# Two- and three-body problem with Floquet-driven zero-range interactions

## TL;DR

This paper investigates how sinusoidal driving of scattering length affects two- and three-body quantum interactions, revealing resonances that can be tuned without heating, with implications for controlling few-body quantum systems.

## Contribution

It introduces a detailed analysis of Floquet-driven zero-range interactions, identifying conditions for resonant enhancement and resonance nature change, and explores their impact on three-body dynamics.

## Key findings

- Resonant enhancement of scattering amplitude at specific drive parameters.
- Existence of curves where the effective scattering length diverges without heating.
- Floquet driving allows tuning of three-body and inelasticity parameters.

## Abstract

We study the two-body scattering problem in the zero-range approximation with a sinusoidally driven scattering length and calculate the relation between the mean value and amplitude of the drive for which the effective scattering amplitude is resonantly enhanced. In this manner we arrive at a family of curves along which the effective scattering length diverges but the nature of the corresponding Floquet-induced resonance changes from narrow to wide. Remarkably, on these curves the driving does not induce heating. In order to study the effect of these resonances on the three-body problem we consider one light and two heavy particles with driven heavy-light interaction in the Born-Oppenheimer approximation and find that the Floquet driving can be used to tune the three-body and inelasticity parameters.