Skip to main content

Thank you for visiting 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:

Domain-wall dynamics in Bose–Einstein condensates with synthetic gauge fields


Interactions in many-body physical systems, from condensed matter to high-energy physics, lead to the emergence of exotic particles. Examples are mesons in quantum chromodynamics and composite fermions in fractional quantum Hall systems, which arise from the dynamical coupling between matter and gauge fields1,2. The challenge of understanding the complexity of matter–gauge interaction can be aided by quantum simulations, for which ultracold atoms offer a versatile platform via the creation of artificial gauge fields. An important step towards simulating the physics of exotic emergent particles is the synthesis of artificial gauge fields whose state depends dynamically on the presence of matter. Here we demonstrate deterministic formation of domain walls in a stable Bose–Einstein condensate with a gauge field that is determined by the atomic density. The density-dependent gauge field is created by simultaneous modulations of an optical lattice potential and interatomic interactions, and results in domains of atoms condensed into two different momenta. Modelling the domain walls as elementary excitations, we find that the domain walls respond to synthetic electric field with a charge-to-mass ratio larger than and opposite to that of the bare atoms. Our work offers promising prospects to simulate the dynamics and interactions of previously undescribed excitations in quantum systems with dynamical gauge fields.

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: Illustration of a Bose–Einstein condensate with a density-dependent gauge field.
Fig. 2: Creation of static and density-dependent gauge fields.
Fig. 3: Domains and domain walls in the presence of a density-dependent gauge field.
Fig. 4: Dynamics of the domain wall in response to a synthetic electric field \({\boldsymbol{ {\mathcal E} }}\).

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The codes for the analysis of data shown within this paper are available from the corresponding author upon reasonable request.


  1. Griffiths, D. Introduction to Elementary Particles (Wiley, 2008).

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

    Article  MathSciNet  CAS  Google Scholar 

  3. Kogut, J. B. An introduction to lattice gauge theory and spin systems. Rev. Mod. Phys. 51, 659–713 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  4. Wilson, K. G. Confinement of quarks. Phys. Rev. D 10, 2445–2459 (1974).

    Article  ADS  CAS  Google Scholar 

  5. Alford, M. G., Schmitt, A., Rajagopal, K. & Schäfer, T. Color superconductivity in dense quark matter. Rev. Mod. Phys. 80, 1455–1515 (2008).

    Article  ADS  CAS  Google Scholar 

  6. Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  8. Zohar, E., Cirac, J. I. & Reznik, B. Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices. Rep. Prog. Phys. 79, 014401 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  9. Cooper, N. R., Dalibard, J. & Spielman, I. B. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  11. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  13. 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 

  14. Baskaran, G. & Anderson, P. W. Gauge theory of high-temperature superconductors and strongly correlated Fermi systems. Phys. Rev. B 37, 580–583 (1988).

    Article  ADS  CAS  Google Scholar 

  15. Cheng, T.-P. & Li, L.-F. Gauge Theory of Elementary Particle Physics (Oxford Univ. Press, 1994).

  16. Levin, M. & Wen, X.-G. Colloquium: photons and electrons as emergent phenomena. Rev. Mod. Phys. 77, 871–879 (2005).

    Article  ADS  CAS  Google Scholar 

  17. Wiese, U.-J. Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories. Ann. Phys. 525, 777–796 (2013).

    Article  MathSciNet  CAS  Google Scholar 

  18. Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2016).

    Article  ADS  Google Scholar 

  19. Clark, L. W. et al. 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).

    Article  ADS  CAS  Google Scholar 

  20. Görg, F. et al. Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter. Nat. Phys. 15, 1161–1167 (2019).

    Article  Google Scholar 

  21. Lienhard, V. et al. Realization of a density-dependent Peierls phase in a synthetic, spin-orbit coupled Rydberg system. Phys. Rev. X 10, 021031 (2020).

    CAS  Google Scholar 

  22. Edmonds, M. J., Valiente, M., Juzeliūnas, G., Santos, L. & Öhberg, P. Simulating an interacting gauge theory with ultracold Bose gases. Phys. Rev. Lett. 110, 085301 (2013).

    Article  ADS  CAS  Google Scholar 

  23. Schweizer, C. et al. Floquet approach to \({{\mathbb{Z}}}_{2}\) lattice gauge theories with ultracold atoms in optical lattices. Nat. Phys. 15, 1168–1173 (2019).

    Article  CAS  Google Scholar 

  24. Yang, B. et al. Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator. Nature 587, 392–396 (2020).

    Article  ADS  CAS  Google Scholar 

  25. Mil, A. et al. A scalable realization of local U(1) gauge invariance in cold atomic mixtures. Science 367, 1128–1130 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. Liu, T., Clark, L. W. & Chin, C. Exotic domain walls in Bose-Einstein condensates with double-well dispersion. Phys. Rev. A 94, 063646 (2016).

    Article  ADS  Google Scholar 

  27. Eckardt, A. Colloquium: atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  28. Struck, J. et al. Tunable gauge potential for neutral and spinless particles in driven optical lattices. Phys. Rev. Lett. 108, 225304 (2012).

    ADS  CAS  Google Scholar 

  29. Shvarchuck, I. et al. Bose-Einstein condensation into nonequilibrium states studied by condensate focusing. Phys. Rev. Lett. 89, 270404 (2002).

    Article  CAS  Google Scholar 

  30. Clark, L. W., Feng, L. & Chin, C. Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition. Science 354, 606–610 (2016).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  31. Parker, C. V., Ha, L.-C. & Chin, C. Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice. Nat. Phys. 9, 769–774 (2013).

    Article  CAS  Google Scholar 

  32. Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591–648 (1979).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  33. Gani, V. A., Kudryavtsev, A. E. & Lizunova, M. A. Kink interactions in the (1+1)-dimensional φ6 model. Phys. Rev. D 89, 125009 (2014).

    Article  ADS  Google Scholar 

  34. Vilenkin, A. Cosmic strings and domain walls. Phys. Rep. 121, 263–315 (1985).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  35. Barbiero, L. et al. Coupling ultracold matter to dynamical gauge fields in optical lattices: from flux attachment to \({{\mathbb{Z}}}_{2}\) lattice gauge theories. Sci. Adv. 5, eaav7444 (2019).

Download references


We thank E. Mueller for helpful discussions and K. Patel for carefully reading the manuscript. This work is supported by the National Science Foundation (NSF) grant no. PHY-2103542, NSF QLCI-HQAN no. 2016136, and the Army Research Office STIR grant W911NF2110108. Z.Z. is supported by the Grainger Graduate Fellowship.

Author information

Authors and Affiliations



K.-X.Y. designed and performed the experiments and analysed the data. All authors contributed to discussions on the experiment and preparation of the manuscript. C.C. supervised the project.

Corresponding author

Correspondence to Cheng Chin.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Peer review information

Nature thanks Pietro Massignan and the other, anonymous, reviewer for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

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

Extended data figures and tables

Extended Data Fig. 1 Estimation of the zero-crossing position.

The population imbalance between the ±k* states in Fig. 2h is fitted to extract the zero-crossing position.

Extended Data Fig. 2 Extraction of ϵexp from magnetization M.

Experiment data in Fig. 3e are fitted to extract the value of ϵexp.

Supplementary information

Source data

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, KX., Zhang, Z. & Chin, C. Domain-wall dynamics in Bose–Einstein condensates with synthetic gauge fields. Nature 602, 68–72 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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