Cold-atom systems with synthetic SU(3) spin-orbit coupling

Chuanwei Zhang

Chuanzhou Zhu

In cold atom, the coupling between "spin" (atomic internal hyperfine states) and "orbit" (atomic center-of-mass motion) can be induced by Raman transition, where different hyperfine states are coupled by a pair of Raman lasers. In recent years, this synthetic spin-orbit coupling has received tremendous attention, as it leads to a variety of novel quantum phenomena in precisely controllable cold atom systems. In this thesis, we first present a comprehensive analysis of one-, two- and many- particle physics of harmonically trapped atoms with spin-orbit coupling, followed by the study of "novel spin-orbit coupling" in two different systems: (1) cold atom spinor mixtures and (2) cold atoms in an optical cavity. In the first system, we consider a spinor mixture consisting of two species of cold atoms, where the spin-orbit coupling can be transmitted from one species to the other, and we discuss novel topological properties and the supersolid stripe phase in this mixture. In the second system, we consider the coupling among three parts: the cavity photon field, the atomic internal hyperfine states, and the atomic external center-of-mass motion, and we discuss how this coupling affects familiar quantum optical phenomena, such as Rabi oscillation and Dicke superradiance phase transition. Our novel systems contribute new and practical platforms for the research field of synthetic spin-orbit coupling in cold atoms.

Chuanzhou Zhu, Lin Dong, Han Pu

Ryan Barnett, G. R. Boyd, Victor M. Galitski

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.

Rytis Juršėnas, Julius Ruseckas, Gediminas Juzeliūnas +1 more

Tudor D. Stanescu, Victor M. Galitski