Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field

Abstract

Surface currents arise in superconductors under magnetic fields and are a key signature of the Meissner effect. Similarly, chiral dynamics have been observed in quantum simulators under synthetic Abelian gauge fields. These simulators offer flexible control, enabling the engineering of non-Abelian gauge fields, although their influence on chiral dynamics remains unclear. Here, we implement a synthetic SU(2) gauge field in a spinful one-dimensional ladder and investigate the resulting chiral dynamics by developing a Raman momentum-lattice technique. We confirm the non-Abelian nature of the synthetic potential by observing the non-Abelian Aharonov–Bohm effect on a single plaquette. Furthermore, we find that the chiral current along the two legs of the ladder is spin dependent and highly tunable through the gauge potential parameters. We experimentally map out different dynamic regimes of the chiral current, revealing the competition between overlaying flux ladders with different spin compositions. Our experiment demonstrates the impact of non-Abelian gauge fields on chiral dynamics and offers a viable approach to implementing exotic synthetic gauge fields using Raman momentum lattices.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Synthesis of the SU(2) gauge fields in the RML.
Fig. 2: Observing the non-Abelian AB effect.
Fig. 3: Spin-dependent chiral dynamics.
Fig. 4: Dynamic regimes of the chiral current.

Similar content being viewed by others

Data availability

Experimental data, any related experimental background information not mentioned in the text, and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

  1. Higgs, P. W. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  2. Kibble, T. W. B. Symmetry breaking in non-Abelian gauge theories. Phys. Rev. 155, 1554–1561 (1967).

    Article  ADS  Google Scholar 

  3. Senthil, T. & Fisher, M. P. A. Z2 gauge theory of electron fractionalization in strongly correlated systems. Phys. Rev. B 62, 7850–7881 (2000).

    Article  ADS  Google Scholar 

  4. Stormer, H. L., Tsui, D. C. & Gossard, A. C. The fractional quantum Hall effect. Rev. Mod. Phys. 71, S298–S305 (1999).

    Article  MathSciNet  Google Scholar 

  5. Lee, P. A. From high temperature superconductivity to quantum spin liquid: progress in strong correlation physics. Rep. Prog. Phys. 71, 012501 (2007).

    Article  ADS  Google Scholar 

  6. Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009).

    Article  ADS  Google Scholar 

  7. Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).

    Article  ADS  Google Scholar 

  8. Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013).

    Article  ADS  Google Scholar 

  9. An, F. A., Meier, E. J. & Gadway, B. Direct observation of chiral currents and magnetic reflection in atomic flux lattices. Sci. Adv. 3, e1602685 (2017).

    Article  ADS  Google Scholar 

  10. Li, H. et al. Aharonov–Bohm caging and inverse Anderson transition in ultracold atoms. Phys. Rev. Lett. 129, 220403 (2022).

    Article  ADS  Google Scholar 

  11. Atala, M. et al. Observation of chiral currents with ultracold atoms in bosonic ladders. Nat. Phys. 10, 588–593 (2014).

    Article  Google Scholar 

  12. Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146–151 (2017).

    Article  Google Scholar 

  13. Fang, K., Yu, Z. & Fan, S. Photonic Aharonov–Bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).

    Article  ADS  Google Scholar 

  14. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).

    Article  ADS  Google Scholar 

  15. Umucalılar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

    Article  ADS  Google Scholar 

  16. Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).

    Article  ADS  Google Scholar 

  17. Schine, N., Ryou, A., Gromov, A., Sommer, A. & Simon, J. Synthetic Landau levels for photons. Nature 534, 671–675 (2016).

    Article  ADS  Google Scholar 

  18. Yang, Z., Gao, F., Yang, Y. & Zhang, B. Strain-induced gauge field and Landau levels in acoustic structures. Phys. Rev. Lett. 118, 194301 (2017).

