Refractive index for matter waves in ultracold gases

An analytical expression for the refractive index of atomic and molecular matter waves in ultracold,oases is obtained. Asymptotic formulas for the refractive index are derived for high and low projectile velocities, and intermediate velocities are investigated with the eikonal approximation. The real and imaginary parts of the matter wave refractive index are expressed via the complex scattering length of elastic and superelastic collisions. It is shown that superelastic collisions dramatically influence the low-energy behavior of the refractive index. A discussion is given of proposed measurements of the real and imaginary parts of the scattering length using the interferometry of slow de Broglie waves.