Coherent spin-mixing dynamics in thermal ${}^{87}\mathrm{Rb}$ spin-1 and spin-2 gases

We study the nonequilibrium coherent spin-mixing dynamics in ferromagnetic spin-1 and antiferromagnetic spin-2 thermal gases of ultracold ${}^{87}\mathrm{Rb}$ atoms. Long-lasting spin population oscillations with magnetic-field-dependent resonances are observed in both cases. Our observations are well reproduced by Boltzmann equations of the Wigner distribution function. Compared to the equation of motion of spinor Bose-Einstein condensates, the only difference here is a factor-of-2 increase in the spin-dependent interaction, which is confirmed directly in the spin-2 case by measuring the relation between the oscillation amplitude and the sample's density.

Figure 1

Coherent spin population oscillation of ${}^{87}\mathrm{Rb}$ spin-1 normal gas and its dependence on magnetic field. (a, b) Exemplary temporal evolution of ${\rho }_0$ at magnetic fields of 0.1 and 0.18 G, respectively. Red solid curves are to guide the eye. (c, d) The magnetic field dependence of the oscillation period $(\circ )$ and amplitude $(\diamond )$ with a resonant feature located near 0.14 G. Error bars here are from fitting of the oscillations. Blue solid curves are fittings with Eq. (4).

Figure 2

Spinor dynamics and its dependence on magnetic field for the ${}^{87}\mathrm{Rb}$ spin-2 normal gas. (a, b) Evolutions of ${\rho }_0\left(▴\right),{\rho }_1(•)$, ${\rho }_{-1}(▿)$, ${\rho }_2\left(\blacksquare \right)$, and ${\rho }_{-2}(⊲)$ at 0.1 and 0.45 G, respectively. Red solid curves in (a) and (b) are fits to the damped sinusoidal function for ${\rho }_0,{\rho }_1$, and ${\rho }_2$ only. The measured periods $(\circ )$ and amplitudes $(\diamond )$ of ${\rho }_0$ vs magnetic fields are summarized in (c) and (d). The accompanying error bars are fitting errors. The blue solid curves here are obtained from numerical calculations with Eq. (4) and the black dashed curve is a plot of $\pi /q$. The insets of (c) and (d) show dependence of the oscillation periods (up triangle) and amplitudes (squares), respectively, on densities at 0.6 G (see text).