Nonclassicality and decoherence of photon-subtracted squeezed states

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.

Figure 1

(Color online) (a) Gaussian Wigner function $W_{\mathrm{sq}}$ of the squeezed vacuum state $\mid \psi ⟩$ for $\theta =0$ and $r=0.31$. (b) The Gaussian Wigner function of a vacuum state.

Figure 2

(Color online) Plots of Wigner functions of single-photon subtracted squeezed states for (a) $r=0.31$ and (b) $r=0.8$ with $\theta =0$.

Figure 3

(Color online) Variation of $C$ in phase space for $r=0.31$ and $\theta =0$.

Figure 4

(Color online) Contour plot for $C=\mathrm{const}$ in phase space for (a) $r=0.31$ and (b) $r=0.8$.

Figure 5

(Color online) Variation of the $Q$-parameter with time in the presence of decoherence due to decay of photon for squeezing parameters $r=0.31$ (red line) and $r=0.8$ (green line).

Figure 6

(Color online) Variation of $P∕{(a^2-4{\mid c\mid }^2)}^{5∕2}$ in phase space for $r=0.31$, $\theta =0$, and $\kappa t=0.1$.

Figure 7

(Color online) Plot of $16C^{\prime }∕(1-e^{-2\kappa t})$ in phase space for (a) $r=0.31$ and (b) $r=0.8$ at times (i) $\kappa t=0.05$, (ii) $\kappa t=0.1$, (iii) $\kappa t=0.3$, and (iv) $\kappa t=0.5$.

Figure 8

(Color online) Wigner function of single-photon subtracted squeezed states for $\theta =0$ and $r=0.31$ at (a) $\kappa t=0.05$, (b) $\kappa t=0.1$, (c) $\kappa t=0.3$, and (d) $\kappa t=0.5$.

Figure 9

(Color online) Wigner function of single-photon squeezed states for $\theta =0$ and $r=0.8$ at (a) $\kappa t=0.1$, (b) $\kappa t=0.3$, (c) $\kappa t=0.5$, and (d) $\kappa t=0.7$.

Figure 10

(Color online) Wigner function in phase space at long times in the presence of phase damping for (a) $r=0.31$ and (b) $r=0.8$.