Four-photon indistinguishability transition

We demonstrate the formation of many-particle interferences of different degrees to determine the transmission of four photons of tunable indistinguishability through a four-port beam splitter array. The probability of certain output events depends nonmonotonically on the degree of distinguishability, due to distinct multiparticle interference contributions to the transmission signal.

Figure 1

(a) Diamond-shaped multiport (balanced) beam splitter array. Four ingoing modes ${\mathrm{â}}_i^{†}$ are redistributed onto the output modes ${\mathrm{b̂}}_j^{†}$. The path length $x_j$ of each incoming mode controls the mutual distinguishability of the particles in the setup. (b) Creation of four photons by spontaneous parametric down conversion, by double passage of a laser pulse through a nonlinear crystal.

Figure 2

Event probabilities of all 35 possible output configurations ${\mathrm{s⃗}}_j$, for distinguishable (black diamonds) and fully indistinguishable particles, with $\varphi =\alpha =0$ (blue squares), $\varphi =0,\hspace{0.5em}\alpha =\pi /4$ (red circles), and $\varphi =\pi /4,\hspace{0.5em}\alpha =0$ (brown triangles).

Figure 3

Evolution of event probabilities during the transition from distinguishable to indistinguishable particles (bottom row). Left: Continuous transition, parametrized by $y$, with $\alpha =0$. Right: Stepwise transition, with corresponding interferometer path lengths, Fig. 1, on top of panel (c), with $x_1=0\hspace{0.5em}\mathrm{\mu }\mathrm{m}$, $\alpha =\pi$. The path lengths $x_2,x_3$, and $x_4$ are tuned from $220\hspace{0.5em}\mu$m to 0 $\mu$m, one after the other. [(a),(c)] Distinguishability-type contributions to the output signal: While for the stepwise transition, at most two distinguishability settings are relevant at a time, several may contribute in the continuous transition. [(b),(d)] Event probabilities of ${\mathrm{s⃗}}_{35}=(1,1,1,1)$ (blue, dashed), ${\mathrm{s⃗}}_{14}=(0,1,0,3)$ (red, dotted), and ${\mathrm{s⃗}}_{21}=(0,2,0,2)$ (green, solid). The shaded areas in (d) represent four-photon interference fringes oscillating as a function of $\varphi$.