Freiburg 2024 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 17: Quantum Information I

Q 17.5: Talk

Tuesday, March 12, 2024, 12:00–12:15, HS 1199

Fourier analysis of many-body transition amplitudes and states — •Gabriel Dufour and Andreas Buchleitner — Physikalisches Institut der Albert-Ludwigs-Universität Freiburg

The Fourier transform over a finite group is a generalisation of the ordinary discrete Fourier transform which allows the analysis of a function’s behaviour under non-abelian transformations of its domain. We apply the Fourier transform over the symmetric group S_N to the set of multiparticle transition amplitudes arising from the permutations of N identical particles. For indistinguishable particles, these amplitudes add up coherently, giving rise to many-particle interference. The Fourier transform provides an analysis of the counting statistics at the output of multiparticle and multimode interferometers in terms of contributions from irreducible symmetry types. We apply this formalism to the interference of partially distinguishable bosons or fermions, whose states can likewise be submitted to a Fourier analysis, and to the determination of suppressed transitions for states of a given symmetry type.

Keywords: Many-particle interference; Quantum statistics; Bosons; Fermions; Group theory