Spin-Orbit Coupling and Berry Phase with Ultracold Atoms in 2D Optical Lattices

Abstract

We show how spin-orbit coupling and Berry phase can appear in two-dimensional optical lattices by coupling atoms' internal degrees of freedom to radiation. The Rashba Hamiltonian, a standard description of spin-orbit coupling for two-dimensional electrons, is obtained for the atoms under certain circumstances. We discuss the possibility of observing associated phenomena, such as the anomalous Hall and spin Hall effects, with cold atoms in optical lattices.

Biaxial spin-nematic phase of two-dimensional disordered rotor models andS=1bosons in optical lattices

“…Building on previous work for S = 1/2 particles 24 , we deduce that atoms with S = 1 experience an external potential of the form V αβ (r) = V (r)δ αβ + B(r) ·Ŝ αβ + N ij (r)Ĝ ijαβ , (A1) with α, β = {−1, 0, 1}. In Eq.…”

“…In Eq. A1, the scalar potential V (r) is proportional to the light intensity, the vector field B(r) is proportional to the electromagnetic spin 24 and couples to the total atomic angular momentum operatorŜ, and the secondrank tensor N ij (r) is proportional to the light nematicity 23 and couples to the quadrupole moment operatorĜ ij : V (r) = b 0 E * (r) · E(r) B(r) = −ib 1 E * (r) × E(r) N ij (r) = b 2 1 2 (E * i (r)E j (r) + E * j (r)E i (r)) − 1 3 E * (r) · E(r)δ ij Ŝ αβ = 1, α|Ŝ|1, β…”

“…The spin dependence of the sinusoidal potential can be achieved by tuning the laser frequency close to the hyperfine splitting (but far away from the fine structure splitting) of the atoms 19,20,21,22,23,24 . In appendix A, we propose a method to obtain a spin-dependent lattice potential with V 1 = V −1 = V 0 .…”

Bragg scattering and the spin structure factor of two-component atomic gases

“…If no external field is present which breaks the rotational symmetry, the Zeeman sublevels of both the ground and the excited states are degenerate, so that the different tensorial components of the light and matter fields can be separated, as originally done in [11]. For our F g = 1/2 case, the effective Hamiltonian has then the form [12]:…”

Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom

“…For real nearest neighbor hoppings, H I has to be taken proportional to the normalization of the raising operator F + = F x + iF y for fixed total angular momentum F such that I (σ ) = I (N − σ )σ for N = 2F + 1. Note that this is exactly the coupling induced by Raman lasers in the far-detuned regime, as shown in [21][22][23][24] and considered in [20] to simulate synthetic edge states with a synthetic dimension. It is obvious that the last term of Eq.…”