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Many-body dynamical delocalization in a kicked one-dimensional ultracold gas


Contrary to a driven classical system that exhibits chaotic behaviour and diffusive energy growth, a kicked quantum system can exhibit the emergence of dynamical localization, which limits energy absorption and leads to the breakdown of ergodicity1,2,3,4. The evolution of dynamically localized states in the presence of many-body interactions has long remained an open question5,6,7. Here we experimentally study an interacting one-dimensional ultracold gas periodically kicked by a pulsed optical lattice and observe the interaction-driven emergence of dynamical delocalization and many-body quantum chaos. The observed dynamics feature sub-diffusive energy growth over a broad parameter range of interaction and kick strengths. These results shed light on interaction-driven transport phenomena in quantum many-body systems, in a regime where theoretical approaches are extremely challenging and provide conflicting predictions.

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Fig. 1: Experimentally realizing the interacting 1D QKR system.
Fig. 2: Momentum and energy evolution for dynamically localized and delocalized rotors.
Fig. 3: Tuning the onset of many-body quantum chaos with interaction and kick strengths.

Data availability

The data that support the findings of this study are available via the Harvard Dataverse at Any additional information is available from the corresponding authors upon reasonable request.

Code availability

The computer codes used for theoretical calculations in this study are available from C.Z. upon reasonable request.


  1. Casati, G., Chirikov, B. V., Izraelev, F. M. & Ford, J. Stochastic behavior of a quantum pendulum under a periodic perturbation. in Stochastic Behavior in Classical and Quantum Hamiltonian Systems 334–352 (Springer, 1979).

  2. Lemarié, G. et al. Observation of the Anderson metal-insulator transition with atomic matter waves: theory and experiment. Phys. Rev. A 80, 043626 (2009).

    Article  ADS  Google Scholar 

  3. Fishman, S., Grempel, D. R. & Prange, R. E. Chaos, quantum recurrences, and Anderson localization. Phys. Rev. Lett. 49, 509 (1982).

  4. Moore, F. L., Robinson, J. C., Bharucha, C. F., Sundaram, B. & Raizen, M. G. Atom optics realization of the quantum δ-kicked rotor. Phys. Rev. Lett. 75, 4598 (1995).

  5. Zhang, C., Liu, J., Raizen, M. G. & Niu, Q. Transition to instability in a kicked Bose-Einstein condensate. Phys. Rev. Lett. 92, 054101 (2004).

    Article  ADS  Google Scholar 

  6. Lellouch, S., Rançon, A., De Bièvre, S., Delande, D. & Garreau, J. C. Dynamics of the mean-field-interacting quantum kicked rotor. Phys. Rev. A 101, 043624 (2020).

    Article  ADS  Google Scholar 

  7. Rylands, C., Rozenbaum, E. B., Galitski, V. & Konik, R. Many-body dynamical localization in a kicked Lieb-Liniger gas. Phys. Rev. Lett. 124, 155302 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  8. Lichtenberg, A. & Lieberman, M. Regular and Chaotic Dynamics (Springer, 1992).

  9. Chirikov, B. V. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52, 263 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  10. Grempel, D. R., Prange, R. E. & Fishman, S. Quantum dynamics of a nonintegrable system. Phys. Rev. A 29, 1639 (1984).

    Article  ADS  Google Scholar 

  11. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958).

    Article  ADS  MathSciNet  Google Scholar 

  12. Moore, F. L., Robinson, J. C., Bharucha, C., Williams, P. E. & Raizen, M. G. Observation of dynamical localization in atomic momentum transfer: a new testing ground for quantum chaos. Phys. Rev. Lett. 73, 2974 (1994).

    Article  ADS  Google Scholar 

  13. Ammann, H., Gray, R., Shvarchuck, I. & Christensen, N. Quantum delta-kicked rotor: experimental observation of decoherence. Phys. Rev. Lett. 80, 4111 (1998).

    Article  ADS  Google Scholar 

  14. d’Arcy, M. B. Godun, R. M., Oberthaler, M. K., Cassettari, D. & Summy, G. S. Quantum enhancement of momentum diffusion in the delta-kicked rotor. Phys. Rev. Lett. 87, 074102 (2001).

  15. Wimberger, S., Guarneri, I. & Fishman, S. Quantum resonances and decoherence for δ-kicked atoms. Nonlinearity 16, 1381 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Duffy, G. J. et al. Experimental investigation of early-time diffusion in the quantum kicked rotor using a Bose-Einstein condensate. Phys. Rev. E 70, 056206 (2004).

    Article  ADS  Google Scholar 

  17. Ullah, A., Reddel, S., Currivan, J. & Hoogerland, M. D. Quantum resonant effects in the delta-kicked rotor revisited. Eur. Phys. J. D 66, 315 (2012).

  18. Gadway, B., Reeves, J., Krinner, L. & Schneble, D. Evidence for a quantum-to-classical transition in a pair of coupled quantum rotors. Phys. Rev. Lett. 110, 190401 (2013).

    Article  ADS  Google Scholar 

  19. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  20. Lukin, A. et al. Probing entanglement in a many-body–localized system. Science 364, 256–260 (2019).

