Oscillation-Induced Frequency Generation in 1D Quantum Droplets under Harmonic-Gaussian Confinements
Abstract
We explore the dynamical behavior of one-dimensional quantum droplets (QDs) governed by the extended Gross-Pitaevskii equation, under harmonic confinement supplemented by a static or time-dependent Gaussian spike (Gs) potential. Employing both variational analytical techniques and numerical simulations, we investigate the evolution of the root-mean-square (RMS) size, excitation spectrum, and phase-space dynamics of QDs. Our study reveals that while the harmonic trap sets the primary confinement, the Gs potential enables precise frequency tuning and control over droplet oscillations. A static Gs amplitude modifies the fundamental oscillation frequency depending on its sign, while a time-modulated Gs induces nonlinear dynamics, including higher harmonics and frequency mixing. Our analysis reveals that the resulting frequency spectrum is strongly influenced by inter- and intra-species interactions as well as by the parameters of the external trap. Notably, we establish a relationship between the frequency shift and the amplitude of the Gaussian spike. Wigner phase-space analysis further uncovers coherent rotational behavior, offering insights into hidden phase dynamics not apparent in real-space density profiles.
Keywords
Cite
@article{arxiv.2507.05902,
title = {Oscillation-Induced Frequency Generation in 1D Quantum Droplets under Harmonic-Gaussian Confinements},
author = {Jagnyaseni Jogania and Saurab Das and Ajay Nath and Jayanta Bera},
journal= {arXiv preprint arXiv:2507.05902},
year = {2025}
}