 Solution

Sound propagation. In the 1997 experiment, a focused laser beam abruptly modified the trapping potential of a dilute condensate, producing a local excitation. A rapid sequence of nondestructive phase-contrast imaging measurements followed the resulting density motion. Measuring propagation speed at different densities tested the sound-like collective excitation spectrum, rather than individual free-particle flight.^[ref] For a weakly interacting uniform condensate, the Bogoliubov spectrum isDensity dependence and trapped-geometry averaging matter when comparing a measured pulse speed with this local uniform formula. A strictly ideal gas would have no nonzero interaction-supported sound speed.

Moving-obstacle dissipation. In the 1999 experiment, a blue-detuned focused beam repelled atoms and acted as an obstacle swept through a sodium condensate. Heating was inferred from the condensate fraction after stirring and re-equilibration. The heating rose markedly near $1.6\mathrm{mm}{\mathrm{s}}^{-1}$, below the quoted peak sound speed $6.2\mathrm{mm}{\mathrm{s}}^{-1}$.^[ref] Landau's criterion $v_L={\inf }_pϵ(p)/p$ motivates a dissipation threshold, but density variation, flow acceleration around the obstacle and vortex nucleation make the observed threshold different from simply substituting the peak sound speed. Together these experiments probe a collective excitation spectrum and the onset of dissipative flow; condensation alone is not a complete demonstration of superfluidity.