Difference between revisions of "Spin Orbit Coupling"
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The experimental realization is published here <ref>PRL 121, 150401 (2018)</ref>. 2 orthogonal beams are sent back and forth to create a square lattice: | The experimental realization is published here <ref>PRL 121, 150401 (2018)</ref>. 2 orthogonal beams are sent back and forth to create a square lattice: | ||
<math>V_{latt}=V_0\cos^2(k_0 x)+V_0\sin^2(k_0 y)</math>. The total Hamiltonian of the system reads as <math>\hat H = \frac{p^2}{2m}+V_{latt}+\Omega_{R}(x,y)+\frac{\delta}{2}\sigma_z</math>, 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. | <math>V_{latt}=V_0\cos^2(k_0 x)+V_0\sin^2(k_0 y)</math>. The total Hamiltonian of the system reads as <math>\hat H = \frac{p^2}{2m}+V_{latt}+\Omega_{R}(x,y)+\frac{\delta}{2}\sigma_z</math>, 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. | ||
| + | |||
| + | # They measure the lifetime of the BEC in 2D SOC, they find it to be 1-3s depending on the lattice depth. | ||
| + | # 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 <math>\sqrt{\langle M_0 \rangle}</math> as a function of Ω, where they find a turning point. | ||
<ref> </ref>. | <ref> </ref>. | ||
<math></math> | <math></math> | ||
Revision as of 15:01, 3 February 2020
Creation of 2D SOC
Square lattice
The experimental realization is published here [1]. 2 orthogonal beams are sent back and forth to create a square lattice:
. The total Hamiltonian of the system reads as 
, 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.
- They measure the lifetime of the BEC in 2D SOC, they find it to be 1-3s depending on the lattice depth.
- 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
as a function of Ω, where they find a turning point.
[2].
