Bosonic, fermionic, and anyonic symmetry in two-photon random scattering

We experimentally demonstrate the importance of two-photon symmetry for the propagation of spatial quantum correlations in a multiple-scattering disordered system. Two distinguishable entangled photons with tunable spatial exchange symmetry are sent through the scattering medium. The two photons are observed to have an ensemble-averaged tendency to cluster together (bosonic symmetry) or to avoid each other (fermionic symmetry). An intermediate degree of clustering is observed for anyonic exchange symmetry.

Figure 1

Experimental setup. From left to right: quantum-entangled photon pairs pass through an optional retarder (to tailor the spatial two-photon symmetry) and scatter from a random medium, comprising two rotating diffusors, before being detected by two photon counters and coincidence logic.

Figure 2

Observation of bosonic and fermionic symmetry in two-photon scattering. (Left, right) False-color plots of the coincidence count rate, observed in the far field of a random scattering medium, vs the detector positions $x_H$ and $x_V$; the left figure is measured for a symmetric ($\varphi =0$) two-photon input field; the right figure applies to the antisymmetric ($\varphi =\pi$) case. (Middle) Projected coincidence rate vs the position difference $x_H-x_V$. The upper (blue) $\varphi =0$ curve exhibits photon bunching; the lower (red) $\varphi =\pi$ curve exhibits photon antibunching.

Figure 3

Graphical explanation of bunching effect. The observed bunching effects originate from the interference of two generic scattering paths of the photon pair from the retarder plane (left), via propagation and scattering (denoted by sharp ss symbols), to the detectors (right).

Figure 4

Observation of anyonic symmetry in two-photon scattering. (Left) Projected coincidence rate vs the position difference $x_H-x_V$ for an input field with anyonic symmetry. The two wiggly (blue and black) curves are measured for $\varphi =\pi /2$ and $\varphi =-\pi /2$, respectively. The nonwiggly (red) curve is measured while scanning in the orthogonal transverse direction $y_H-y_V$. (Right) False color plots of the coincidence count rate observed at $\varphi =\pi /2$ while scanning either in the $(x_H,x_V)$ plane (top right) or in the $(y_H,y_V)$ plane (bottom right). The scale of both figures is identical to that of Figs. 2a and 2(c).