Observation of two sound modes in a binary superfluid gas

We study the propagation of sound waves in a binary superfluid gas with two symmetric components. The binary superfluid is constituted using a Bose-Einstein condensate of $^{23}\mathrm{Na}$ in an equal mixture of two hyperfine ground states. Sound waves are excited in the condensate by applying a local spin-dependent perturbation with a focused laser beam. We identify two distinct sound modes, referred to as density sound and spin sound, where the densities of the two spin components oscillate in phase and out of phase, respectively. The observed sound propagation is explained well by the two-fluid hydrodynamics of the binary superfluid. The ratio of the two sound speeds is precisely determined from a timescale analysis of the sound wave propagation, without the need of absolute density calibration, and we find it in quantitatively good agreement with the known interaction properties of the binary system.