Non-Gaussian Statistics from Individual Pulses of Squeezed Light

We describe the observation of a “degaussification” protocol that maps individual pulses of squeezed light onto non-Gaussian states. This effect is obtained by sending a small fraction of the squeezed vacuum beam onto an avalanche photodiode, and by conditioning the single-shot homodyne detection of the remaining state upon the photon-counting events. The experimental data provide clear evidence of phase-dependent non-Gaussian statistics. This protocol is closely related to the first step of an entanglement distillation procedure for continuous variables.

Figure 1

Simplified experimental setup.

Figure 2

Normalized probability distribution for the (unconditioned) squeezed vacuum state, obtained from the pulsed homodyne detection. The squeezed quadrature variance is 1.75 dB below SNL, while the amplified quadrature variance is 3.1 dB above. The SNL curve corresponds to the vacuum state, where the shot noise variance is taken equal to $1/2$.

Figure 3

Experimental (dots) and theoretical (line) quadrature distribution of the postselected homodyne measurements for the amplified quadrature (a) and the squeezed one (b), normalized as in Fig. 2. Parameters used in the calculation are $s=0.43$, $R=0.115$, $\eta =0.75$, and $\xi =0.7$.

Figure 4

Phase-dependent quadrature distributions of the conditioned homodyne measurements, together with the vacuum reference (line and dots). The thick solid line is obtained from Eq. (3) with $R=0.01$. The thin gray line is obtained from the complete calculation and $R=0.115$. (a) corresponds to the amplified quadrature while (b) shows the squeezed one. The squeezing parameter is $s=0.43$, and perfect single mode detection efficiency has been assumed.

Figure 5

(a) Theoretical Wigner function $W$ of the output state of the “degaussification” protocol, assuming $s=0.43$, $R=0.115$, and perfect detection ($\eta =\xi =1$). (b) Reconstructed Wigner function from the experimental data ($\eta =0.75$, $\xi =0.7$). The values of $W$ at the origin of phase space are, respectively, $W_{\mathrm{th}}(0,0)=-0.26$ and $W_{\exp }(0,0)=0.067$.