• Open Access

Entanglement Growth in Quench Dynamics with Variable Range Interactions

J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley
Phys. Rev. X 3, 031015 – Published 13 September 2013

Abstract

Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the buildup of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter-range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counterintuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter-range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 2 June 2013

DOI:https://doi.org/10.1103/PhysRevX.3.031015

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

J. Schachenmayer1, B. P. Lanyon2, C. F. Roos2, and A. J. Daley1

  • 1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
  • 2Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences and Institute for Experimental Physics, University of Innsbruck, Innsbruck, Austria

Popular Summary

Advances in experiments with atomic, molecular, and optical systems have made it possible to realize quantum simulators—experiments that are so microscopically well understood that they can be used to simulate properties of strongly interacting many-body quantum systems that are difficult to calculate on classical computers. One emerging line of investigation explores out-of-equilibrium dynamics generated in a quantum “quench,” where one system parameter (e.g., the interaction strength) is suddenly changed. Most such investigations so far have involved short-range interactions, but systems of trapped ions now allow the experimental realization of spin models with a controllable interaction range, promising a new vista of quantum phenomena. Keeping pace with that front-of-the-line experimental development, we investigate theoretically the nonequilibrium dynamics after a quantum quench in such systems and report predictions of very different characteristics of their quantum dynamics depending on the range of the interactions.

The system we investigate is a linear chain of trapped ions, which can be effectively modeled as an interacting quantum spin chain. The range of the interaction, which decays approximately algebraically as a function of the distance r between the ions in the chain, is treated as a control variable, reflecting the current experimental capability. We find the counterintuitive result that the quantum entanglement between separated blocks in the chain grows in time much faster in cases of shorter-range interactions (decaying faster than 1/r) than in cases of longer-range interactions (decaying slower than 1/r). The reason, as we have revealed, lies in the fundamentally different dynamics in these two cases: For shorter-range interactions, the dynamics involves local production of quasiparticle excitations that propagate through the system, and for longer-range interactions, the dynamics is dominated by direct spin-spin interactions.

This difference is fundamentally interesting and is also important. In particular, the dynamics with longer-range interactions studied here can actually be easier to simulate on a classical computer using current techniques than those generated by the shorter-range interactions. In this sense, our work can act as a guide for generating large-scale entanglement in these experiments, providing necessary conditions to explore regimes that might go beyond what is possible with current numerical techniques.

Key Image

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 3, Iss. 3 — July - September 2013

Subject Areas
Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×