- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Quantum walk of two anyons across a statistical boundary

Liam L.H. Lau1,*,† and Shovan Dutta2,‡,§

  • 1Gonville & Caius College, University of Cambridge, Trinity Street, Cambridge CB2 1TA, United Kingdom
  • 2T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

  • *Present address: Rutgers University.
  • †liam.lh.lau@physics.rutgers.edu
  • ‡Present address: Max Planck Institute for the Physics of Complex Systems.
  • §sdutta@pks.mpg.de
PDF

Phys. Rev. Research 4, L012007 – Published 31 January, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012007

Abstract

We model a quantum walk of identical particles that can alter their exchange statistics by hopping across a domain wall in a one-dimensional lattice. Such a “statistical boundary” is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find that the two-particle interference is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wave packet can get completely reflected or split into a superposition of a reflected wave and an antibunched wave. This leads to striking dynamics with two domain walls, where bunched waves can get trapped in between or fragment into multiple correlated single-particle wave packets. These findings can be realized with density-dependent hopping in present-day atomic setups and open up a paradigm of intrinsically many-body phenomena at statistical boundaries.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, London, 2006), Vol. 2.
  2. J. M. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cimento Soc. Ital. Fis., B 37, 1 (1977).
  3. F. Wilczek, Quantum Mechanics of Fractional-Spin Particles, Phys. Rev. Lett. 49, 957 (1982).
  4. G. S. Canright and S. M. Girvin, Fractional statistics: Quantum possibilities in two dimensions, Science 247, 1197 (1990).
  5. A. Stern, Anyons and the quantum Hall effect—a pedagogical review, Ann. Phys. (Amsterdam) 323, 204 (2008).
  6. H. Yao and S. A. Kivelson, Exact Chiral Spin Liquid with Non-Abelian Anyons, Phys. Rev. Lett. 99, 247203 (2007).
  7. 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).
  8. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Direct observation of anyonic braiding statistics, Nat. Phys. 16, 931 (2020).
  9. F. D. M. Haldane, “Fractional Statistics” in Arbitrary Dimensions: A Generalization of the Pauli Principle, Phys. Rev. Lett. 67, 937 (1991).
  10. F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990), Vol. 5.
  11. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (Amsterdam) 321, 2 (2006).
  12. S. Greschner, L. Cardarelli, and L. Santos, Probing the exchange statistics of one-dimensional anyon models, Phys. Rev. A 97, 053605 (2018).
  13. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  14. V. Lahtinen and J. Pachos, A short introduction to topological quantum computation, SciPost Phys. 3, 021 (2017).
  15. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  16. E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriksson, K.-M. C. Fu, M. Greiner, K. R. A. Hazzard, R. G. Hulet, A. J. Kollar, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe et al., Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021).
  17. T. Keilmann, S. Lanzmich, I. McCulloch, and M. Roncaglia, Statistically induced phase transitions and anyons in 1D optical lattices, Nat. Commun. 2, 361 (2011).
  18. O. Jürgensen, F. Meinert, M. J. Mark, H.-C. Nägerl, and D.-S. Lühmann, Observation of Density-Induced Tunneling, Phys. Rev. Lett. 113, 193003 (2014).
  19. F. Meinert, M. J. Mark, K. Lauber, A. J. Daley, and H.-C. Nägerl, Floquet Engineering of Correlated Tunneling in the Bose-Hubbard Model with Ultracold Atoms, Phys. Rev. Lett. 116, 205301 (2016).
  20. L. W. Clark, B. M. Anderson, L. Feng, A. Gaj, K. Levin, and C. Chin, Observation of Density-Dependent Gauge Fields in a Bose-Einstein Condensate Based on Micromotion Control in a Shaken Two-Dimensional Lattice, Phys. Rev. Lett. 121, 030402 (2018).
  21. F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, and T. Esslinger, Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter, Nat. Phys. 15, 1161 (2019).
  22. C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15, 1168 (2019).
  23. V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Léséleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. Büchler, T. Lahaye, and A. Browaeys, Realization of a Density-Dependent Peierls Phase in a Synthetic, Spin-Orbit Coupled Rydberg System, Phys. Rev. X 10, 021031 (2020).
