Spin Orbit Coupling

Creation of 2D SOC

Square lattice

The experimental realization is published here . 2 orthogonal beams are sent back and forth to create a square lattice: $V_{latt}=V_0\cos^2(k_0 x)+V_0\sin^2(k_0 y)$. The total Hamiltonian of the system reads as $\hat H = \frac{p^2}{2m}+V_{latt}+\Omega_{R}(x,y)+\frac{\delta}{2}\sigma_z$, where δ is the two-photon detuning. By tuning the phase between two beams δφ it is possible to transition from 1D to 2D SOC. For phases δφ=0, π, they demonsrate 1D SOC. For phases δφ=±π/2 they have symmetrical 2D SOC. .