# Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: a relay-race mechanism

## TL;DR

This paper investigates how weak dipole-dipole interactions induce a long-time tail in the nonlinear ac absorption of localized systems, revealing a relay-race mechanism of multi-generation Rabi oscillations.

## Contribution

It introduces a novel relay-race mechanism explaining long-time oscillations in ac absorption due to interaction-induced second-generation Rabi oscillations.

## Key findings

- Long-time oscillations occur at frequencies much lower than the Rabi frequency.
- Second-generation Rabi oscillations are driven by fields generated during initial Rabi cycles.
- Non-diagonal dipole-dipole interactions facilitate the formation of these long-time tails.

## Abstract

In conventional solid-state electron systems with localized states the ac absorption is linear since the inelastic widths of the energy levels exceeds the drive amplitude. The situation is different in the systems of cold atoms in which phonons are absent. Then even a weak drive leads to saturation of the ac absorption within resonant pairs, so that the population of levels oscillates with the Rabi frequency. We demonstrate that, in the presence of weak dipole-dipole interactions, the response of the system acquires a long-time component which oscillates with frequency much smaller than the Rabi frequency. The underlying mechanism of this long-time behavior is that the fields created in the course of the Rabi oscillations serve as resonant drive for the second-generation Rabi oscillations in pairs with level spacings close to the Rabi frequency. The frequency of the second-generation oscillations is of the order of interaction strength. As these oscillations develop, they can initiate the next-generation Rabi oscillations, and so on. Formation of the second-generation oscillations is facilitated by the non-diagonal component of the dipole-dipole interaction tensor.