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  • Letter
  • Open Access

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

Sushanth Varada1,2, Christian Spånslätt3,1, and Matteo Acciai4,1

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Phys. Rev. B 111, L201407 – Published 28 May, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L201407

Abstract

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.

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References (83)

  1. M. G. G. Laidlaw and C. M. DeWitt, Feynman Functional integrals for systems of indistinguishable particles, Phys. Rev. D 3, 1375 (1971).
  2. J. M. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cimento B 37, 1 (1977).
  3. G. A. Goldin, R. Menikoff, and D. H. Sharp, Particle statistics from induced representations of a local current group, J. Math. Phys. 21, 650 (1980).
  4. F. Wilczek, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. 49, 957 (1982).
  5. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982).
  6. R. B. Laughlin, Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50, 1395 (1983).
  7. R. De-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, and D. Mahalu, Direct observation of a fractional charge, Nature (London) 389, 162 (1997).
  8. L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Observation of the e/3 fractionally charged Laughlin quasiparticle, Phys. Rev. Lett. 79, 2526 (1997).
  9. H. Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, J.-M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, Q. Dong, U. Gennser, Y. Jin, and G. Fève, Fractional statistics in anyon collisions, Science 368, 173 (2020).
  10. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Direct observation of anyonic braiding statistics, Nat. Phys. 16, 931 (2020).
  11. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers, Nat. Commun. 13, 344 (2022).
  12. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Fabry-Pèrot interferometry at the ν=2/5 fractional quantum Hall state, Phys. Rev. X 13, 041012 (2023).
  13. N. L. Samuelson, L. A. Cohen, W. Wang, S. Blanch, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Anyonic statistics and slow quasiparticle dynamics in a graphene fractional quantum Hall interferometer, arXiv:2403.19628.
  14. T. Werkmeister, J. R. Ehrets, M. E. Wesson, D. H. Najafabadi, K. Watanabe, T. Taniguchi, B. I. Halperin, A. Yacoby, and P. Kim, Anyon braiding and telegraph noise in a graphene interferometer, Science 388, 730 (2025).
  15. B. Rosenow, I. P. Levkivskyi, and B. I. Halperin, Current correlations from a mesoscopic anyon collider, Phys. Rev. Lett. 116, 156802 (2016).
  16. M. Ruelle, E. Frigerio, J.-M. Berroir, B. Plaçais, J. Rech, A. Cavanna, U. Gennser, Y. Jin, and G. Fève, Comparing fractional quantum Hall Laughlin and Jain topological orders with the anyon collider, Phys. Rev. X 13, 011031 (2023).
  17. P. Glidic, O. Maillet, A. Aassime, C. Piquard, A. Cavanna, U. Gennser, Y. Jin, A. Anthore, and F. Pierre, Cross-correlation investigation of anyon statistics in the ν=1/3 and 2/5 fractional quantum Hall states, Phys. Rev. X 13, 011030 (2023).
  18. J.-Y. M. Lee, C. Hong, T. Alkalay, N. Schiller, V. Umansky, M. Heiblum, Y. Oreg, and H.-S. Sim, Partitioning of diluted anyons reveals their braiding statistics, Nature (London) 617, 277 (2023).
  19. T. Morel, J.-Y. M. Lee, H.-S. Sim, and C. Mora, Fractionalization and anyonic statistics in the integer quantum Hall collider, Phys. Rev. B 105, 075433 (2022).
  20. J.-Y. M. Lee, C. Han, and H.-S. Sim, Fractional mutual statistics on integer quantum Hall edges, Phys. Rev. Lett. 125, 196802 (2020).
