Adiabaticity in a time-dependent trap: a universal limit for the loss by touching the continuum

TL;DR

This paper investigates the universal limit of the probability for a bound state to remain in a time-dependent trap as it approaches and leaves the continuum threshold, with implications for cold atoms and wave guides.

Contribution

It introduces a universal limit for the survival probability of a bound state in a slowly varying trap near the continuum threshold, linking it to the approach dynamics.

Findings

The survival probability tends to a universal limit in the adiabatic regime.

The limit depends only on how the bound state approaches and leaves the threshold.

Numerical analysis confirms the universality across various trapping potentials.

Abstract

We consider a time dependent trap externally manipulated in such a way that one of its bound states is brought into an instant contact with the continuum threshold, and then down again. It is shown that, in the limit of slow evolution, the probability to remain in the bound state, $P^{stay}$ tends to a universal limit, and is determined only by the manner in which the adiabatic bound state approaches and leaves the threshold. The task of evaluating the $P^{stay}$ in the adiabatic limit can be reduced to studying the loss from a zero range well, and is performed numerically. Various types of trapping potentials are considered. Applications of the theory to cold atoms in traps, and to propagation of traversal modes in tapered wave guides are proposed.