SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms

Ryan Barnett, G. R. Boyd, and Victor Galitski
Phys. Rev. Lett. 109, 235308 – Published 5 December 2012

Abstract

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as “SU(3) spin-orbit-coupling,” where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically nontrivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states—the hallmark feature of such an SU(3) topological insulator.

  • Figure
  • Received 17 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.235308

© 2012 American Physical Society

Authors & Affiliations

Ryan Barnett1,2,3, G. R. Boyd2, and Victor Galitski1,2

  • 1Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
  • 2Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
  • 3Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 109, Iss. 23 — 7 December 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×