  21. J.-Y. M. Lee and H.-S. Sim, Non-Abelian anyon collider, Nat. Commun. 13, 1 (2022).
  22. E. G. Idrisov, I. P. Levkivskyi, E. V. Sukhorukov, and T. L. Schmidt, Current cross correlations in a quantum Hall collider at filling factor two, Phys. Rev. B 106, 085405 (2022).
  23. T. Jonckheere, J. Rech, B. Grémaud, and T. Martin, Anyonic statistics revealed by the Hong-Ou-Mandel dip for fractional excitations, Phys. Rev. Lett. 130, 186203 (2023).
  24. N. Schiller, Y. Shapira, A. Stern, and Y. Oreg, Anyon statistics through conductance measurements of time-domain interferometry, Phys. Rev. Lett. 131, 186601 (2023).
  25. K. Iyer, F. Ronetti, B. Grémaud, T. Martin, J. Rech, and T. Jonckheere, Finite width of anyons changes their braiding signature, Phys. Rev. Lett. 132, 216601 (2024).
  26. M. Thamm and B. Rosenow, Effect of the soliton width on nonequilibrium exchange phases of anyons, Phys. Rev. Lett. 132, 156501 (2024).
  27. C. Han, J. Park, Y. Gefen, and H.-S. Sim, Topological vacuum bubbles by anyon braiding, Nat. Commun. 7, 11131 (2016).
  28. B. Lee, C. Han, and H.-S. Sim, Negative excess shot noise by anyon braiding, Phys. Rev. Lett. 123, 016803 (2019).
  29. C. K. Hong, Z. Y. Ou, and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett. 59, 2044 (1987).
  30. S. Ol'khovskaya, J. Splettstoesser, M. Moskalets, and M. Büttiker, Shot noise of a mesoscopic two-particle collider, Phys. Rev. Lett. 101, 166802 (2008).
  31. E. Bocquillon, F. D. Parmentier, C. Grenier, J.-M. Berroir, P. Degiovanni, D. C. Glattli, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Electron quantum optics: Partitioning electrons one by one, Phys. Rev. Lett. 108, 196803 (2012).
  32. T. Jonckheere, J. Rech, C. Wahl, and T. Martin, Electron and hole Hong-Ou-Mandel interferometry, Phys. Rev. B 86, 125425 (2012).
  33. E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Coherence and Indistinguishability of single electrons emitted by independent sources, Science 339, 1054 (2013).
  34. J. Dubois, T. Jullien, C. Grenier, P. Degiovanni, P. Roulleau, and D. C. Glattli, Integer and fractional charge Lorentzian voltage pulses analyzed in the framework of photon-assisted shot noise, Phys. Rev. B 88, 085301 (2013).
  35. J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau, and D. C. Glattli, Minimal-excitation states for electron quantum optics using levitons, Nature (London) 502, 659 (2013).
  36. D. Ferraro, A. Feller, A. Ghibaudo, E. Thibierge, E. Bocquillon, G. Fève, Ch. Grenier, and P. Degiovanni, Wigner function approach to single electron coherence in quantum Hall edge channels, Phys. Rev. B 88, 205303 (2013).
  37. E. Bocquillon, V. Freulon, F. D. Parmentier, J.-M. Berroir, B. Plaçais, C. Wahl, J. Rech, T. Jonckheere, T. Martin, C. Grenier, D. Ferraro, P. Degiovanni, and G. Fève, Electron quantum optics in ballistic chiral conductors, Ann. Phys. 526, 1 (2014).
  38. D. C. Glattli and P. Roulleau, Hanbury-Brown Twiss noise correlation with time controlled quasi-particles in ballistic quantum conductors, Physica E 76, 216 (2016).
  39. A. Marguerite, E. Bocquillon, J.-M. Berroir, B. Plaçais, A. Cavanna, Y. Jin, P. Degiovanni, and G. Fève, Two-particle interferometry in quantum Hall edge channels, Phys. Status Solidi B 254, 1600618 (2017).
  40. C. Wahl, J. Rech, T. Jonckheere, and T. Martin, Interactions and charge fractionalization in an electronic Hong-Ou-Mandel interferometer, Phys. Rev. Lett. 112, 046802 (2014).
  41. V. Freulon, A. Marguerite, J.-M. Berroir, B. Plaçais, A. Cavanna, Y. Jin, and G. Fève, Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization, Nat. Commun. 6, 6854 (2015).
