Two cold atoms in a time-dependent harmonic trap in one dimension

We analyze the dynamics of two atoms with a short‐ranged pair interaction in a one‐dimensional harmonic trap with time‐dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non‐interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occurs we find that the interaction can significantly reduce the rate of energy increase. The implications for applications of our findings to cool or heat the system are also discussed. This paper studies a two‐body problem with a short‐range interaction potential in a time‐dependent one‐dimensional trap. The study focuses on the time dynamics of this system in between the limiting cases of zero and infinitely strong interactions, for which the problem is solvable. It is shown that for some parameters the interaction changes the dynamics noticably and has to be taken into account to describe some modern experimental setups.