Exchange-phase erasure in anyonic Hong-Ou-Mandel interferometry

Deepika Sundarraman, Thomas Gilliss, Cody C. Leary

Sushanth Varada, Christian Spånslätt, Matteo Acciai

Two-particle interferometry is an important tool for extracting the exchange statistics of quantum particles. We theoretically investigate the prospects of such interferometry to probe the statistics of pointlike anyonic excitations injected in a Hong-Ou-Mandel (HOM) setup based on a quantum point contact device in the fractional quantum Hall regime. We compute the standard HOM ratio, i.e., the ratio of tunneling noises for two- and one-particle injections, and find that for pointlike anyons it only depends on the temperature and the anyon scaling dimension. Importantly, the latter is not necessarily related to the exchange phase. In fact, we establish that the HOM ratio does not reveal the exchange phase of the injected anyons: For injection-time delays that are small compared to the thermal timescale, we find that the exchange phase accumulated due to time-domain braiding between injected and thermally activated anyons is erased due to two mutually canceling subprocesses. In contrast, for time delays large compared to the thermal time, only a single subprocess contributes to the braiding, but the accumulated phase is canceled in the HOM ratio. These findings suggest caution when interpreting HOM interferometry experiments with anyons, and approaches beyond the standard HOM ratio are thus necessary to extract anyonic statistics with two-particle interferometry experiments.

Navin B. Lingaraju, Hsuan‐Hao Lu, Suparna Seshadri +4 more

The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.

Z. Y. Ou

Ayman F. Abouraddy, Timothy M. Yarnall, Giovanni Di Giuseppe

There is a fundamental dimensional mismatch between the Hong-Ou-Mandel (HOM) interferometer and two-photon (2P) states: while the latter are represented using two temporal (or spectral) dimensions, the HOM interferometer allows access to only one temporal dimension. We introduce a linear 2P interferometer containing two independent delays spanning the 2P state. By ``unlocking'' the fixed phase relationship between the interfering 2P probability amplitudes in a HOM interferometer, one of these probability amplitudes now serves as a delay-free 2P reference against which the other beats, thereby resolving ambiguities in 2P state identification typical of HOM interferometry and extending its utility to a large family of 2P states.

Parsa Bonderson, Kirill Shtengel, Johannes K. Slingerland