    Article  Google Scholar 

  21. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  22. Deissler, B. et al. Delocalization of a disordered bosonic system by repulsive interactions. Nat. Phys. 6, 354–358 (2010).

    Article  Google Scholar 

  23. Pikovsky, A. S. & Shepelyansky, D. L. Destruction of Anderson localization by a weak nonlinearity. Phys. Rev. Lett. 100, 094101 (2008).

    Article  ADS  Google Scholar 

  24. Flach, S., Krimer, D. O. & Skokos, C. Universal spreading of wave packets in disordered nonlinear systems. Phys. Rev. Lett. 102, 024101 (2009).

    Article  ADS  Google Scholar 

  25. Notarnicola, S., Silva, A., Fazio, R. & Russomanno, A. Slow heating in a quantum coupled kicked rotors system. J. Stat. Mech. 2020, 024008 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  26. Chicireanu, R. & Rançon, A. Dynamical localization of interacting bosons in the few-body limit. Phys. Rev. A 103, 043314 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  27. Vuatelet, V. & Rançon, A. Effective thermalization of a many-body dynamically localized Bose gas. Phys. Rev. A 104, 043302 (2021).

    Article  ADS  Google Scholar 

  28. Lieb, E. H. & Liniger, W. Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev. 130, 1605 (1963).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Lieb, E. H. Exact analysis of an interacting Bose gas. II. The excitation spectrum. Phys. Rev. 130, 1616 (1963).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Yang, C. N. & Yang, C. P. Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys. 10, 1115 (1969).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Ketterle, W. & Van Druten, N. J. Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions. Phys. Rev. A 54, 656 (1996).

    Article  ADS  Google Scholar 

  32. Petrov, D. S., Shlyapnikov, G. V. & Walraven, J. T. M. Regimes of quantum degeneracy in trapped 1D gases. Phys. Rev. Lett. 85, 3745 (2000).

    Article  ADS  Google Scholar 

  33. Griffin, A. Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures. Phys. Rev. B 53, 9341 (1996).

    Article  ADS  Google Scholar 

  34. Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).

    Article  Google Scholar 

  35. Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks-Girardeau gas. Science 305, 1125–1128 (2004).

    Article  Google Scholar 

  36. Hou, J. et al. Momentum-space Josephson effects. Phys. Rev. Lett. 120, 120401 (2018).

    Article  ADS  Google Scholar 

  37. Cherroret, N., Vermersch, B., Garreau, J. C. & Delande, D. How nonlinear interactions challenge the three-dimensional Anderson transition. Phys. Rev. Lett. 112, 170603 (2014).

    Article  ADS  Google Scholar 

  38. Vermersch, B., Delande, D. & Garreau, J. C. Bogoliubov excitations in the quasiperiodic kicked rotor: stability of a kicked condensate and the quasi–insulator-to-metal transition. Phys. Rev. A 101, 053625 (2020).

    Article  ADS  Google Scholar 

  39. Meier, E. J. et al. Observation of the topological anderson insulator in disordered atomic wires. Science 362, 929–933 (2018).

    Article  Google Scholar 

  40. Cao, A. et al. Prethermal dynamical localization and the emergence of chaos in a kicked interacting quantum gas. Preprint at (2021).

  41. Hansen, A. H. et al. Quantum degenerate mixture of ytterbium and lithium atoms. Phys. Rev. A 84, 011606 (2011).

    Article  ADS  Google Scholar 

  42. Roy, R., Green, A., Bowler, R. & Gupta, S. Rapid cooling to quantum degeneracy in dynamically shaped atom traps. Phys. Rev. A 93, 043403 (2016).

    Article  ADS  Google Scholar 

  43. Roy, R., Green, A., Bowler, R. & Gupta, S. Two-element mixture of Bose and Fermi superfluids. Phys. Rev. Lett. 118, 055301 (2017).

    Article  ADS  Google Scholar 

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We thank D. Weld, A. Rançon and V. Galitski for helpful discussions. Work at the University of Washington is supported by the Air Force Office of Scientific Research (FA9550-19-1-0012) and the National Science Foundation (PHY-1806212). K.C.M. is supported by an IC postdoctoral fellowship. The work at the University of Texas at Dallas is supported by the Air Force Office of Scientific Research (FA9550-20-1-0220), National Science Foundation (PHY-1806227 and PHY-2110212) and Army Research Office (W911NF-17-1-0128).

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Authors and Affiliations



J.H.S.T., K.C.M. and X.T. performed the experimental measurements and data analysis. S.G. conceived the experiment and supervised the work. Y.S. and X.-W.L. performed the GP and HFB numerical simulations. C.Z. supervised the theoretical work. All the authors contributed to the preparation of the manuscript.

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Correspondence to Chuanwei Zhang or Subhadeep Gupta.

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

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Supplementary Figs. 1–10, Table 1 and Discussion.

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See Toh, J.H., McCormick, K.C., Tang, X. et al. Many-body dynamical delocalization in a kicked one-dimensional ultracold gas. Nat. Phys. 18, 1297–1301 (2022).

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