Aim By utilizing the multi-mode squeezing state theory, the properties of the equal-order N-th power Y squeezing of state ｜Ψ~((4))_(oe)V〉_q are studied.Methods According to the linear superposition principle of quantum mechanics, the fifth kind of four-state superposition multi-mode superposition states light field ｜Ψ~((4))_(oe)V〉_q is constructed with multi-mode imaginary-odd and even coherent states.Results ①When squeezing order N is an even number, state ｜Ψ~((4))_(oe)V〉_q never represents the equal-order N-th power Y squeezing: a. When N=4 m(m=1,2,3,…) state ｜Ψ~((4))_(oe)V〉_q presents the equal-order N-th minimum uncertainty state; b. When N=4 m′-2 (m′=1,2,3,…), state ｜Ψ~((4))_(oe)V〉_q represents half coherent state. ②When N is odd number, in different conditions, the first and second orthogonal phase components of state ｜Ψ~((4))_(oe)V〉_q respectively represents the odd or even number equal-order N-th power Y squeezing effects.Conclusion The new properties of the equal-order N-th power Y squeezing of state (｜Ψ~((4))_(oe)V〉_q) are found.
Aim By utilizing the multi-mode squeezing state theory, the properties of the equal-order N-th power Y squeezing of state ｜Ψ~((4))_(oe)V〉q are studied.Methods According to the linear superposition principle of quantum mechanics, the fifth kind of four-state superposition multi-mode superposition states light field ｜Ψ~((4))(oe)V〉q is constructed with multi-mode imaginary-odd and even coherent states.Results ①When squeezing order N is an even number, state ｜Ψ~((4))(oe)V〉q never represents the equal-order N-th power Y squeezing: a. When N=4 m(m=1,2,3,…) state ｜Ψ~((4))(oe)V〉q presents the equal-order N-th minimum uncertainty state; b. When N=4 m′-2 (m′=1,2,3,…), state ｜Ψ~((4))(oe)V〉q represents half coherent state. ②When N is odd number, in different conditions, the first and second orthogonal phase components of state ｜Ψ~((4))(oe)V〉q respectively represents the odd or even number equal-order N-th power Y squeezing effects.Conclusion The new properties of the equal-order N-th power Y squeezing of state (｜Ψ~((4))(oe)V〉_q) are found.
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.
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.
According to the linear superposition principle mechanics,the four-state superposition multi -mode superposition state light fidle is composed by multi -mode imaginary odd and complexconjugation coherent states,and its general results of N-th power Y squeezing are got out by the multi-mode squeezing state theory by numeric analying,it is found that:when parameters squeezng order N, total number of multi -modeq,average photon numbers of every mode Rj2 and modules of
superposition probability amplitudes r0(re)are take different values,the state will represents:
a.the equal-order N-Y minimum uncertainty states b. half coherent states effect c.the first and second orthometric component represent N-th power Y squeezing d. half-squeezing state.
According to the linear superposition principle in quantum mechanics,the superposition light field composed by multimode odd coherent state and multimode complex
conjugation imaginary odd coherent state Utilized the multimode squeezed state theory.the
properties of equal-power N-th power Y-squeezing of the state is studide,and it is found that:1)when squeezing number N=4P (P=1,2,3,...),if the initial phase of each vertical order (?),the phase difference θ1-θ2 and other parameters take different fixed value,the first quadrature component
of the state always presents different degree and periodic changing equal-order N-th power Y-squeezing;2)when squeezing number N=4P'-2 (P'=1,2,3,...) if the initial phase of each vertical order (?)j,the phase defference θ1-θ2 and other parameters take different fixed value,the second
quadrature component of the state always presents different degree and perindic changing equal-power N-th power Y-squeezing.
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, the eighth kind of multi-mode superposition state light field with two state superpositions is constructed, and thery of multi-mode squeezed state is utilized to study the properties of generalized nonlinear even-number-order and equal-order N-th power Y-squeezing of the state |Ψ (2) 8 q mentioned above. It is found that the state |Ψ (2) 8 q is a typical multi-mode nonclassical light field. It can display even-number-order equal-order N-th power Y-squeezing effects that change periodically, and under the other conditions. It can present the phenomenon of degenerate equal-order N-th power Y-squeezing.