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International Conference on Quantum Information

Study of nonclassicality and decoherence of photon-subtracted squeezed vacuum

Asoka Biswas, G. S. Agarwal

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We discuss nonclassical properties of single-photon subtracted squeezed vacuum states and study its decoherence under different models. We find that the state is especially robust under phase diffusion model though its phase properties are lost.
DOI
10.1364/icqi.2007.jwc47

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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.
Extending the recent work completed by Biswas and Agarwal [Phys. Rev. A75, 032104 (2007)] to the case of m-photon-subtracted squeezed vacuum states (m-PSSVSs), we focus our study on nonclassicality and decoherence of the m-PSSVSs. The nonclassical properties are investigated in terms of the squeezing character, the oscillation of photon-number distribution, and the partial negativity of Wigner function (WF).We then study the effect of decoherence on the m-PSSVSs in two different channels, viz., thermal process and phase damping. In each case, the time-evolution of density operators and WFs of such states is derived analytically. After undergoing the thermal channel, the initial pure m-PSSVSs evolve into a mixed state that turns out to be a Laguerre polynomial of combination of creation and annihilation operators within normal ordering; however, they become another mixed state with the exponential decay due to phase damping. At long times, these fields decay to a highly classical thermal field as a result of thermal noise, but they still keep nonclassicality in the phase-damping channel.
We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$κt>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).
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.