Difference between revisions of "Spin Orbit Coupling"
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===Square lattice=== | ===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: | 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. This Hamiltonian exhibits precise inversion and C4 symmetries. 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 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. | # 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. | ||
| + | # They measure band topology. | ||
<ref> </ref>. | <ref> </ref>. | ||
<math></math> | <math></math> | ||
Revision as of 15:04, 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. This Hamiltonian exhibits precise inversion and C4 symmetries. 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. - They measure band topology.
[2].
