Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate

We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent -wave scattering lengths is Bohr radii.

Figure 1

(a) Theoretical prediction of the ground-state fractional population ${\rho }_0$ as a function of magnetization $m$ and applied magnetic field $B$, assuming a spin-dependent interaction energy $c=h\times 20.5\mathrm{Hz}$. The thick line lying in the ${\rho }_0=0$ plane indicates the boundary between the ${\rho }_0=0$ and the ${\rho }_0>0$ regions. (b) Measurement.

Figure 2

Period (a) and amplitude (b) of spin oscillations as a function of applied magnetic field, following a sudden change in spin state. Solid lines are predictions from solving Eq. (2). The theoretical prediction of the period diverges at about $27\mu \mathrm{T}$. Shaded regions are $\pm 1$ standard deviation about the mean values (from Monte Carlo simulation, see text.) Inset: Fractional Zeeman population (solid dots) and magnetization (open circles) as a function of time after the spinor condensate is driven to ${\rho }_0=0.5$, $m=0$. $B=6.1\mu \mathrm{T}$. The solid line is a sinusoidal fit.