In this paper, according to the linear superposition principle in quantum mechanics, non-symmetry state superimposition state light fields ψII(ab )〉q of different intensities are constructed with both the multi-mode complex conjugation coherent state of contrary state {-Z(ja*)}〉q and the multi-mode imaginary conjugation coherent state of contrary state {-iZ(jb*)}〉q, by utilizing the theory of multimode squeezed states, and the properties of the multi-mode superimposition state of differ-intensities of nonsymmetrical superimpositions state with distinguishable two quantum states are studied. It is found that when qΣj=1 R(ja*)N= qΣj=1R(jb*)Nor q∏j=1R(ja)N= q∏j=1R(jb*)N,whilethe quantization conditions are satisfied by the constructed state ψII(ab)〉q with distinguishable two quantum states {-Z(ja*)}〉q and {-iZ(jb*)}〉q of the intensity of the corresponding mode (that is so-called average photon number), no matter how to change the cavity mode and the initial phases of the whole mode, the difference of the initial phases of states (θnq(aR )-θnq(bI)) and the probability amplitude superposition of two states rnq(aR)(or rnq(bI )), the light field state of the superimposition state ψII(ab)〉q is always in the equal-order N-Y minimum uncertainty state and the equal-order N-H minimum uncertainty state.
In this paper, according to the linear superposition principle in quantum mechanics, non-symmetry state superimposition state light fields ψII(ab )〉q of different intensities are constructed with both the multi-mode complex conjugation coherent state of contrary state {-Z(ja*)}〉q and the multi-mode imaginary conjugation coherent state of contrary state {-iZ(jb*)}〉q, by utilizing the theory of multimode squeezed states, and the properties of the multi-mode superimposition state of differ-intensities of nonsymmetrical superimpositions state with distinguishable two quantum states are studied. It is found that when qΣj=1 R(ja*)N= qΣj=1R(jb*)Nor q∏j=1R(ja)N= q∏j=1R(jb*)N,whilethe quantization conditions are satisfied by the constructed state ψII(ab)〉q with distinguishable two quantum states {-Z(ja*)}〉q and {-iZ(jb*)}〉q of the intensity of the corresponding mode (that is so-called average photon number), no matter how to change the cavity mode and the initial phases of the whole mode, the difference of the initial phases of states (θnq(aR )-θnq(bI)) and the probability amplitude superposition of two states rnq(aR)(or rnq(bI )), the light field state of the superimposition state ψII(ab)〉q is always in the equal-order N-Y minimum uncertainty state and the equal-order N-H minimum uncertainty state.
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.
In this paper,by utilizing the theory of multi-squeezed states,the conditions of Equal-order N-H uncertainty state and Equal-order N-H minimum uncertainty state on multi-mode light field state of differ intensity of nonsymmetry superimpositions state with distinguishable two quantum states are studied.It finds out(1) when qN is even the intensity and the initial phase is all equal,the light field state always presents Equal-order N-H minimum uncertainty state;(2) the intensity and the initial phase are not equal,but under certain conditions,the light field state also presents Equal-order N-H minimum uncertainty state.
According to the linear superposition principle mechanics,the four-state superposition multi-mode superposition state light field |Ψ~((4))_(oe)Ⅷ〉_q is composed by multi-mode imaginary odd and complicit conjugation coherent states,and its general results of N-th power Y squeezing are got out by the multi-mode squeezing state theory.By numeric analyzing,it is found that: when parameters squeezed order N,total number of multi-mode q,average photon numbers of every mode state R~2_j and modulo of superposition probability amplitudes r_o(r_e) are taken different values,the state |Ψ~((4))_(oe)Ⅷ〉_q will represent by the equal-order N-Y minimum uncertainty states,half coherent states effect,half squeezing state effect,the first or the second orthogonal component represent N-th power Y squeezing.6 refs.
Based on the superposition theory in the quantum mechanics, a kind of non-symmetry multi-mode Quantum superposition stateψq is constituted by the complex conjugate multi-mode coherent state{-zj(a)*}q and the imaginary conjugate coherent state{izj(a)*}q. By using the multimode squeezed states theory, the properties of equal-power even-order sum-squeezing ofψq is studied under the product of cavity order sum and squeezing order N, qN is even number, scilicet qN=2p(p=1,2,3,······). It is found that the two quardrature phase components of the ψq always present ultimately equal-power even-order sum-squeezing effect which changes periodically whether p is odd number or even number, while some phase conditions are satisfied respectively by sum of initial phase of each single modejj, and the initial mixing-phase Δθ+[(Rj(a)Rj(b)] which is composed of initial phase difference Δθ between the two components of the ψq mentioned above and the sum of Rj(a)Rj(b) products of amplitude of each mode in {zj(a)*}q and amplitude Rj(b) of each mode in. The squeezing-intensity under p is odd number is bigger.There is not this result in symmetry multi-mode superposition states.
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.
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.