Trapping of particles by lasers: the quantum Kapitza pendulum

It is demonstrated that a bound rapidly oscillating potential typically traps particles even if its time average vanishes. In particular, it is shown that in one dimension there is always a resonance state and its energy and lifetime are calculated from an effective time-independent potential. This is the quantum analogue of the classical Kapitza pendulum. This work may be relevant for the manipulation of cold atoms and for the suppression of photo-ionization by electromagnetic fields.