- 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

Measuring the adiabatic non-Hermitian Berry phase in feedback-coupled oscillators

Yaashnaa Singhal1,*, Enrico Martello2,*, Shraddha Agrawal1, Tomoki Ozawa3,†, Hannah Price2,‡, and Bryce Gadway1,§

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
  • 2School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
  • 3Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan

  • *These authors contributed equally to this work.
  • †tomoki.ozawa.d8@tohoku.ac.jp
  • ‡H.Price.2@bham.ac.uk
  • §bgadway@illinois.edu
PDF

Phys. Rev. Research 5, L032026 – Published 24 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032026

Abstract

The geometrical Berry phase is key to understanding the behavior of quantum states under cyclic adiabatic evolution. When generalized to non-Hermitian systems with gain and loss, the Berry phase can become complex and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site PT-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realize this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for noncyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov-Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken PT symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards further studies of non-Hermitian and topological physics in synthetic metamaterials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. London A 392, 45 (1984).
  2. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  3. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  4. J. C. Garrison and E. M. Wright, Complex geometrical phases for dissipative systems, Phys. Lett. A 128, 177 (1988).
  5. G. Dattoli, R. Mignani, and A. Torre, Geometrical phase in the cyclic evolution of non-Hermitian systems, J. Phys. A: Math. Gen. 23, 5795 (1990).
  6. F. Keck, H. J. Korsch, and S. Mossmann, Unfolding a diabolic point: A generalized crossing scenario, J. Phys. A: Math. Gen. 36, 2125 (2003).
  7. S.-D. Liang and G.-Y. Huang, Topological invariance and global berry phase in non-Hermitian systems, Phys. Rev. A 87, 012118 (2013).
  8. A. Mondragón and E. Hernández, Berry phase of a resonant state, J. Phys. A: Math. Gen. 29, 2567 (1996).
  9. M. V. Berry and M. R. Dennis, The optical singularities of birefringent dichroic chiral crystals, Proc. R. Soc. London A 459, 1261 (2003).
  10. M. V. Berry, Physics of nonhermitian degeneracies, Czech. J. Phys. 54, 1039 (2004).
  11. A. I. Nesterov and F. A. de la Cruz, Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points, J. Phys. A: Math. Theor. 41, 485304 (2008).
  12. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Observation of PT-Symmetry Breaking in Complex Optical Potentials, Phys. Rev. Lett. 103, 093902 (2009).
  13. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity–time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).
  14. C. Coulais, D. Sounas, and A. Alù, Static non-reciprocity in mechanical metamaterials, Nature (London) 542, 461 (2017).
  15. M. Brandenbourger, X. Locsin, E. Lerner, and C. Coulais, Non-reciprocal robotic metamaterials, Nat. Commun. 10, 4608 (2019).
  16. C. Scheibner, W. T. M. Irvine, and V. Vitelli, Non-Hermitian Band Topology and Skin Modes in Active Elastic Media, Phys. Rev. Lett. 125, 118001 (2020).
  17. C. Scheibner, A. Souslov, D. Banerjee, P. Surowka, W. T. M. Irvine, and V. Vitelli, Odd elasticity, Nat. Phys. 16, 475 (2020).
  18. D. Zhou and J. Zhang, Non-Hermitian topological metamaterials with odd elasticity, Phys. Rev. Res. 2, 023173 (2020).
  19. A. Ghatak, M. Brandenbourger, J. van Wezel, and C. Coulais, Observation of Non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial, Proc. Natl. Acad. Sci. USA (2020).
  20. R. Anandwade, Y. Singhal, S. N. M. Paladugu, E. Martello, M. Castle, S. Agrawal, E. Carlson, C. Battle-McDonald, T. Ozawa, H. M. Price, and B. Gadway, Synthetic mechanical lattices with synthetic interactions, Phys. Rev. A 108, 012221 (2023).
  21. Y. Choi, C. Hahn, J. W. Yoon, and S. H. Song, Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators, Nat. Commun. 9, 2182 (2018).
