Violation of local realism with spatially multimode parametric down-conversion pumped by spatially incoherent light

Abstract

We experimentally demonstrate a violation of local realism with highly spatially multimode polarization-entangled two-photon states produced by spontaneous parametric down-conversion (SPDC) pumped by a spatially incoherent light source-a light-emitting diode (LED). While existing studies have observed such a violation only by post-selecting the LED-pumped SPDC photons into a single spatial detection mode, we achieve a Clauser-Horne-Shimony-Holt inequality violation of $S = 2.532 \pm 0.069 > 2$ using a spatially multimode detection setup that collects nearly 4,080 SPDC spatial modes. These results indicate that coherent pump sources, such as lasers, are not required for SPDC-based entanglement generation. Our work could enable novel and practical sources of entangled photons for quantum technologies such as device-independent quantum key distribution and quantum-enhanced sensing.

Figures (4)

• Figure 1: (a) Schematic of the experimental setup. The SPDC processes for generating polarization-entangled photons occur in the ppKTP crystal, which is placed inside the PSI. M$_{1-4}$: silver mirrors; PBS: polarizing beam splitter; HWP: half-wave plate; dPBS and dHWP: dual-wavelength PBS and HWP; DM: dichroic mirror; ppKTP: periodically-poled potassium titanyl phosphate; QWP: quarter-wave plate; BPF-810(405): band-pass filter centered at 810(405) nm with a bandwidth of 10(1.5) nm; MMF-200-0.39(50-0.22): multi-mode fibre with a core diameter of 200(50) $\mu$m and an NA of 0.39(0.22). OBJ: microscope objective with 20$\times$ magnification and 0.4 NA. (b) Schematic of the procedure for measuring the number of generated and detected spatial modes (not to scale). Inset images show the multimode-laser-pumped SPDC field intensity at z = 0 mm and 30 mm from the PPKTP crystal output face, compared to the effective collection aperture using MMFs (dashed red circles). The solid green circles show the collection aperture of SMFs for comparison.
• Figure 2: Polarization correlation fringes of (a) LED-pumped SPDC and (b) laser-pumped SPDC measured by projecting the signal and idler photons into different linear polarization bases represented by angles $\theta_{s(i)}$ with the horizontal polarization. Specifically, we denote the cases of $\theta_{s} = 0^\circ, 45^\circ, 90^\circ, 135^\circ$ as measurements in the horizontal (H), diagonal (D), vertical (V), and anti-diagonal (A) bases, respectively. The markers represent the experimentally measured coincidence rates in H (circles), V (squares), A (triangles), and D (diamonds) bases. The solid lines represent the sinusoidal fitting of the experimental data. The error bars in (b) are indiscernible since they are much smaller than the markers' sizes.
• Figure 3: Real and imaginary parts of the density matrices of the two-photon states produced with (a) LED-pumped SPDC and (b) laser-pumped SPDC. All elements of the density matrices have uncertainties less than 0.03 for LED-pumped SPDC and less than 0.003 for laser-pumped SPDC.
• Figure 4: (a) Schematic diagram of probing the effects of wavefront distortion on the produced two-photon state. The laser pump beam enters the PSI at two alternative paths with a horizontal shift of $\sim1$ mm. The inset depicts the effect of wavefront distortion, which introduces different polarization phase retardation at different transverse positions of the pump beam. The uneven distances between the two cemented prisms are exaggerated for illustration purposes. The reconstructed density matrices of two-photon states produced in (b) path 1 and (c) path 2.