Full Characterization of Gaussian Bipartite Entangled States by a Single Homodyne Detector

We present the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement, and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of optical parametric oscillator signals and represent a tool for quantum technology based on continuous variable entanglement.

Figure 1

Experimental setup: A type-II PPKTP-OPO is pumped by the second harmonic of a Nd:YAG laser. At the OPO output, a half- and a quarter-wave plate and a PBS select the mode for homodyning.

Figure 2

Left: Experimental homodyne traces and reconstructed CM; right: reconstructed Wigner functions. Top plots are for mode $c$ and bottom ones for $d$. Arrows on the homodyne plots show the maximum and minimum variances. $\theta$ is the relative phase between the signal and the LO.

Figure 3

Left: Joint photon number distribution $p(n,m)$ for the entangled state of modes $a$ and $b$ at the output of the OPO. Right: Single-mode photon distributions $p(n)$ for modes $a$ and $c$ (top right) and $b$ and $d$ (bottom right). The single-mode distributions of modes $a$ and $b$ are thermal and correspond to the marginals of $p(n,m)$. The distributions for modes $c$ and $d$ are those of squeezed thermal states.