Two Cold Atoms in a Time-Dependent Harmonic Trap in One Dimension

TL;DR

This paper investigates the dynamics of two interacting atoms in a one-dimensional harmonic trap with a time-varying frequency, revealing how interactions influence energy behavior under sudden and periodic changes.

Contribution

It provides a detailed analysis of two-atom dynamics in a time-dependent trap, highlighting differences between interacting and non-interacting cases, especially near parametric resonance.

Findings

Interacting and non-interacting systems behave similarly under sudden frequency changes.

Interactions can suppress energy growth near parametric resonance.

Results have implications for controlling system temperature via trap modulation.

Abstract

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 dicussed.