    Article  ADS  Google Scholar 

  19. Mathew, J. P., Pino, J. D. & Verhagen, E. Synthetic gauge fields for phonon transport in a nano-optomechanical system. Nat. Nanotechnol. 15, 198–202 (2020).

    Article  ADS  Google Scholar 

  20. Chen, Y. et al. Synthetic gauge fields in a single optomechanical resonator. Phys. Rev. Lett. 126, 123603 (2021).

    Article  ADS  Google Scholar 

  21. Xiao, M., Chen, W.-J., He, W.-Y. & Chan, C. T. Synthetic gauge flux and Weyl points in acoustic systems. Nat. Phys. 11, 920–924 (2015).

    Article  Google Scholar 

  22. Bardeen, J. Theory of the Meissner effect in superconductors. Phys. Rev. 97, 1724–1725 (1955).

    Article  ADS  Google Scholar 

  23. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  24. Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Colloquium: artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).

    Article  ADS  Google Scholar 

  25. Goldman, N., Juzeliūnas, G., Öhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).

    Article  ADS  Google Scholar 

  26. Zhai, H. Degenerate quantum gases with spin-orbit coupling: a review. Rep. Prog. Phys. 78, 026001 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  27. Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).

    Article  ADS  Google Scholar 

  28. Wang, P. et al. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).

    Article  ADS  Google Scholar 

  29. Huang, L. et al. Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases. Nat. Phys. 12, 540–544 (2016).

    Article  Google Scholar 

  30. Wu, Z. et al. Realization of two-dimensional spin-orbit coupling for Bose–Einstein condensates. Science 354, 83–88 (2016).

    Article  ADS  Google Scholar 

  31. Liu, X.-J., Law, K. T. & Ng, T. K. Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms. Phys. Rev. Lett. 112, 086401 (2014).

    Article  ADS  Google Scholar 

  32. Di Liberto, M., Goldman, N. & Palumbo, G. Non-Abelian Bloch oscillations in higher-order topological insulators. Nat. Commun. 11, 5942 (2020).

    Article  ADS  Google Scholar 

  33. Wang, Z.-Y. et al. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling. Science 372, 271–276 (2021).

    Article  ADS  Google Scholar 

  34. Sun, W. et al. Highly controllable and robust 2D spin-orbit coupling for quantum gases. Phys. Rev. Lett. 121, 150401 (2018).

    Article  ADS  Google Scholar 

  35. Zhang, S.-L. & Zhou, Q. Two-leg Su–Schrieffer–Heeger chain with glide reflection symmetry. Phys. Rev. A 95, 061601 (2017).

    Article  ADS  Google Scholar 

  36. Lang, L.-J., Zhang, S.-L. & Zhou, Q. Nodal Brillouin-zone boundary from folding a Chern insulator. Phys. Rev. A 95, 053615 (2017).

    Article  ADS  Google Scholar 

  37. Li, C.-H. et al. Bose–Einstein condensate on a synthetic topological Hall cylinder. PRX Quantum 3, 010316 (2022).

    Article  ADS  Google Scholar 

  38. Khan, N., Wang, P., Fu, Q., Shang, C. & Ye, F. Observation of period-doubling Bloch oscillations. Phys. Rev. Lett. 132, 053801 (2024).

    Article  ADS  Google Scholar 

  39. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).

    Article  ADS  Google Scholar 

  40. Liang, M.-C. et al. Realization of Qi–Wu–Zhang model in spin-orbit-coupled ultracold fermions. Phys. Rev. Res. 5, L012006 (2023).

    Article  Google Scholar 

  41. Sugawa, S., Salces-Carcoba, F., Perry, A. R., Yue, Y. & Spielman, I. B. Second Chern number of a quantum-simulated non-Abelian Yang monopole. Science 360, 1429–1434 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  42. Sugawa, S., Salces-Carcoba, F., Yue, Y., Putra, A. & Spielman, I. Wilson loop and Wilczek–Zee phase from a non-Abelian gauge field. npj Quan. Inf. 7, 144 (2021).

