Measurement of the spin-density wave propagation speed in a spinor Bose-Einstein condensate

We experimentally measure the propagation speed of spin-density waves in a spin-1 antiferromagnetic spinor Bose-Einstein condensate of $^{23}$Na atoms. Spin-density waves are generated by perturbing the condensate with a focused laser beam, whose frequency is tuned between the $D_1$ and $D_2$ transitions of the Na atom to generate a spin-dependent potential, which is attractive for the $m=1$ spin component and repulsive for the $m=-1$ spin component. By abruptly turning off the laser beam placed at the center of the condensate, we create a magnetization pulse wave that is a composite of a density dip of the $m=-1$ component and a density bump of $m=1$, and we measure its propagation speed in the condensate. The measured propagation speed is compared with that of mass-density wave which is excited in a similar manner with a spin-independent 532 nm laser beam. We find that the propagation speed of spin-density wave is about 20% of that of mass-density wave, showing that the spin-dependent interaction coefficient for the Na atom in the $F=1$ state is twice larger than the conventional value from [PRL 99, 070403 (2007)].