Echo spectroscopy and atom optics billiards

We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as “echo spectroscopy” Phys. Rev. Lett., 2003;90:0230011]–4]]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results for the stability of eigenstates of an atom-optics billiard of the Bunimovich type, and discuss its behavior under different types of perturbations. Finally, we propose to use special geometrical constructions to make a dephasing free dipole trap.