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

Interferometric signature of different spectral symmetries of biphoton states