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Chinese Physics C

Statistic Properties of the Excited Even and Odd q-Coherent States

Jun Jiang

Published Jan 1, 2002• 0 citations
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Abstract

In this paper, the excited odd q-coherent state a +m qα o q and excited even q-coherent state a +m qα e q are constructed. The q and m dependences of mean photon number and sub-Poissonian character and antibunching effect are numerically studied. It is shown that when the q is far from 1, the second-order q-correlation function exhibits oscillating phenomenon, whose amplitude and period are independent of m; but the mean photon number and the Mandel Q q parameter increase greatly as m increases; and the sub-Poissonian character is not equivalent to the antibunching effect unless q→1.

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Chinese Physics C•Jan 1, 2003•0 citations
In this paper, the excited odd q-coherent state a +m qα o q and excited even q-coherent state a +m qα e q are constructed. The q and m dependences of mean photon number and sub-Poissonian character and antibunching effect are numerically studied. It is shown that when the q is far from 1, the second-order q-correlation function exhibits oscillating phenomenon, whose amplitude and period are independent of m; but the mean photon number and the Mandel Q q parameter increase greatly as m increases; and the sub-Poissonian character is not equivalent to the antibunching effect unless q→1.
The excited odd qs-coherent state and excited even qs-coherent state are constructed. The q , s , and m dependences of the antibunching effect are numerically studied. It is shown that for small r , the excited even qs-coherent state exhibits strong antibunching effect but the even qs-coherent state exhibits strong bunching effect; When the q ( q ≤ 1) is far from 1, as r2 increase, the second-order qs-correlation function exhibits oscillating phenomenon (i.e. alternates between antibunching effect and bunching effect) , whose amplitude and period increase as s and q decrease, but are approximately independent of m; When q→1, the second-order qs-correlation function also exhibits oscillating phenomenon, whose amplitude and period not only increase as 5 decreases but also are dependent on m; In general, the second-order qs -correlation function is more sensitive to s than to q .
This paper defines the Mandel Q-parameter of the q-deformed coherent state,and deduces the relation between the q-deformed Mandel Q-parameter and the q-deformed second-order correlation function.It proves that both the sub-Poissonian character and the antibunching effect in the q-deformed coherent state are not equivalent.The sub-Poissonian character of the photon-added k-boson q-coherent state is numerically studied.The result indicates that the sub-Poissonian character is evidently dependent on increased number m of photons.
The sub-poissonian photon statistical character of the excited k-boson q-coherent states a~(+m)_q|z,k,j_q(k≥3) is numerically studied.It is shown that the sub-poissonian photon statistical character is evidently dependent on m.When j = 0,the excited states(m≠0) can exhibit the sub-poissonian photon statistical character,but the unexcited states(m=0) cannot.When j≠0,both the excited states and the unexcited states can exhibit sub-poissonian photon statistical character.The sub-poissonian photon statistical character only appears in small x(x=|z|~2),which differs from the antibunching effect.
The squeezing property of the excited odd qs coherent state a +m qs α o qs and excited even qs coherent state a +m qs α e qs is numerically studied. It is shown that: (1) When the q(q≤1 ) or s is far from 1, the state a +m qs α o qs and state a +m qs α e qs exhibit strong qs squeezing, and as r 2 increases the qs squeezing function Δ e 1( Δ o 1) exhibits the oscillating phenomenon of increasing amplitude and increasing period. As m increases and s decreases, the amplitude of Δ e 1( Δ o 1) increases greatly. As s decreases, the period of Δ e 1( Δ o 1) increases but is independent of m. The m can be regard as the third parameter for controling the qs squeezing. (2) In general, the qs squeezing function Δ e 1( Δ o 1) is more sensitive to s than to q . That is, it is more resultful to control the qs squeezing by adjusting the parameter s than by adjusting the parameter q .