory was utilized to study the effects of higher order unequal-order N_jth power Y-squeezing on the multi-mode quantum superposition state |Ψ_q that was made of the linear superpositions of the two nonsymmetry multi-mode coherent states |{z~((a)*)_j}_q and |{-z~((b)*)_j}_q.It was found that two quardrature phase components in state |Ψ_q could always display respectively the generalized nonliear higher-order unequal order N_jth power Y-squeezing effects which change periodically while some conditions are satisfied respectively by the product N_jφ_j of the initial phase φ_j of each mode, moreover the squeezing order number N_j of each mode(here j=1,2,3,...,q), and by the initial phase difference θ~((R))_(pq)-θ~((R))_(nq) between the two components of state |Ψ_q.The squeezing intensity was bigger when all of squeezing order number N_j of each mode were odd number.
In this paper, the multi-mode squeezed state theory is utilized to study the effects of even number-order unequal-power Njth power Y-squeezing on the two kind of multi-mode quantum superposition statesψ(2)± ■ that is made of the linear superposition of the multimode coherent stateR(a)j exp(-iφ■)■ and the multi-mode imaginary coherent states±iR(b)j exp(-iφ■)■.when the squeezing order number Nj of each mode is even number, viz. Nj=2pj(j=1,2,3,......q, pj=1,2,3,......), it is found that two kind ofψ(2)± ■can always display respectively the generalized nonlinear even-number-order unequal-power Njth power Y-squeezing effects which changes periodically while the some conditions are satisfied respectively by the initial phase φj of each mode,and by initial mixing-phase (θ[R]pq -θ(I)nq )■■R(a)j R(b)j which is composed of the initial phase difference θ(R)pq -θ(I)nq between the two components of the stateψ(2)± ■mentioned above and the sum ■R(a)j R(b)j of the products R(a)j R(b)j of amplitudes R(a)j and R(b)j .The squeezing-intensity is bigger when the pj is odd number.
In this paper,a kind of nonsymmetry multi-mode quantum superposition state Ψ〉_q is constituted by the complex conjugate multi-mode coherent state z~((a)*)_j〉_q and the contrary state -iz~((b)*)_j〉_q of imaginary conjugate coherent state iz~((b)*)_j〉_q.It is studied for the equal-order even-number-order Y-squeezing effect in Ψ〉_q, by using multi-mode squeezed state theory.When squeezing order N is even number ,viz. N=2p(p=1,2,3,…),it is found that the two quardrature phase components on the Ψ〉_q present alternately equal-order even-number-orderY-squeezing effect which changes periodically whether p is odd number or even number,while some phase conditions are saisfied respectively by the initital phase φ_i of each mode in Ψ〉_q and by the initital mixing-phase Δθ+∑qj=1[R~((a))_jR~((b))_j] which is composed of the initital phase difference between the two components of the state Ψ〉_q and the sum ∑qj=1[R~((a))_jR~((b))_j] of the product R~((a))_jR~((b))_j of amplitude of each mode in z~((a)*)_j〉_q and amplitude R~((b))_j of each mode in -iz~((b)*)_j〉_q . The squeezing-intensity odd-number p is bigger than that under even-number p,which is not the result in symmetry multi-mode superposition state.
Based on the superposition theory in the quantum mechanics, the nonsymmetry
multi-mode Quantum superposition state light field |ψ1f(2)q is constituted by complex conjugate multi-mode coherent state light field \{zj(a)*}q and reversed state |{-Zj(b)*}q of complex conjugate multi-mode coherent state. By using higer-order squeezing theory in multi-mode state, It is studied that equal power higher-order sum-squeezing properties in the |ψ1f(2)q,it is found: 1) When Rj(a) = Rj(b) = Rj and ψj(a) - ψj(b) = ±(2k1 + 1)π(k1 = 0, 1, 2, 3, ...... ), the
two quardrature phase components in the |ψ1f(2)q are all in N - H smallest uncertain state; 2) When Rj (a) = Rj(b) = Rj and ψj(a) = ψj(b) = ψj equal power higher-order sum-squeezing in
\ψ1f(2)q looks like the results in the literature 3; 3) When Rj(a)#Rj(b) and ψj(a) =ψj(b) = ψj and
the certain conditions are saisfied by and , The two quardrature phase
components in |ψ1f(2)q all present respectively equal power higher-order oum-squeezing effect which changes periodically whether qN is odd number or even number, but squeezing-intensity under qN is odd number is bigger then squeezing-intensity under qN is even number.
By utilizing the theory of multi-mode squeezed states, the property is studied on the generalized nonlinear unequal-order N j -th power Y-squeezing on a new type of multi-mode superimposition state light field | Ψ (2) msc q with distinguishable two quantum states. It is found that when squeezed orde N j=2p , no matter what p=2m+1(m=0,1,2,...) ,while the initial phases of corresponding mode φ j(j=1,2,3...,q) , the difference of initial phasas of states [θ (R) nq -θ (I) nq -∑[DD(]qj=1R 2 j] and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions. and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions.
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.