  We theoretically investigate a two-dimensional harmonically-trapped gas of
identical atoms with Rashba spin-orbit coupling and no interatomic
interactions. In analogy with the spin Hall effect in uniform space, the gas
exhibits a spin Hall mode. In particular, in response to a displacement of the
center-of-mass of the system, spin-dipole moment oscillations occur. We
determine the properties of these oscillations exactly, and find that their
amplitude strongly depends on the spin-orbit coupling strength and the quantum
statistics of the particles.
