Pattern formation in ring condensates subjected to bichromatic driving

TL;DR

This paper explores how bichromatic periodic modulation of interaction strength in ring condensates can induce and control complex nonlinear density patterns, with analytical, numerical, and reduced-model analyses demonstrating precise mode selection and pattern formation.

Contribution

It provides an analytical stability analysis using a biharmonic Mathieu equation, combined with numerical simulations and a reduced five-mode model, to understand pattern formation under bichromatic driving.

Findings

Identification of instability regions via Floquet spectrum analysis

Control over excited modes through driving parameters

Agreement between analytical, numerical, and reduced-model results

Abstract

We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is analytically derived through a suitable biharmonic variant of the Mathieu equation and computing the associated Floquet spectrum. It reveals the complex interplay between the driving parameters, i.e., amplitude, frequencies, and the so-called frequencies' mixing angle, which dictate the instability onset and the selective enhancement of higher-order resonance tongues, thus offering precise control over the excited modes. These results are in agreement with time-dependent mean-field simulations evidencing the emergence of density wave modulations of specific momenta, while enabling a deeper understanding of the nonlinear stage of the relevant instability. Further insights on the ensuing unstable nonlinear dynamics are provided through a reduced {five-mode} model which captures the instability onset, the oscillatory behavior of the mode populations and the phase-space dynamics, in agreement with the mean-field predictions. Our study highlights the versatility of bichromatic driving to generate and control complex nonlinear patterns that are within reach in present day ultracold atom experiments.