Higher-order wave-particle duality

The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality $D^2+V^2\le 1$, with $D$ being the path distinguishability and $V$ being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.

Figure 1

Distinguishability and visibility are measured in the open (removing the beam splitter, BS) and closed (employing the BS) interferometer, respectively.

Figure 2

Mach-Zehnder interferometer with the input of a Fock state in one port and the vacuum in the other port, where VBS is a variable beam splitter with adjustable reflectivity $R$, PZT is a phase shifter, and the 50:50 BS (beam splitter) equally splits the light beam.