Abstract
Understanding the dynamics of isolated quantum many-body systems is a central open problem at the intersection between statistical physics and quantum physics. Despite important theoretical effort1, no generic framework exists yet to understand when and how an isolated quantum system relaxes to a steady state. Regarding the question of how, it has been conjectured2,3 that equilibration must occur on a local scale in systems where correlations between distant points can establish only at a finite speed. Here, we provide the first experimental observation of this local equilibration hypothesis. In our experiment, we quench a one-dimensional Bose gas by coherently splitting it into two parts. By monitoring the phase coherence between the two parts we observe that the thermal correlations of a prethermalized state4,5 emerge locally in their final form and propagate through the system in a light-cone-like evolution. Our results underline the close link between the propagation of correlations 2,3,6,7 and relaxation processes in quantum many-body systems.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863–883 (2011).
Calabrese, P. & Cardy, J. Time dependence of correlation functions following a quantum quench. Phys. Rev. Lett. 96, 011368 (2006).
Cramer, M., Dawson, C. M., Eisert, J. & Osborne, T. J. Exact relaxation in a class of nonequilibrium quantum lattice systems. Phys. Rev. Lett. 100, 030602 (2008).
Gring, M. et al. Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012).
Berges, J., Borsányi, S. & Wetterich, C. Prethermalization. Phys. Rev. Lett. 93, 142002 (2004).
Lieb, E. H. & Robinson, D. W. The finite group velocity of quantum spin systems. Commun. Math. Phys. 28, 251–257 (1972).
Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).
Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).
Srednicki, M. Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994).
Rigol, M., Dunjko, V., Yurovsky, V. & Olshanii, M. Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons. Phys. Rev. Lett. 98, 050405 (2007).
Kinoshita, T., Wenger, T. & Weiss, D. A quantum newton’s cradle. Nature 440, 900–903 (2006).
Gaunt, A. L., Fletcher, R. J., Smith, R. P. & Hadzibabic, Z. A superheated Bose-condensed gas. Nature Phys. 9, 271–274 (2013).
Sadler, L. E., Higbie, J. M., Leslie, S. R., Vengalattore, M. & Stamper-Kurn, D. M. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate. Nature 443, 312–315 (2006).
Ritter, S. et al. Observing the formation of long-range order during Bose-Einstein condensation. Phys. Rev. Lett. 98, 090402–090402 (2007).
Trotzky, S. et al. Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas. Nature Phys. 8, 325–330 (2012).
Gerving, C. S. et al. Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose-Einstein condensate. Nature Commun. 3, 1169 (2012).
Petrov, D., Shlyapnikov, G. & Walraven, J. Regimes of quantum degeneracy in trapped 1d gases. Phys. Rev. Lett. 85, 3745–3749 (2000).
Schumm, T. et al. Matter-wave interferometry in a double well on an atom chip. Nature Phys. 1, 57–62 (2005).
Kuhnert, M. et al. Multimode dynamics and emergence of a characteristic length scale in a one-dimensional quantum system. Phys. Rev. Lett. 110, 090405 (2013).
Cronin, A. D., Schmiedmayer, J. & Pritchard, D. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009).
Reichel, J. & Vuletic, V. (eds) Atom Chips (Wiley, 2011).
Whitlock, N. K. & Bouchoule, I. Relative phase fluctuations of two coupled one-dimensional condensates. Phys. Rev. A 68, 053609 (2003).
Betz, T. et al. Two-point phase correlations of a one-dimensional bosonic Josephson junction. Phys. Rev. Lett. 106, 020407 (2011).
Mathey, L. & Polkovnikov, A. Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench. Phys. Rev. A 81, 60033 (2010).
Bravyi, S., Hastings, M. B. & Verstraete, F. Lieb-Robinson bounds and the generation of correlations and topological quantum order. Phys. Rev. Lett. 97, 050401 (2006).
Läuchli, A. M. & Kollath, C. Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model. J. Stat. Mech. P05018 (2008).
Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).
Kitagawa, T., Imambekov, A., Schmiedmayer, J. & Demler, E. The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise. New J. Phys. 13, 073018 (2011).
Hauke, P. & Tagliacozzo, L. Spread of correlations in long-range interacting systems. Preprint at http://arxiv.org/abs/1304.7725 (2013).
Burrell, C. K. & Osborne, T. J. Bounds on the speed of information propagation in disordered quantum spin chains. Phys. Rev. Lett. 99, 167201 (2007).
Langen, T. et al. Prethermalization in one-dimensional Bose gases: description by a stochastic Ornstein-Uhlenbeck process. Eur. Phys. J. Special Top. 217, 43–53 (2013).
Acknowledgements
We would like to thank D. Adu Smith and M. Gring for contributions in the early stage of the experiment, I. Mazets, V. Kasper and J. Berges for discussions and J-F. Schaff and T. Schumm for comments on the manuscript. This work was supported by the Austrian Science Fund (FWF) through the Wittgenstein Prize and the EU through the projects QIBEC and AQUTE. T.L. and M.K. thank the FWF Doctoral Programme CoQuS (W1210); R.G. is supported by the FWF through the Lise Meitner Programme M 1423.
Author information
Authors and Affiliations
Contributions
T.L. and R.G. performed the experiment, analysed the data and carried out the theoretical modelling. J.S. conceived the experiment and the leading scientific questions. All authors contributed to the interpretation of the data and the writing of the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information (download PDF )
Supplementary Information (PDF 713 kb)
Rights and permissions
About this article
Cite this article
Langen, T., Geiger, R., Kuhnert, M. et al. Local emergence of thermal correlations in an isolated quantum many-body system. Nature Phys 9, 640–643 (2013). https://doi.org/10.1038/nphys2739
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/nphys2739
