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Acta Sinica Quantum Optica

Quantum Statistical Properties of the Superposition of Excited SU(2) Coherent States

Junjie Tang

Published Jan 1, 2009• 0 citations
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Abstract

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.

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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.
The quantum statistical properties in the system of a two-mode SU(1,1)coherent field interacting with a two-level atom are investigated by solving Milburn equation.The effects on the quantum statistical properties induced by the intrinsic decoherence,the two-mode photon number and the mean photon number are analyzed.The results show that the intrinsic decoherence strengthens the anti-bunching effect of the two-mode and the correlation intensity between the two modes and makes the first mode of the field always to be sub-Poissonian.The second-order coherence degree of the two-mode field also exhibits obvious collapse- revival effect with the intrinsic decoherence.The first mode of the field is sub-Poissonian with the evolution of the time.The photon anti-bunching appears and the correlation between the two modes of light is both positive and non-classical.But in most of the time,the second mode of the field is Poissonian with the evolution of the time and the photon bunching appears.
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.
Statistic properties of photon in the system of a two-mode field initially in a coherent state resonantly interacting with a three-level V-type atom are investigated by means of the quantum theory and numerical calculations.The dependence of the statistic properties of photon on the total photon number of the two-mode,the partition parameter and the coupling constant are discussed for three cases:①no state-selective atomic measurement;②direct state-selective atomic measurement;③state-selective atomic measurement after the application of a classical field.The results indicate that when the direct state-selective measurement is performed on the atom,the average intensity of the sub-poisson statistic distribution of mode a is enhanced;when the partition parameter is decreased,the average intensity of the sub-poisson statistic distribution of mode a is reduced and that of mode b is enhanced;when the state-selective mesurement is performed on the atom,the Cauchy-Schwarz inequality is violated;when the total photon number of the two modes is increased or the direct state-selective measurement is performed on the atom,the anti-correlation character between the two modes is preserved,but the average intensity of the anti-correlation is reduced.
The superposition of excited coherent states was constructed by superpositioning two excited coherent states of the same intensity and mutual phase conjugation,and their Wigner functions,second-order coherence degree and Mandel Q factors were calculated,upon which their non-classical properties were analyzed.The numerical results show that,the Wigner functions of the superposition of excited coherent states may become negative,and their second-order coherence degree and Mandel Q factors are both less than 1.Hence,the research shows that the quasi-probability distribution of the superposition of excited coherent states may become negative,and their light field has anti-bunching effects,with the distribution of photon number being of sub-Poisson distribution.Therefore,these superposition states are quantum states with non-classical properties.