Fig. 2

Comparison between classical and quantum dynamics. For various initial tilting angles θ = 0.2π, 0.3π, 0.4π, and 0.5π, we plot the experimental data for the four lowest spin populations, \(p_{m_S}\), and compare them with simulations. a Comparison with GDTWA simulations (solid lines) on a 7 × 3 × 7 cluster allowing the quadratic Zeeman field B_Q to be the only fitting parameter [here: B_Q = −3.0 Hz]. b Comparison with the classical mean-field results (dotted lines) [here: B_Q = 1.1 Hz]. The two plots on the right show quantitative comparison between data and simulations for θ = 0.3π, 0.4π, and 0.5π with a reduced χ² criteria, for different values of B_Q. We excluded the θ = 0.2π case here since it shows no significant dynamics. The best agreement with GDTWA simulations is a factor of three better than with classical simulations. The deviation with the classical simulations is most obvious at short times, and clearly increases with increasing θ. The arrows indicate the expected equilibrium population maximizing entropy, for each angle. The orange solid line in panel (a) (for θ = 0.5π) is the result of the perturbative expansion, Eq. (3). The shaded area indicates the range of variation of the populations for evolutions with ΔB_Q = ±0.3 Hz and uncertainties in the tilting angles with θ = (0.2 ± 0.018π), (0.3 ± 0.012)π, (0.4 ± 0.012)π, and (0.5 ± 0.01)π (estimated from the experiment). Error bars correspond to statistical standard deviations