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ACTA PHOTONICA SINICA

Statistical Propertities of Excited Entangled Coherent States

Wang Zhong-jie

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

A new kind of entangled coherent states-excited entangled coherent states was obtained by acting boson inverse operators on some mode of entangled coherent states.The result shows that the new states are eigenstates of the 2k-th power of the annihilation operator.Because of the entanglement between the modes of the field,the mean number of mode a increased,and the mean number of mode b changed by photon-adding.After adding photons,sub-poissonian photon statistics and violation of the Cauchy-Schwatz inequality of the fields can be enhanced obviously,but the degree of intermode anticorrelation was weakened by the photon excitations.

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A new kind of entangled coherent states-excited entangled coherent states was obtained by acting boson inverse operators on some mode of entangled coherent states.The result shows that the new states are eigenstates of the 2k-th power of the annihilation operator.Because of the entanglement between the modes of the field,the mean number of mode a increased,and the mean number of mode b changed by photon-adding.After adding photons,sub-poissonian photon statistics and violation of the Cauchy-Schwatz inequality of the fields can be enhanced obviously,but the degree of intermode anticorrelation was weakened by the photon excitations.
The superposition of excited double-mode SU(2) coherent state |ψ=Cm(|M,ξ;m+ei|M,ξ*;m) is constructed and its quantum statistical properties are investigated with numeric method.The results exhibit that when the photons are added to the mode b of the double mode SU(2) coherent state,the two field modes can preserve anti-relation character,and presents a special effect of light amplification;the sub-Poissonian photon statistics properties of mode b is obvious enhanced and that of mode a is slightly weakened;anti-bunching effect of two modes of field are all enhanced,but as the quantum number of excitation m is increased,the anti-relation character of the two modes of field is weakened.
The mode of a photon-added double-mode SU(2) coherent state｜M,ξ;m〉=A_(Mξm)a~(+m)｜M,ξ〉is introduced and its quantum statistics property is investigated with numeric method. The results exhibit that when the photons are added to the mode aof the double mode SU(2) coherent state, the two field modes can preserve anti-relation character. The violation of Cauchy-Schwartz inequality, the sub-Poissonian photon statistics property of mode aand anti-bunching effect of mode bare enhanced, but the sub-Poissonian photon statistics property of mode band anti-bunching effect of mode a are weakened.
We introduce a new entangled state, which is composed of two photon-added coherent states. We discuss the entanglement of this state by using several sufficient entanglement criteria, such as higher-order entanglement criterion, EPR criterion, SU(1,1) algebra and Cauchy–Schwarz inequality. These criteria reflect some entanglement effects of this new state, but fail to find the degree of entanglement directly. Thus, we use the covariance to measure the entanglement in this state. Our findings show that the degree of entanglement decreases with the increasing of photon-number and the amplitude of the coherent states. One interesting result is that the new entangled state becomes a maximally entangled state when the photon-added number is 1 and the amplitude of the coherent states is zero, which is just one of the four Bell states.