Fig. 6

GPE simulated SDM at various Ω_F and the extracted SDM damping compared with experiment. a, b GPE simulations of the 1D momentum-space density distributions of the two bare spin components as a function of t_hold for the SDM at Ω_F = 0 and Ω_F = 1.3 E_r, respectively. The 1D momentum density ρ_σ(k_y) is obtained by integrating the 3D momentum density along k_x and k_z, i.e., \(\rho _\sigma \left( {k_y} \right) = {\int} {\kern 1pt} \rho _\sigma \left( {k_x,k_y,k_z} \right)dk_xdk_z\). Then, these integrated 1D atomic momentum densities for sequential hold times (t_hold) are combined to show the atomic density in momentum space along the SOC direction versus t_hold. c GPE simulations of the SDM damping versus t_hold at various Ω_F. The violet lines are the ħk_spin (defined as the difference between the CoM momenta of the two spin components) as a function of t_hold for various Ω_F. The CoM momentum (ħk_↑,↓) of each bare spin component (at a given t_hold) is calculated by taking a density-weighted average of the corresponding 1D momentum density distributions such as those shown in a, b. The black lines are damped sinusoidal fits for the calculated ħk_spin to extract the corresponding SDM damping (1/Q) which is shown in d along with the experimental data reproduced from Fig. 3f. e Replotting of d with 1/Q shown in logarithmic scale. f–j In situ (real space) atomic densities calculated from GPE simulations. f Initial in situ 2D density at Ω = Ω_I (right before applying spin-dependent electric fields E_σ). g–j In situ 2D density at t_hold = 1.5 ms (after the application of E_σ) for Ω_F = 0, 0.4 E_r, 0.9 E_r, and 1.3 E_r, respectively. For f–j, the density is designated by brightness and the bare spin polarization by colors (red: ↓, blue: ↑, white: equal spin populations). The 2D densities ρ_σ(x, y) in f–j are obtained by integrating the 3D atomic density along z, i.e., \(\rho _\sigma (x,y) = {\int} {\kern 1pt} \rho _\sigma (x,y,z)dz\). In this figure, the simulations used the following parameters representative of our experiment: Ω_I = 5.2 E_r, δ_R = 0, N_c = 1.6 × 10⁴, ω_z = 2π × 37 Hz, ω_x = ω_y = 2π × 205 Hz, t_E = 1.0 ms