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Physical Review A

Effects of the vacuum state on the statistics of nonclassical states

N. Alioui, Akila Frahi-Amroun, C. Bendjaballah

Published Oct 10, 2007• 1 citation
Publisher

Abstract

Based on the calculation of the Wigner function, some statistical properties of the superposition of two coherent states with a vacuum state are demonstrated. The distance variation difference function is calculated for these states. Application of homodyne statistics shows that the addition (subtraction) of the vacuum state can improve the classical channel capacity of a noiseless binary symmetric system.

DOI
10.1103/physreva.76.043810

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Based on the calculation of the Wigner function, some statistical properties of the superposition of two coherent states with a vacuum state are demonstrated. The distance variation difference function is calculated for these states. Application of homodyne statistics shows that the addition (subtraction) of the vacuum state can improve the classical channel capacity of a noiseless binary symmetric system.
The statistical properties of m -coherent superposition operation (μ a + va † ) m on the single-mode squeezed vacuum state (M-SSVS) and its decoherence in a thermal environment are studied. Converting the M-SSVS to a squeezed Hermite polynomial excitation state, we obtain a compact expression for the normalization factor of M-SSVS, which is the Legendre polynomial of the squeezing parameter. We also derive the explicit expression of the Wigner function (WF) of the M-SSVS, and find the negative region of the WF in phase space. The decoherence effect on this state is then discussed by deriving the time evolution of the WF. Using the negativity of the WF, the loss of nonclassicality is then discussed.
The statistical properties of m-coherent superposition operation(μa + νa■)m on the single-mode squeezed vacuum state(M-SSVS) and its decoherence in a thermal environment are studied.Converting the M-SSVS to a squeezed Hermite polynomial excitation state,we obtain a compact expression for the normalization factor of M-SSVS,which is the Legendre polynomial of the squeezing parameter.We also derive the explicit expression of the Wigner function(WF) of the M-SSVS,and find the negative region of the WF in phase space.The decoherence effect on this state is then discussed by deriving the time evolution of the WF.Using the negativity of the WF,the loss of nonclassicality is then discussed.
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We discuss nonclassical properties of single-photon subtracted squeezed vacuum states in terms of the sub-Poissonian statistics and the negativity of the Wigner function. We derive a compact expression for the Wigner function from which we find the region of phase space where Wigner function is negative. We find an upper bound on the squeezing parameter for the state to exhibit sub-Poissonian statistics. We then study the effect of decoherence on the single-photon subtracted squeezed states. We present results for two different models of decoherence, viz. amplitude decay model and the phase diffusion model. In each case we give analytical results for the time evolution of the state. We discuss the loss of nonclassicality as a result of decoherence. We show through the study of their phase-space properties how these states decay to vacuum due to the decay of photons. We show that phase damping leads to very slow decoherence, slower than the photon-number decay.
Master equations of density operators can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The solution of master equations of density operators is given.We get the Wigner function evolution formula in phase space and photon number distribution formula of the state,which is a superposition of vacuum state and single-photon state initially in laser process.By numerical calculation we plot its Wigner function and photon number distribution evolution curves,when cavity gain constant and cavity loss constant are both equal to certain values.The effect of decoherence on nonclassical property of the state is discussed by comparing negative area size and the depth of negativity of Wigner function.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease and then vanish with dissipation.In addition,we calculate the variation of negative volume of Wigner function with dissipation time.We find that it decreases with dissipation time increasing.These results show that the nonclassical properties of the state are weakened and then disappear with dissipation time increasing.