Experimental Generation of Continuous-Variable Hyperentanglement in an Optical Parametric Oscillator

We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement criterion as well as by the continuous-variable version of the Peres-Horodecki criterion visualized on an equivalent Poincaré sphere.

Figure 1

Experimental setup. Three-mirror ring cavity (RC), dichroic beam splitter (DBS), polarizing beam splitter (PBS), half-wave plate (HWP), piezoelectric element for controlling phases (PZT), LO, mode converter for the generation of the LO of the ${\mathrm{HG}}_{10}$ mode from the ${\mathrm{HG}}_{01}$ mode (MC), spectrum analyzer (SA), balanced homodyne detectors (BHD). (b1) Placement of the KTP crystals in the OPO. $x$, $y$, and $z$ are the axes of the KTP crystal; half-wave plate (HWP). (b2) The 45° angles between the crystal axes [($Y$, $Z$), solid lines] and the optical axes of the half-wave plate (dashed lines).

Figure 2

Experimental results of entanglement. (a) The correlation noise of ${\mathrm{HG}}_{01}$ modes. (b) The correlation noise of ${\mathrm{HG}}_{10}$ modes. (a1) Trace 1 (red line): $⟨{\mathrm{\Delta }}^2(X_{i,H01}+X_{s,H01})⟩$; trace 3 (blue line): $⟨{\mathrm{\Delta }}^2(X_{i,H01}-X_{s,H01})⟩$. (a2) Trace 1 (red line): $⟨{\mathrm{\Delta }}^2(P_{i,H01}-P_{s,H01})⟩$; trace 3 (blue line): ($⟨{\mathrm{\Delta }}^2(P_{i,H01}+P_{s,H01})⟩$. (b1) Trace 1 (red line): $⟨{\mathrm{\Delta }}^2(X_{i,H10}+X_{s,H10})⟩$; trace 3 (blue line): $⟨{\mathrm{\Delta }}^2(X_{i,H10}-X_{s,H10})⟩$. (b2) Trace 1 (red line): $⟨{\mathrm{\Delta }}^2(P_{i,H10}-P_{s,H10})⟩$; trace 3 (blue line): $⟨{\mathrm{\Delta }}^2(P_{i,H10}+P_{s,H10})⟩$. Trace 2 (black line): SNL.

Figure 3

Entanglement descriptions mapped on Poincaré spheres. (a) OAM. (a1) Location of output beams on the orbital Poincaré sphere. (a2) Noise volume of beam $i$ before any measurement of beam $s$. (a3) and (a4) Conditional knowledge of beam $i$ given measurements of ${\widehat{O}}_1$ & ${\widehat{O}}_3$ and ${\widehat{O}}_2$ & ${\widehat{O}}_3$, respectively, on beam $s$. (b) SAM. (a1) and (a2) Locations of output beams $i$ and $s$, respectively, on the spin Poincaré sphere. (a3) Noise volume of beam $i$ before any measurement of beam $s$. (a4) Conditional knowledge of beam $i$ given measurements of ${\widehat{O}}_1$ on beam $s$. The dashed circles show the SNL. If the conditional knowledge is better than the dashed circles, the states are entangled.