Interferometric signature of different spectral symmetries of biphoton states

TL;DR

This paper explores how the spectral symmetry of biphoton states affects their interferometric signatures in a generalized Mach-Zehnder setup, revealing phase-sensitive spectral features and simulating anyonic statistics.

Contribution

It demonstrates the phase-sensitive measurement of biphoton spectral symmetry using a generalized MZ interferometer and links spectral symmetry to specific Fourier transform signatures.

Findings

Symmetric biphoton states produce a Fourier transform of energy conservation.

Antisymmetric states reveal the phase-matching function distribution.

The technique can simulate anyonic statistics through spectral engineering.

Abstract

In this paper, we investigate the influence of the symmetry of the biphoton wavefunction on the coincidence measurement of the generalized Mach-Zehnder (MZ) interferometer, where there are a temporal and frequency shift operations between the two beam-splitters. We show that the generalized MZ interferometer is the measurement of the short-time Fourier transform of the function modeling the energy conservation of a spontaneous parametric down-conversion process if the full biphoton state is symmetric, and of the symmetric characteristic distribution of the phase-matching function if the state is antisymmetric. Thus, this technique is phase-sensitive to the spectral distribution of the photon pairs. Finally, we investigate in detail the signature of a pair of anyons whose peculiar statistics can be simulated by engineering the spectrum of photon pairs.