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Quantum Spin Dimers from Chiral Dissipation in Cold-Atom Chains

Tomás Ramos, Hannes Pichler, Andrew J. Daley, and Peter Zoller
Phys. Rev. Lett. 113, 237203 – Published 3 December 2014
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    Abstract

    We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a one-dimensional (1D) bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasicondensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left- and right-moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.

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    • Received 19 August 2014

    DOI:https://doi.org/10.1103/PhysRevLett.113.237203

    © 2014 American Physical Society

    Authors & Affiliations

    Tomás Ramos1,2,*, Hannes Pichler1,2, Andrew J. Daley3,4, and Peter Zoller1,2

    • 1Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
    • 2Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
    • 3Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
    • 4Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

    • *tomas.ramos@uibk.ac.at

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    Vol. 113, Iss. 23 — 5 December 2014

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    • Figure 1
      Figure 1

      The 1D spin chain coupled to a 1D chiral bosonic reservoir. (a) Driven spins decay into right- and left-moving reservoir modes with rates γR and γL. For γR≠γL, quantum spin dimers (indicated by |D⟩) are formed as the unique pure steady state. (b-d) Implementation with a two-species mixture of cold atoms. (b) Spins are represented by the two lowest vibrational states of atoms a on each site of a 1D optical lattice, which can “decay” due to collisions with a 1D SOC quasi-BEC, representing the bath. (c) SOC of atoms b due to coupling of two internal states |↑⟩ and |↓⟩ via a Raman process [29]. (d) Dispersion relations ℏωkβ of the bath excitations in the plane wave phase. The red and blue arrows indicate excitations of atoms b from the quasi-BEC (circle at km) to wave vectors kL and kR, resonant with ℏω.

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    • Figure 2
      Figure 2

      Tunability of decay asymmetry into chiral left- and right-moving modes (a) γL/γR as a function of ℏΩ0/E0 for ga↓=ga↑ (solid line) and ga↓=0 (dashed line). The dash-dotted line shows the reservoir spin polarization ρ¯↓/ρ¯↑. (b) Density fluctuation coefficients Q−λ(k) (λ=↑,↓) in the lower branch for ℏΩ0=0.2E0. The wave vectors for left- and right-moving excitations ks (s=L,R) are indicated, where Q−λ(ks) show their strong spin polarization. Other parameters are ρ¯=6.14k0, ma/mb=2, g↑↑=g↑↓=g↓↓=0.23E0/k0, ga↑=−0.37E0/k0, ℏω=1.46E0, and δ0=−0.004E0.

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    • Figure 3
      Figure 3

      Dynamical formation of spin dimers as the unique steady state of the driven-dissipative spin chain. We plot the entropy Sj,j+1(t) of all adjacent spin pairs (solid lines) and the purity P(t) of the total state (black dashed line) for the initial condition |Ψ(0)⟩=⊗j=1N|g⟩j. Results are shown for Ω=0.5γR and (a) N=10, γL=0, (b) N=10, γL=0.4γR, (c) N=9, γL=0, (d) N=9, γL=0.4γR.

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    • Figure 4
      Figure 4

      Robustness of the dimerized steady state against imperfections for N=6. (a) Pair purities P2j−1,2j and total purity P as a function of ε (see text), for γL=0.1 (dashed line) and γL=0.4γR (solid line). (b) P2j−1,2j and P as a function of decay outside the 1D bath γ′, for γL=0 (dashed line) and γL=0.4γR (solid line). We fix Ω=0.5γR.

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