  42. A. Marguerite, C. Cabart, C. Wahl, B. Roussel, V. Freulon, D. Ferraro, Ch. Grenier, J.-M. Berroir, B. Plaçais, T. Jonckheere, J. Rech, T. Martin, P. Degiovanni, A. Cavanna, Y. Jin, and G. Fève, Decoherence and relaxation of a single electron in a one-dimensional conductor, Phys. Rev. B 94, 115311 (2016).
  43. C. Cabart, B. Roussel, G. Fève, and P. Degiovanni, Taming electronic decoherence in one-dimensional chiral ballistic quantum conductors, Phys. Rev. B 98, 155302 (2018).
  44. G. Rebora, M. Acciai, D. Ferraro, and M. Sassetti, Collisional interferometry of levitons in quantum Hall edge channels at ν=2, Phys. Rev. B 101, 245310 (2020).
  45. I. Taktak, M. Kapfer, J. Nath, P. Roulleau, M. Acciai, J. Splettstoesser, I. Farrer, D. A. Ritchie, and D. C. Glattli, Two-particle time-domain interferometry in the fractional quantum Hall effect regime, Nat. Commun. 13, 5863 (2022).
  46. M. Acciai, P. Roulleau, I. Taktak, D. C. Glattli, and J. Splettstoesser, Influence of channel mixing in fermionic Hong-Ou-Mandel experiments, Phys. Rev. B 105, 125415 (2022).
  47. M. Acciai, P. Roulleau, D. C. Glattli, and J. Splettstoesser, Impact of channel mixing on the visibility of two-particle interferometry in quantum Hall edge states, JPS Conf. Proc. 38, 011174 (2023).
  48. D. C. Glattli, A. De, C. Boudet, M. Kapfer, I. Farrer, D. Ritchie, and P. Roulleau, Electronic Hong Ou Mandel interferences to unveil the 2/3 fractional quantum Hall edge channel dynamics, Research Square preprint (2025).
  49. M. Ruelle, E. Frigerio, E. Baudin, J.-M. Berroir, B. Plaçais, B. Grémaud, T. Jonckheere, T. Martin, J. Rech, A. Cavanna, U. Gennser, Y. Jin, G. Ménard, and G. Fève, Time-domain braiding of anyons, arXiv:2409.08685.
  50. Ya. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000).
  51. G. Campagnano, O. Zilberberg, I. V. Gornyi, D. E. Feldman, A. C. Potter, and Y. Gefen, Hanbury Brown–Twiss interference of anyons, Phys. Rev. Lett. 109, 106802 (2012).
  52. X.-G. Wen, Topological orders and edge excitations in fractional quantum Hall states, Adv. Phys. 44, 405 (1995).
  53. M. Moskalets, First-order correlation function of a stream of single-electron wave packets, Phys. Rev. B 91, 195431 (2015).
  54. J. Rech, D. Ferraro, T. Jonckheere, L. Vannucci, M. Sassetti, and T. Martin, Minimal excitations in the fractional quantum Hall regime, Phys. Rev. Lett. 118, 076801 (2017).
  55. L. Vannucci, F. Ronetti, J. Rech, D. Ferraro, T. Jonckheere, T. Martin, and M. Sassetti, Minimal excitation states for heat transport in driven quantum Hall systems, Phys. Rev. B 95, 245415 (2017).
  56. F. Ronetti, L. Vannucci, D. Ferraro, T. Jonckheere, J. Rech, T. Martin, and M. Sassetti, Crystallization of levitons in the fractional quantum Hall regime, Phys. Rev. B 98, 075401 (2018).
  57. D. Ferraro, F. Ronetti, L. Vannucci, M. Acciai, J. Rech, T. Jockheere, T. Martin, and M. Sassetti, Hong-Ou-Mandel characterization of multiply charged Levitons, Eur. Phys. J. Spec. Top. 227, 1345 (2018).
  58. F. Ronetti, L. Vannucci, D. Ferraro, T. Jonckheere, J. Rech, T. Martin, and M. Sassetti, Hong-Ou-Mandel heat noise in the quantum Hall regime, Phys. Rev. B 99, 205406 (2019).
  59. T. Martin, Noise in mesoscopic physics, in Nanophysics: Coherence and Transport, edited by H. Bouchiat, Y. Gefen, S. Guéron, G. Montambaux, and J. Dalibard, Les Houches Vol. 81 (Elsevier, Waltham, MA, 2005), pp. 283–359.
  60. C. L. Kane and M. P. A. Fisher, Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Phys. Rev. B 46, 15233 (1992).
  61. L. P. Pryadko, E. Shimshoni, and A. Auerbach, Coulomb interactions and delocalization in quantum Hall constrictions, Phys. Rev. B 61, 10929 (2000).
  62. B. Rosenow and B. I. Halperin, Nonuniversal behavior of scattering between fractional quantum Hall Edges, Phys. Rev. Lett. 88, 096404 (2002).
