Decay rates and energies of free magnons and bound states in dissipative XXZ chains

C. D. Parmee and N. R. Cooper
Phys. Rev. A 99, 063615 – Published 18 June 2019

Abstract

Chains of coupled two-level atoms behave as one-dimensional quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g., systems in which the magnons decay due to optical emission. In this paper, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that while the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound-state solutions for a system where both the XY interaction and nonlocal dissipation are nearest neighbor or next-nearest neighbor, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental setup that should allow the realization of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide. We demonstrate that this model can exhibit many key features of our simpler models.

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  • Received 19 December 2018

DOI:https://doi.org/10.1103/PhysRevA.99.063615

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

C. D. Parmee and N. R. Cooper

  • TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, England, United Kingdom

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Issue

Vol. 99, Iss. 6 — June 2019

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