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Journal of Jiangsu Teachers University of Technology

The Equal-order Nth Power H-Squeezing in A Sort Amplitude-mixing Superposition Light Field State with Two Nonsymmetry Quantum Sate

Meng Ji-de

Published Jan 1, 2003• 0 citations
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Abstract

Based on the liear superposition theory in the quantum mechanics,a kind of amplitude - mixing nonsymmetry superposition light field stateψ q isconstituted by multi - mode coherent light field state{z j(a)* } q and{z j(b)* } q .By using higher - order squeezing theory in multi - mode state,equal - order Nth power H-squeezing propertiesof theψ q isfound:when the certain phase conditionsare satis - fied,the two quardrature componentsofψ q present any order equal - order Nth power H - squeezing which changesperiodically.

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Journal of Shaanxi Normal University•Jan 1, 2004•0 citations
Based on the liear superposition theory in the quantum mechanics,a kind of amplitude - mixing nonsymmetry superposition light field stateψ q isconstituted by multi - mode coherent light field state{z j(a)* } q and{z j(b)* } q .By using higher - order squeezing theory in multi - mode state,equal - order Nth power H-squeezing propertiesof theψ q isfound:when the certain phase conditionsare satis - fied,the two quardrature componentsofψ q present any order equal - order Nth power H - squeezing which changesperiodically.
Based on the superposition theory in the quantum mechanics, the multi-mode superposition light field state is constituted by two nonsymrnetry multi-mode coherent states and which intensities are unequal. By using higer-order squeezing theory in multi-mode states, the equal-power Nth power H-squeezing properties of the is studied. It is found that when the certain phase conditions are satisfied,the two quardrature phase components in the present alternately equal-power Nth power H-squeezing effect which changes periodically, whether qN which is the product of cavity-mode total number q and squeezing -order N is odd number or even number.
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.
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,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.
In the paper, the properties of equal-order N-th power H-squeezing in a kind of intense asymmetrical multimode superposition state light field |Ψ (ab) I q with the superposition of macroscopically distinct two quantum states is studied in detail, By utilizing the theory of multimode squeezed states. It is found that if the products of squeezed order number N and cavity mode number q is an even number, under some conditions the state |Ψ (ab) I q can also present the effects of equal-order N-th Power H-squeezing in the first positive ponderance or second pvsitive ponderance.
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.