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Journal of Hubei University

The nonclassical properties of the photon-added two-mode squeezed vacuum state and its superposition state

Yu You-wen

Published Jan 1, 2007• 0 citations
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Abstract

The superposition state from the photon-added two-mode squeezed vacum state a+m|ξ〉 is constructed,and its noclassical properties are numerically studied under the principle of superposition in quantum mechanics.The results reveal that under certain conditions,the mean photon number of the superposition state exhibits oscillating phenomenon of collapses and revivals,bot sub-Poissonian photon statistical character and the phase squeezing of the field in the superposition state are stronger than ones in the single photon-added two-mode squeezed vacuum state.

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The superposition state from the photon-added two-mode squeezed vacum state a+m|ξ〉 is constructed,and its noclassical properties are numerically studied under the principle of superposition in quantum mechanics.The results reveal that under certain conditions,the mean photon number of the superposition state exhibits oscillating phenomenon of collapses and revivals,bot sub-Poissonian photon statistical character and the phase squeezing of the field in the superposition state are stronger than ones in the single photon-added two-mode squeezed vacuum state.
We introduce states a † m | ξ ⟩ and a m | ξ ⟩, where| ξ ⟩ is a two-mode squeezed vacuum state. We examine the properties of these states by analytic derivation. Because of the entanglement between the modes of the field, photon adding (or substracting) for one of the modes results in interesting outcomes. For a two-mode squeezed vacuum state, the effect of annihilation of m a-photons is just the same as creation of m b-photons. Annihilation of photons of mode a (or mode b ) actually increases the mean number of photons of mode a and mode b . We also calculate Mandel Q parameter, cross-correlation function and squeezing of the field.
With a squeezing operation on the qubit state,we obtain a coherent superposition state of a squeezed vacuum state and a squeezed single photon state with certain weight rate.The coherent superposition state depends on the squeezing parameter and weight factor,I and its nonclassicality and non-Gaussian properties are researched.It is investigated by the sub-Poissonian statistics distribution of Mandel′s Q parameter and the negativity of the Wigner function.The non-Gaussianity of coherent superposition qubit state can be improved by adjusting the squeezing parameter and the weight factor.
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.
Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane [Formula: see text]-oscillator. We consider in details the role of noncommutativity parameter [Formula: see text] on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.
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 two-mode photon-added state defined by |?, q; m>?=?a+mb+m|?, q> up to a normalization constant is introduced, where |?, q> is a pair coherent state and m an integer. It is shown that the fields in such a state have remarkable quantum features such as sub-Poissonian statistics, violations of Cauch-Schwarz inequalities, correlations in the number fluctuations and squeezing. We examine the influence of photon-adding on the properties of pair coherent state, and propose a method of generating two-mode photon-added states in the context of cavity quantum electrodynamics.