The Effect of Even-number-order Equal-order N-th power Y-squeezingon the Eighth Kind of Multi-mode Superposition StateLight Field with Two State Superpositions
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.
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.
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.
A new type of multi-mode superposition state light field |Ψ (2) n qis constructed, which is made of the linear superposition of macroscopically distinct two quantum state named the contrary state |{-iz * j} q of multi-mode imaginary conjugate coherent state |{iz * j} q and multi-mode vacuum state |Ψ (2) n q in this paper. By using the theory of multi-mode squeezed state, the property of generalized nonlinear equal-order N-th power Y-squeezing of the state |Ψ (2) n q mentioned above is studied firstly in detail. A series of significative new squeezing phenomenons are displayed.
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.
The properties of generalized nonlinear unequalled-order N j-th power H-squeezing in the two kinds of multi-mode superposition state light fields Ψ (2) +,3 q and Ψ (2) -,4 q constructed in document are studied in detail. By a large number of calculation, it is found that the two kinds multi-mode superposition states mentioned above can display any unequalled-order N j-th power H-squeezing that changes periodically and that the significative new phenomena of similitude squeezing and degenerate squeezing exist between the two superposition states. These results mentioned above demonstrate that the document is only the specific example of this paper under the certain conditions.
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.
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.