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Topology by dissipation in atomic quantum wires

Nature Physics volume 7, pages 971–977 (2011)Cite this article

Abstract

Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as ‘topologically protected’ quantum memory and computing. So far, topological phases have been exclusively discussed in a Hamiltonian context. Here we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems with engineered dissipation. The specific system studied here is a quantum wire of spinless atomic fermions in an optical lattice coupled to a bath. The key feature of the dissipative dynamics described by a Lindblad master equation is the existence of Majorana edge modes, representing a non-local decoherence-free subspace. The isolation of the edge states is enforced by a dissipative gap in the p-wave paired bulk of the wire. We describe dissipative non-Abelian braiding operations within the Majorana subspace, and illustrate the insensitivity to imperfections. Topological protection is granted by a non-trivial winding number of the system density matrix.

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Figure 1: Schematic set-up for the dissipative Majorana quantum wire.
Figure 2: Microscopic implementation scheme for the Majorana Liouvillian equations (2), (3).
Figure 3: Characterization of the topological stationary state for a quantum wire with 50 lattice sites without (full circles) and with (open circles) static disorder.
Figure 4: Dissipative braiding.
Figure 5: Visualization of the topological invariant ν for chirally symmetric mixed states.

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Acknowledgements

We thank C. Bardyn, V. Gurarie, A. Imamoglu, C. Kraus and M. Troyer for helpful discussions. We acknowledge support by the Austrian Science Fund (FOQUS), the European Commission (AQUTE, NAMEQUAM), the Institut für Quanteninformation GmbH and a grant from the US Army Research Office with funding from the Defense Advanced Research Projects Agency OLE program.

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Authors and Affiliations

  1. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria

    Sebastian Diehl, Enrique Rico, Mikhail A. Baranov & Peter Zoller

  2. Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria

    Sebastian Diehl, Enrique Rico, Mikhail A. Baranov & Peter Zoller

  3. RRC ‘Kurchatov Institute’, Kurchatov Square 1, 123182 Moscow, Russia

    Mikhail A. Baranov

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Correspondence to Sebastian Diehl.

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Diehl, S., Rico, E., Baranov, M. et al. Topology by dissipation in atomic quantum wires. Nature Phys 7, 971–977 (2011). https://doi.org/10.1038/nphys2106

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