  22. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  23. W. Gou, T. Chen, D. Xie, T. Xiao, T.-S. Deng, B. Gadway, W. Yi, and B. Yan, Tunable Nonreciprocal Quantum Transport through a Dissipative Aharonov-Bohm Ring in Ultracold Atoms, Phys. Rev. Lett. 124, 070402 (2020).
  24. J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, and L. Luo, Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat. Commun. 10, 855 (2019).
  25. C. Coulais, R. Fleury, and J. van Wezel, Topology and broken Hermiticity, Nat. Phys. 17, 9 (2021).
  26. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  27. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  28. S. Longhi, Bloch oscillations in complex crystals with PT symmetry, Phys. Rev. Lett. 103, 123601 (2009).
  29. R. Hayward and F. Biancalana, Complex Berry phase dynamics in PT-symmetric coupled waveguides, Phys. Rev. A 98, 053833 (2018).
  30. N. Silberstein, J. Behrends, M. Goldstein, and R. Ilan, Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems, Phys. Rev. B 102, 245147 (2020).
  31. R. Hayward and F. Biancalana, Monopole-antimonopole instability in non-Hermitian coupled waveguides, Phys. Rev. A 101, 043846 (2020).
  32. C. Dembowski, H.-D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, Experimental Observation of the Topological Structure of Exceptional Points, Phys. Rev. Lett. 86, 787 (2001).
  33. C. Dembowski, B. Dietz, H.-D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, and A. Richter, Encircling an exceptional point, Phys. Rev. E 69, 056216 (2004).
  34. T. Gao, E. Estrecho, K. Y. Bliokh, T. C. H. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. Truscott, R. Dall, and E. A. Ostrovskaya, Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard, Nature (London) 526, 554 (2015).
  35. R. Uzdin, A. Mailybaev, and N. Moiseyev, On the observability and asymmetry of adiabatic state flips generated by exceptional points, J. Phys. A: Math. Theor. 44, 435302 (2011).
  36. M. V. Berry, Optical polarization evolution near a Non-Hermitian degeneracy, J. Opt. 13, 115701 (2011).
  37. J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, Dynamically encircling an exceptional point for asymmetric mode switching, Nature (London) 537, 76 (2016).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032026 for a more detailed discussion and analysis of the theoretical model and for a more detailed description of the data analysis.
  39. H. Shen, B. Zhen, and L. Fu, Topological Band Theory for Non-Hermitian Hamiltonians, Phys. Rev. Lett. 120, 146402 (2018).
  40. S. Massar, Applications of the complex geometric phase for metastable systems, Phys. Rev. A 54, 4770 (1996).
  41. G Nenciu and G Rasche, On the adiabatic theorem for nonself-adjoint Hamiltonians, J. Phys. A: Math. Gen. 25, 5741 (1992).
  42. J. Höller, N. Read, and J. G. E. Harris, Non-Hermitian adiabatic transport in spaces of exceptional points, Phys. Rev. A 102, 032216 (2020).
  43. N. Hatano and D. R. Nelson, Localization Transitions in Non-Hermitian Quantum Mechanics, Phys. Rev. Lett. 77, 570 (1996).
  44. G. Salerno, T. Ozawa, H. M. Price, and I. Carusotto, Floquet topological system based on frequency-modulated classical coupled harmonic oscillators, Phys. Rev. B 93, 085105 (2016).
  45. G. Salerno and I. Carusotto, Dynamical decoupling and dynamical isolation in temporally modulated coupled pendulums, Europhys. Lett. 106, 24002 (2014).
  46. Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115, 485 (1959).
  47. V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in PT-symmetric systems, Rev. Mod. Phys. 88, 035002 (2016).
  48. Y. Lumer, Y. Plotnik, M. C. Rechtsman, and M. Segev, Nonlinearly Induced PT Transition in Photonic Systems, Phys. Rev. Lett. 111, 263901 (2013).
  49. S. Yao, F. Song, and Z. Wang, Non-Hermitian Chern Bands, Phys. Rev. Lett. 121, 136802 (2018).
  50. F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems, Phys. Rev. Lett. 121, 026808 (2018).
  51. K. Kawabata, K. Shiozaki, and M. Ueda, Anomalous helical edge states in a non-Hermitian chern insulator, Phys. Rev. B 98, 165148 (2018).

Outline

Information

Phys. Rev. Research 5, L032026– Published 24 August, 2023
  • Received 23 March 2023
  • Revised 8 July 2023
  • Accepted 12 July 2023
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