  24. S. Greschner and L. Santos, Anyon Hubbard Model in One-Dimensional Optical Lattices, Phys. Rev. Lett. 115, 053002 (2015).
  25. J. Arcila-Forero, R. Franco, and J. Silva-Valencia, Critical points of the anyon-Hubbard model, Phys. Rev. A 94, 013611 (2016).
  26. F. Lange, S. Ejima, and H. Fehske, Anyonic Haldane Insulator in One Dimension, Phys. Rev. Lett. 118, 120401 (2017).
  27. G. Tang, S. Eggert, and A. Pelster, Ground-state properties of anyons in a one-dimensional lattice, New J. Phys. 17, 123016 (2015).
  28. Y. Hao and S. Chen, Dynamical properties of hard-core anyons in one-dimensional optical lattices, Phys. Rev. A 86, 043631 (2012).
  29. L. Wang, L. Wang, and Y. Zhang, Quantum walks of two interacting anyons in one-dimensional optical lattices, Phys. Rev. A 90, 063618 (2014).
  30. L. Piroli and P. Calabrese, Exact dynamics following an interaction quench in a one-dimensional anyonic gas, Phys. Rev. A 96, 023611 (2017).
  31. 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).
  32. A. M. Kaufman, M. C. Tichy, F. Mintert, A. M. Rey, and C. A. Regal, The Hong–Ou–Mandel effect with atoms, Adv. At., Mol., Opt. Phys. 67, 377 (2018).
  33. T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, Comparison of the Hanbury Brown–Twiss effect for bosons and fermions, Nature (London) 445, 402 (2007).
  34. M. Schellekens, R. Hoppeler, A. Perrin, J. V. Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, Hanbury Brown Twiss effect for ultracold quantum gases, Science 310, 648 (2005).
  35. P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science 347, 1229 (2015).
  36. A. P. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, Quantum walks of correlated photons, Science 329, 1500 (2010).
  37. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, Two-Particle Bosonic-Fermionic Quantum Walk via Integrated Photonics, Phys. Rev. Lett. 108, 010502 (2012).
  38. J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, and J. L. O'Brien, Observing fermionic statistics with photons in arbitrary processes, Sci. Rep. 3, 1539 (2013).
  39. A. M. Childs, Universal Computation by Quantum Walk, Phys. Rev. Lett. 102, 180501 (2009).
  40. S. E. Venegas-Andraca, Quantum walks: a comprehensive review, Quantum Inf. Process. 11, 1015 (2012).
  41. 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).
  42. M. D. Girardeau, Anyon-Fermion Mapping and Applications to Ultracold Gases in Tight Waveguides, Phys. Rev. Lett. 97, 100402 (2006).
  43. A. Kundu, Exact Solution of Double δ Function Bose Gas through an Interacting Anyon Gas, Phys. Rev. Lett. 83, 1275 (1999).
  44. M. Bonkhoff, K. Jägering, S. Eggert, A. Pelster, M. Thorwart, and T. Posske, Bosonic Continuum Theory of One-Dimensional Lattice Anyons, Phys. Rev. Lett. 126, 163201 (2021).
  45. M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  46. M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Zakrzewski, E. Zohar, and M. Lewenstein, Cold atoms meet lattice gauge theory, Philos. Transact. Royal Soc. A 380, 20210064 (2021).
  47. C. Sträter, S. C. L. Srivastava, and A. Eckardt, Floquet Realization and Signatures of One-Dimensional Anyons in an Optical Lattice, Phys. Rev. Lett. 117, 205303 (2016).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012007 for characterizations of the slow bunched waves, deviations from the effective-repulsion picture, dynamics of particles coincident from opposite directions with different initial separations, and insensitivity to the width of statistical regions surrounding a well.
  49. A. K. Kolezhuk, F. Heidrich-Meisner, S. Greschner, and T. Vekua, Frustrated spin chains in strong magnetic field: Dilute two-component Bose gas regime, Phys. Rev. B 85, 064420 (2012).
  50. L. Cardarelli, S. Greschner, and L. Santos, Engineering interactions and anyon statistics by multicolor lattice-depth modulations, Phys. Rev. A 94, 023615 (2016).
  51. K.-X. Yao, Z. Zhang, and C. Chin, Dynamics of domain walls in a Bose-Einstein condensate driven by density-dependent gauge field, arXiv:2105.15052.

Outline

Information

Phys. Rev. Research 4, L012007– Published 31 January, 2022
  • Received 17 August 2021
  • Accepted 9 December 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation