Zero-Transmission Law for Multiport Beam Splitters

The Hong-Ou-Mandel effect is generalized to a configuration of $n$ bosons prepared in the $n$ input ports of a Bell multiport beam splitter. We derive a strict suppression law for most possible output events, consistent with a generic bosonic behavior after suitable coarse graining.

Figure 1

Event probability for a given number of occupied ports, for $n=14$. (Red) rectangles denote classical combinatorics, (blue) triangles the quantum mechanical probability distribution, and (black) circles our (bosonic) estimate for the quantum result. The inset shows the same distribution on a linear scale. Note that events with 14 occupied ports are strictly suppressed in the quantum case.

Figure 2

Quantum enhancement as a function of the number of particles (vertical axis), and of the number of occupied ports (horizontal axis).

Figure 3

Probability to find exactly $k$ particles (horizontal axis) in one port, for $n=14$. (Red) rectangles denote the classical, (blue) triangles the quantum calculation, and (black) circles the estimate (7). The inset shows the distribution on a linear scale for small $k$. Note that events with 13 particles in one port are totally suppressed in the quantum case.