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Research Article

Emergence of coherence and the dynamics of quantum phase transitions

Simon Braun, Mathis Friesdorf, Sean S. Hodgman, Michael Schreiber, Jens Philipp Ronzheimer, Arnau Riera, Marco del Rey, Immanuel Bloch, Jens Eisert, and View ORCID ProfileUlrich Schneider
PNAS first published March 9, 2015; https://doi.org/10.1073/pnas.1408861112
Simon Braun
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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Mathis Friesdorf
cDahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany;
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Sean S. Hodgman
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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Michael Schreiber
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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Jens Philipp Ronzheimer
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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Arnau Riera
cDahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany;
dMax-Planck-Institut für Gravitationsphysik, 14476 Potsdam-Golm, Germany; and
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Marco del Rey
eInstituto de Fisica Fundamental, Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain
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Immanuel Bloch
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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Jens Eisert
cDahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany;
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Ulrich Schneider
aFakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany;
bMax-Planck-Institut für Quantenoptik, 85748 Garching, Germany;
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  • ORCID record for Ulrich Schneider
  • For correspondence: ulrich.schneider@lmu.de
  1. Edited by William D. Phillips, National Institute of Standards and Technology, Gaithersburg, MD, and approved February 9, 2015 (received for review May 19, 2014)

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Significance

Quantum phase transitions are characterized by a dramatic change of the ground-state behavior; famous examples include the appearance of magnetic order or superconductivity as a function of doping in cuprates. In this work, we explore how a system dynamically crosses such a transition and in particular, investigate in detail how coherence emerges when an initially incoherent Mott insulating system enters the superfluid regime. We present results from an experimental study using ultracold atoms in an optical lattice as well as numerical simulations and find a rich behavior beyond the scope of any existing theory. This quantum simulation of a complex many-body system is an important stepping stone for a deeper understanding of the intricate dynamics of quantum phase transitions.

Abstract

The dynamics of quantum phase transitions pose one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the 1D Bose–Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We, thereby, perform a largely certified analog quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions, where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behavior of the coherence length, reminiscent of the Kibble–Zurek mechanism. However, we find nonuniversal exponents that cannot be captured by this mechanism or any other known model.

  • ultracold atoms
  • optical lattice
  • Mott insulator
  • nonequilibrium dynamics
  • quantum simulation

Footnotes

  • ↵1To whom correspondence should be addressed. Email: ulrich.schneider{at}lmu.de.
  • Author contributions: I.B., J.E., and U.S. designed research; S.B., M.F., S.S.H., M.S., J.P.R., A.R., M.d.R., and J.E. performed research; S.B. and M.F. analyzed data; and S.B., M.F., I.B., J.E., and U.S. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1408861112/-/DCSupplemental.

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Emerging coherence at a quantum phase transition
Simon Braun, Mathis Friesdorf, Sean S. Hodgman, Michael Schreiber, Jens Philipp Ronzheimer, Arnau Riera, Marco del Rey, Immanuel Bloch, Jens Eisert, Ulrich Schneider
Proceedings of the National Academy of Sciences Mar 2015, 201408861; DOI: 10.1073/pnas.1408861112

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Emerging coherence at a quantum phase transition
Simon Braun, Mathis Friesdorf, Sean S. Hodgman, Michael Schreiber, Jens Philipp Ronzheimer, Arnau Riera, Marco del Rey, Immanuel Bloch, Jens Eisert, Ulrich Schneider
Proceedings of the National Academy of Sciences Mar 2015, 201408861; DOI: 10.1073/pnas.1408861112
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