  63. E. Papa and A. H. MacDonald, Interactions suppress quasiparticle tunneling at Hall bar constrictions, Phys. Rev. Lett. 93, 126801 (2004).
  64. D. Ferraro, A. Braggio, M. Merlo, N. Magnoli, and M. Sassetti, Relevance of multiple quasiparticle tunneling between edge states at ν=p/(2np+1), Phys. Rev. Lett. 101, 166805 (2008).
  65. A. Braggio, D. Ferraro, M. Carrega, N. Magnoli, and M. Sassetti, Environmental induced renormalization effects in quantum Hall edge states due to 1/f noise and dissipation, New J. Phys. 14, 093032 (2012).
  66. R. Kumar, S. K. Srivastav, C. Spånslätt, K. Watanabe, T. Taniguchi, Y. Gefen, A. D. Mirlin, and A. Das, Observation of ballistic upstream modes at fractional quantum Hall edges of graphene, Nat. Commun. 13, 213 (2022).
  67. M. Acciai, G. Zhang, and C. Spånslätt, Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias, SciPost Phys. 18, 058 (2025).
  68. K. Kobayashi and M. Hashisaka, Shot noise in mesoscopic systems: From single particles to quantum liquids, J. Phys. Soc. Jpn. 90, 102001 (2021).
  69. For correct units of noise, one should in principle replace the integration over t in Eq. (13) by ∫−T0/2T0/2dt/T0, with T0 a very long averaging time. This replacement, however, has no impact on the dimensionless HOM ratio (14).
  70. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.111.L201407 which includes details on (i) the derivation of the HOM ratio and (ii) a comparison to HOM interferometry of electrons.
  71. T. Christen and M. Büttiker, Low frequency admittance of a quantum point contact, Phys. Rev. Lett. 77, 143 (1996).
  72. A. Prêtre, H. Thomas, and M. Büttiker, Dynamic admittance of mesoscopic conductors: Discrete-potential model, Phys. Rev. B 54, 8130 (1996).
  73. J. Meair and P. Jacquod, Scattering theory of nonlinear thermoelectricity in quantum coherent conductors, J. Phys.: Condens. Matter 25, 082201 (2013).
  74. N. Dashti, M. Acciai, S. Kheradsoud, M. Misiorny, P. Samuelsson, and J. Splettstoesser, Readout of quantum screening effects using a time-dependent probe, Phys. Rev. Lett. 127, 246802 (2021).
  75. However, ϑ appears in the noise jointly with the scaling dimension δ, making an extraction of only ϑ challenging.
  76. H.-S. Sim (private communication).
  77. C. L. Kane, M. P. A. Fisher, and J. Polchinski, Randomness at the edge: Theory of quantum Hall transport at filling ν=2/3, Phys. Rev. Lett. 72, 4129 (1994).
  78. I. Protopopov, Y. Gefen, and A. Mirlin, Transport in a disordered ν=2/3 fractional quantum Hall junction, Ann. Phys. 385, 287 (2017).
  79. C. Nosiglia, J. Park, B. Rosenow, and Y. Gefen, Incoherent transport on the ν=2/3 quantum Hall edge, Phys. Rev. B 98, 115408 (2018).
  80. C. Spånslätt, Y. Gefen, I. V. Gornyi, and D. G. Polyakov, Contacts, equilibration, and interactions in fractional quantum Hall edge transport, Phys. Rev. B 104, 115416 (2021).
  81. M. Hein and C. Spånslätt, Thermal conductance and noise of Majorana modes along interfaced ν=52 fractional quantum Hall states, Phys. Rev. B 107, 245301 (2023).
  82. S. Varada, Anyon colliders: A time-dependent quantum Hall particle collider to reveal fractional statistics in the Laughlin sequence, Master's thesis, Chalmers University of Technology, 2023.
  83. S. Varada, C. Spånslätt, and M. Acciai, Data for “Exchange-phase erasure in anyonic Hong-Ou-Mandel interferometry”, Zenodo (2025), doi: 10.5281/zenodo.15356728.

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Phys. Rev. B 111, L201407– Published 28 May, 2025
  • Received 5 March 2025
  • Revised 7 May 2025
  • Accepted 14 May 2025
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