Trapping of quantum particles and light beams by switchable potential wells

We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as scanning tunneling microscopy or photo-switchable quantum dots. The same models, based on the linear Schrödinger equation with time-dependent trapping potentials, apply to the description of optical planar systems designed for the switching of trapped light beams. The analysis is carried out in the analytical form, using exact solutions of the Schrödinger equation. The first dynamical problem considered in this work is the retention of a particle released from a trap which was suddenly turned off, while another local trap was switched on at a distance-immediately or with a delay. In this case, we demonstrate that the maximum of the retention rate is achieved at a specific finite value of the strength of the new trap, and at a finite value of the temporal delay, depending on the distance between the two traps. Another problem is retrapping of the bound particle when the addition of the second trap transforms the single-well setting into a double-well potential (DWP). In that case, we find probabilities for the retrapping into the ground or first excited state of the DWP. We also analyze effects entailed by the application of a kick to a bound particle, the most interesting one being a kick-induced transition between the DWP's ground and excited states. In the latter case, the largest transition probability is achieved at a particular strength of the kick.