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Equal-order N-H Minimum Uncertainty State in Multi-mode Light Field State of Superimpositions State with Two Quantum States

XI Cai-ping

Published Jan 1, 2006• 0 citations
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Abstract

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.

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Chinese Journal of Quantum Electronics•Jan 1, 2004•0 citations
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.
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 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.
According to the theory of multi-mode squeezed state, the property of equal order N-th power H-squeezing effect on multi-mode light field state of different intensity and unsymmetrical superimpositions is studied. It is found that while the quantization conditions are satisfied by constructed state, two results will be obtained. First, the first and the second quadrature component of the quantum state can always present the effect of periodic changed equal-order N-th power H-sequence. Second, the state can always present equal-order N-th power H-sequence of squeezing occurrence.
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 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.