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.
This is a preview of subscription content, access via your institution
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the findings of this study are available via the Harvard Dataverse at https://doi.org/10.7910/DVN/9WLJXE. Any additional information is available from the corresponding authors upon reasonable request.
The computer codes used for theoretical calculations in this study are available from C.Z. upon reasonable request.
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).
Lemarié, G. et al. Observation of the Anderson metal-insulator transition with atomic matter waves: theory and experiment. Phys. Rev. A 80, 043626 (2009).
Fishman, S., Grempel, D. R. & Prange, R. E. Chaos, quantum recurrences, and Anderson localization. Phys. Rev. Lett. 49, 509 (1982).
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).
Zhang, C., Liu, J., Raizen, M. G. & Niu, Q. Transition to instability in a kicked Bose-Einstein condensate. Phys. Rev. Lett. 92, 054101 (2004).
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).
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).
Lichtenberg, A. & Lieberman, M. Regular and Chaotic Dynamics (Springer, 1992).
Chirikov, B. V. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52, 263 (1979).
Grempel, D. R., Prange, R. E. & Fishman, S. Quantum dynamics of a nonintegrable system. Phys. Rev. A 29, 1639 (1984).
Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958).
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).
Ammann, H., Gray, R., Shvarchuck, I. & Christensen, N. Quantum delta-kicked rotor: experimental observation of decoherence. Phys. Rev. Lett. 80, 4111 (1998).
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).
Wimberger, S., Guarneri, I. & Fishman, S. Quantum resonances and decoherence for δ-kicked atoms. Nonlinearity 16, 1381 (2003).
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).
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).
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).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Lukin, A. et al. Probing entanglement in a many-body–localized system. Science 364, 256–260 (2019).
Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).
Deissler, B. et al. Delocalization of a disordered bosonic system by repulsive interactions. Nat. Phys. 6, 354–358 (2010).
Pikovsky, A. S. & Shepelyansky, D. L. Destruction of Anderson localization by a weak nonlinearity. Phys. Rev. Lett. 100, 094101 (2008).
Flach, S., Krimer, D. O. & Skokos, C. Universal spreading of wave packets in disordered nonlinear systems. Phys. Rev. Lett. 102, 024101 (2009).
Notarnicola, S., Silva, A., Fazio, R. & Russomanno, A. Slow heating in a quantum coupled kicked rotors system. J. Stat. Mech. 2020, 024008 (2020).
Chicireanu, R. & Rançon, A. Dynamical localization of interacting bosons in the few-body limit. Phys. Rev. A 103, 043314 (2021).
Vuatelet, V. & Rançon, A. Effective thermalization of a many-body dynamically localized Bose gas. Phys. Rev. A 104, 043302 (2021).
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).
Lieb, E. H. Exact analysis of an interacting Bose gas. II. The excitation spectrum. Phys. Rev. 130, 1616 (1963).
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).
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).
Petrov, D. S., Shlyapnikov, G. V. & Walraven, J. T. M. Regimes of quantum degeneracy in trapped 1D gases. Phys. Rev. Lett. 85, 3745 (2000).
Griffin, A. Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures. Phys. Rev. B 53, 9341 (1996).
Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).
Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks-Girardeau gas. Science 305, 1125–1128 (2004).
Hou, J. et al. Momentum-space Josephson effects. Phys. Rev. Lett. 120, 120401 (2018).
Cherroret, N., Vermersch, B., Garreau, J. C. & Delande, D. How nonlinear interactions challenge the three-dimensional Anderson transition. Phys. Rev. Lett. 112, 170603 (2014).
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).
Meier, E. J. et al. Observation of the topological anderson insulator in disordered atomic wires. Science 362, 929–933 (2018).
Cao, A. et al. Prethermal dynamical localization and the emergence of chaos in a kicked interacting quantum gas. Preprint at https://arxiv.org/abs/2106.09698v1 (2021).
Hansen, A. H. et al. Quantum degenerate mixture of ytterbium and lithium atoms. Phys. Rev. A 84, 011606 (2011).
Roy, R., Green, A., Bowler, R. & Gupta, S. Rapid cooling to quantum degeneracy in dynamically shaped atom traps. Phys. Rev. A 93, 043403 (2016).
Roy, R., Green, A., Bowler, R. & Gupta, S. Two-element mixture of Bose and Fermi superfluids. Phys. Rev. Lett. 118, 055301 (2017).
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).
The authors declare no competing interests.
Peer review information
Nature Physics thanks Jakub Zakrzewski and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
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). https://doi.org/10.1038/s41567-022-01721-w
This article is cited by
Nature Physics (2022)