Faraday waves in BEC with engineering three-body interactions

TL;DR

This paper investigates how periodic modulations of two- and three-body interactions in Bose-Einstein condensates induce Faraday waves, offering a new way to control and measure three-body interaction parameters.

Contribution

It introduces models of time-dependent three-body interactions with quadratic and quartic dependence on the scattering length, and demonstrates their role in generating and tuning Faraday waves.

Findings

Faraday waves depend on modulation frequency, amplitude, and background scattering length.

Modulation amplitude can be used to estimate three-body interaction parameters.

Numerical simulations confirm theoretical predictions of wave formation and dependence.

Abstract

We consider Bose-Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length $a_s$, are studied. It is shown that parametric instabilities in the condensate leads to the generation of Faraday waves (FW), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of $a_s$. In an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also through the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross-Pitaevskii equation.