    Article  ADS  Google Scholar 

  43. Horváthy, P. A. Non-Abelian Aharonov–Bohm effect. Phys. Rev. D. 33, 407–414 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  44. Yang, Y. et al. Synthesis and observation of non-Abelian gauge fields in real space. Science 365, 1021–1025 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  45. Chen, Y. et al. Non-Abelian gauge field optics. Nat. Commun. 10, 3125 (2019).

    Article  ADS  Google Scholar 

  46. Huo, M.-X., Nie, W., Hutchinson, D. A. & Kwek, L. C. A solenoidal synthetic field and the non-Abelian Aharonov–Bohm effects in neutral atoms. Sci. Rep. 4, 5992 (2014).

    Article  Google Scholar 

  47. Dhar, A. et al. Chiral mott insulator with staggered loop currents in the fully frustrated Bose–Hubbard model. Phys. Rev. B 87, 174501 (2013).

    Article  ADS  Google Scholar 

  48. Sachdeva, R., Metz, F., Singh, M., Mishra, T. & Busch, T. Two-leg-ladder Bose–Hubbard models with staggered fluxes. Phys. Rev. A 98, 063612 (2018).

    Article  ADS  Google Scholar 

  49. Osterloh, K., Baig, M., Santos, L., Zoller, P. & Lewenstein, M. Cold atoms in non-Abelian gauge potentials: from the Hofstadter “moth" to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005).

    Article  ADS  Google Scholar 

  50. Goldman, N., Kubasiak, A., Gaspard, P. & Lewenstein, M. Ultracold atomic gases in non-Abelian gauge potentials: the case of constant Wilson loop. Phys. Rev. A 79, 023624 (2009).

    Article  ADS  Google Scholar 

  51. Yang, Y., Zhen, B., Joannopoulos, J. D. & Soljačić, M. Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs. Light Sci. Appl. 9, 177 (2020).

    Article  ADS  Google Scholar 

  52. Zamora, A., Szirmai, G. & Lewenstein, M. Layered quantum Hall insulators with ultracold atoms. Phys. Rev. A 84, 053620 (2011).

    Article  ADS  Google Scholar 

  53. Goldman, N. et al. Realistic time-reversal invariant topological insulators with neutral atoms. Phys. Rev. Lett. 105, 255302 (2010).

    Article  ADS  Google Scholar 

  54. Xiao, T. et al. Periodic driving induced helical floquet channels with ultracold atoms in momentum space. Eur. Phys. J. D. 74, 152 (2020).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge the support from the National Key Research and Development Programme of China under Grant Nos. 2023YFA1406703 and 2022YFA1404203, The National Natural Science Foundation of China under Grant Nos. U21A20437, 12074337, 11974331, 12374479 and 12174339, Natural Science Foundation of Zhejiang Province under Grant No. LR21A040002 and LR23A040003, Zhejiang Province Plan for Science and Technology Grant No. 2020C01019, the Fundamental Research Funds for the Central Universities under Grant Nos. 2021FZZX001-02 and 226-2023-00131, the China Postdoctoral Science Foundation under Grant No. 2023M733122 and the Science Specialty Programme of Sichuan University under Grant No. 2020SCUNL210.

Author information

Authors and Affiliations

Contributions

Q.L., Z.D., H.W. and H.L. performed the experiments and data analysis. J.P. and Q.L. performed the theoretical modelling and calculations. Z.Y., W.Y. and B.Y. initiated and supervised this project. All authors discussed the results and contributed to the preparation of the manuscript.

Corresponding authors

Correspondence to Zhaoju Yang, Wei Yi or Bo Yan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Eric Meier and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Table 1 and Discussion.

Source data

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, Q., Dong, Z., Pan, JS. et al. Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field. Nat. Phys. 20, 1738–1743 (2024). https://doi.org/10.1038/s41567-024-02644-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-024-02644-4

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing