Wavepackets falling under a mirror

Abstract

We depict and analyze a new effect for wavepackets falling freely under a barrier or well. The effect appears for wavepackets whose initial spread is smaller than the combination $\text{ds}\sqrt{\frac{l_g^3}{|z_0|}}$, between the gravitational length scale $\text{ds}{l}_g=\frac{1}{(2m^{2}g{)}^{1/3}}$ and the initial location of the packet $z_0$. It consists of a diffractive structure that is generated by the falling and spreading wavepacket and the waves reflected from the obstacle. The effect is enhanced when the Gross-Pitaevskii interaction for positive scattering length is included. The theoretical analysis reproduces the essential features of the effect. Experiments emanating from the findings are proposed.

Comments: Latex format, 23 pages, 11 eps figures, Airy packet treatment added