Quasi-bound states in periodically driven scattering
Haggai Landa (LPTMS)
I will discuss the interaction of a cold atom co-trapped with an ion in a Paul trap, a platform which in recent years promises to make possible investigations of ion-neutral interactions in the ultracold regime. The main theoretical and experimental difficulty in this system is due to the time dependence of the ion trap, which is periodically modulated by an AC voltage. We present a general approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians and derive an explicit expansion for scattering problems with mixed cylindrical and spherical symmetry . Using this method we study quasi-bound states of a spherically-symmetric potential in three dimensions subject to an axial driving force. The analysis of the ion-atom system is completed by solving self-consistently the time-dependent wavefunctions of the atom together with the periodic force it exerts on the ion .
 H. Landa, arXiv: 1506.08779
 H. Landa and G. V. Shlyapnikov, in preparation