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.

1. They measure the lifetime of the BEC in 2D SOC, they find it to be 1-3s depending on the lattice depth.
2. They measure the stripe and magnetic phases. They build the hystograms for different magnetizations, for the one they have a single peak at M=0 they call it a stripe phase. For the magnetic phase they have two sharp peaks at M=±1. The phase transition point is found as $\sqrt{\langle M_0 \rangle}$ as a function of Ω, where they find a turning point.

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