Testing Higher-Order Quantum Interference with Many-Particle States

Quantum theory permits interference between indistinguishable paths but, at the same time, restricts its order. Single-particle interference, for instance, is limited to the second order, that is, to pairs of single-particle paths. To date, all experimental efforts to search for higher-order interferences beyond those compatible with quantum mechanics have been based on such single-particle schemes. However, quantum physics is not bound to single-particle interference. We here experimentally study many-particle higher-order interference using a two-photon-five-slit setup. We observe nonzero two-particle interference up to fourth order, corresponding to the interference of two distinct two-particle paths. We further show that fifth-order interference is restricted to ${10}^{-3}$ in the intensity-correlation regime and to ${10}^{-2}$ in the photon-correlation regime, thus providing novel bounds on higher-order quantum interference.

Figure 1

(a) Setup to measure the interference hierarchy in single-particle and two-particle interferences. Coherent photons are sent through two slit masks, S1 and S2, and measured in the far field, either (i) by a charge coupled device (CCD) or (ii) by two single photon avalanche diodes (SPADs). (b) Fixed base slit mask S1 with dimensions $a=25\mu \mathrm{m}$, $b=200\mu \mathrm{m}$, and $d=500\mu \mathrm{m}$. The dimensions of the movable slit mask S2 are $2r=400\mu \mathrm{m}$ with a spacing $\mathrm{\Delta }=1000\mu \mathrm{m}$. (c) The layout of slit mask S2 contains 33 configurations.

Figure 2

Interference hierarchy in (a) the intensity-correlation and (b) the photon-correlation regime from (i) second order to (iv) fifth order (related formulas are taken from Ref. [38]). (a) Experimental data (solid) and quantum theory (dashed) of single-particle (blue, left) and two-particle (red, right) interference orders. Fourth-order two-particle interference exhibits a tiny modulation, clearly visible with a good signal-to-noise ratio and most pronounced at the center (inset). (b) Histograms of the single-particle (blue) and two-particle (red) interference hierarchy at $\delta =0$ in the photon-counting regime.

Figure 3

Two-particle Sorkin parameter ${\kappa }^{(2)}$ from Eq. (5) for 100 measurement sets in (a) the intensity-correlation regime and (b) the photon-correlation regime. In (b), the error bars are enlarged by a factor of 100.