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Chinese Physics B

The entropic squeezing of superposition of two arbitrary coherent states

LU Dao-ming

Published Feb 1, 2008• 4 citations
Publisher

Abstract

In this paper the superpositions of two arbitrary coherent states |Ψ〉 = a |β〉 + b e iϕ |mβe iδ 〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.

DOI
10.1088/1674-1056/17/2/042

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In this paper the superpositions of two arbitrary coherent states |Ψ〉 = a |β〉 + b e iϕ |mβe iδ 〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.
In this paper, the quantum statistical properties of the superposition state,a｜ β〉+beiφ｜mβeiδ〉,which involves two arbitrary coh erent states, are investigated. The results show that this kind of super-positio n states generally exhibits squeezing effect or anti-bunching effect. The quantu m effects of the superposed state depend on β2 and the amplitude coe fficient m, as well as the changes of the phase difference between two coherent states δ, and the phase difference between two superposition coefficients φ al so plays an important role in squeezing or anti-bunching effects.
The influence of coherent state strength,phase angle and squeezing parameter on position and momentum entropic squeezing for squeezed even and odd coherent were discussed by numerical calculations.The results show that both the two states exhibit the entropic squeezing,and the maximum squeezing in squeezed even coherent state is greater than that of squeezed odd coherent state.The squeezing is related to the strength of coherent state,phase angle and squeezing parameter,in which the squeezing is related to the strength of coherent state,phase angle and squeezing parameter,in which the squeezing parameter is the principal factor.The squeezing of position entropy (or momentum entropy) for squeezed even coherent state will reach its maximum under the condition that the squeezing parameter ｜β｜=0.95 and other parameters are fixed.But this character does not exist in squeezed odd coherent state.
The amplitude-kth power characters of the superposition state |ψ=a|β+be~(iφ)|mβe~(iδ) of the generalized coherent states are studied, the results show that the possible kth-power squeezing can be expressed as k≠2nπ/δ when m=i, with n an integer and δthe phase difference between the two generalized coherent states; When m≠1, the kth-power can be even and odd; when δ=π the power of the squeezing can only be odd; when δ=π/2, the power of squeezing can be even and odd. These results show that the parameter phase difference δ plays the key role in determining the possible power of squeezing.
The quantum statistical properties of the superposition state, which involve two arbitrary coherent states |β〉 and |mβeiδ〉, are investigated from two aspects, such as the phase distribution and Winger function. The results show that the non-classical properties of the superposition state depend on β2, amplitude coefficient m, the phase difference between the coherent states δ, and the phase difference between the superposition coefficients . When selected suitable parameters the superposition state exhibits quantum effect. The phase distribution and Wigner function of an equally populated mixture of two coherent states are derived, too. By comparison the results show that the presence of the coherence terms makes the superposition state with full quantum-mechanical behavior.