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Register a new userSU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms
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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 non-trivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an exact 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.
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We consider the simulation of non-abelian gauge potentials in ultracold atom systems with atom-field interaction in the $Lambda$ configuration where two internal states of an atom are coupled to a third common one with a detuning. We find the simulated non-abelian gauge potentials can have the same structures as those simulated in the tripod configuration if we parameterize Rabi frequencies properly, which means we can design spin-orbit coupling simulation schemes based on those proposed in the tripod configuration. We show the simulated spin-orbit coupling in the $Lambda$ configuration can only be of a form similar to $p_{x}sigma_{y}$ even when the Rabi frequencies are not much smaller than the detuning.
We theoretically explore atomic Bose-Einstein condensates (BECs) subject to position-dependent spin-orbit coupling (SOC). This SOC can be produced by cyclically laser coupling four internal atomic ground (or metastable) states in an environment where the detuning from resonance depends on position. The resulting spin-orbit coupled BEC phase-separates into domains, each of which contain density modulations - stripes - aligned either along the x or y direction. In each domain, the stripe orientation is determined by the sign of the local detuning. When these stripes have mismatched spatial periods along domain boundaries, non-trivial topological spin textures form at the interface, including skyrmions-like spin vortices and anti-vortices. In contrast to vortices present in conventional rotating BECs, these spin-vortices are stable topological defects that are not present in the corresponding homogenous stripe-phase spin-orbit coupled BECs.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.
Spin-orbit coupling (SOC) is an essential ingredient in topological materials, conventional and quantum-gas based alike.~Engineered spin-orbit coupling in ultracold atom systems --unique in their experimental control and measurement opportunities-- provides a major opportunity to investigate and understand topological phenomena.~Here we experimentally demonstrate and theoretically analyze a technique for controlling SOC in a two component Bose-Einstein condensate using amplitude-modulated Raman coupling.
We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with true spin-orbit coupling, involving spin-changing hoppings.
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