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Quantum simulation of dynamical maps with trapped ions

Nature Physics volume 9, pages 361–367 (2013)Cite this article

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Abstract

Dynamical maps describe general transformations of the state of a physical system—their iteration interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single-particle level. Here we extend the concept of dynamical maps to a many-particle context, where the time evolution involves both coherent and dissipative elements: we experimentally explore the stroboscopic dynamics of a complex many-body spin model with a universal trapped ion quantum simulator. We generate long-range phase coherence of spin by an iteration of purely dissipative quantum maps and demonstrate the characteristics of competition between combined coherent and dissipative non-equilibrium evolution—the hallmark of a previously unobserved dynamical phase transition. We assess the influence of experimental errors in the quantum simulation and tackle this problem by developing an efficient error detection and reduction toolbox based on quantum feedback.

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Figure 1: Competing dissipative and Hamiltonian dynamical maps in the spin or hard-core boson model.
Figure 2: Experimental procedure to implement open-system dynamical maps.
Figure 3: Experimental results of dissipatively induced delocalization through composite dynamical maps with 3+1 ions.
Figure 4: Experimental results for competing dissipative and coherent dynamics with 3+1 and 4+1 ions.
Figure 5: Experimental error detection and reduction techniques.

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Acknowledgements

We gratefully acknowledge support by the Austrian Science Fund (FWF), through the SFB FoQus (FWF Project No. F4002-N16 and F4016-N16) and the START grant Y 581-N16 (S.D.), by the European Commission (AQUTE), as well as the Institut für Quantenoptik und Quanteninformation GmbH. This research was funded by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the Army Research Office grant W911NF-10-1-0284. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US Government. M.M. acknowledges support by the CAM research consortium QUITEMAD S2009-ESP-1594, European Commission PICC: FP7 2007-2013, Grant No. 249958, and the Spanish MICINN grant FIS2009-10061.

Author information

Author notes

  1. J. T. Barreiro

    Present address: Present address: Fakultät für Physik, Ludwig-Maximilians-Universität München and Max-Planck Institute of Quantum Optics, Germany,

  2. P. Schindler and M. Müller: These authors contributed equally to this work

Authors and Affiliations

  1. Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria

    P. Schindler, D. Nigg, J. T. Barreiro, E. A. Martinez, M. Hennrich, T. Monz & R. Blatt

  2. Departamento de Física Teórica I, Universidad Complutense, Avenida Complutense s/n, 28040 Madrid, Spain

    M. Müller

  3. Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria

    S. Diehl & P. Zoller

  4. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstrasse 21A, 6020 Innsbruck, Austria

    S. Diehl, P. Zoller & R. Blatt

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Contributions

M.M., P.S., J.T.B. and S.D. developed the research, based on theoretical ideas conceived with P.Z.; P.S. and D.N. performed the experiments; P.S. and T.M. analysed the data; P.S., J.T.B., D.N., T.M., E.A.M., M.H. and R.B. contributed to the experimental set-up; P.S., M.M. and S.D wrote the manuscript, with revisions provided by J.T.B., P.Z. and R.B; all authors contributed to the discussion of the results and manuscript.

Corresponding authors

Correspondence to P. Zoller or R. Blatt.

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Schindler, P., Müller, M., Nigg, D. et al. Quantum simulation of dynamical maps with trapped ions. Nature Phys 9, 361–367 (2013). https://doi.org/10.1038/nphys2630

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