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

Abstract

Chains of coupled two-level atoms behave as 1D 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 work, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that whilst 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 with nearest-neighbour and next-nearest-neighbour XY interaction and nonlocal dissipation, 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 set-up that should allow the realisation of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide (PCW). We demonstrate that this model can exhibit many key features of our simpler models.

Cooperative quantum-optical planar arrays of atoms

“…By including only up to two electronic excitations, some nonlinear interactions can be incorporated while maintaining numerical tractability in larger arrays. Two-excitation systems exhibit intriguing phenomena such as fermionization of the excitations [64,65], multiple subradiant excitations forming a superposition of singly excited subradiant states [64], entanglement [66], and bound dimer states [67,68]. Software packages are available to numerically solve these systems as well [63].…”

Dynamical scaling of correlations generated by short- and long-range dissipation

“…Spatially extended dissipative processes, however, are more poorly understood although they can themselves generate correlations and have the potential to steer a quantum system into an entangled state just like coherent interactions. So far, studies of dissipative dynamics have only focused on channels whose spatial profile has limited tunability [69][70][71][72].…”