Oscillation-Induced Frequency Generation in 1D Quantum Droplets under Harmonic-Gaussian Confinements

TL;DR

This paper investigates how Gaussian potentials influence oscillation frequencies of one-dimensional quantum droplets, revealing controllable frequency tuning and complex nonlinear dynamics through analytical and numerical methods.

Contribution

It introduces a combined variational and numerical approach to analyze frequency control in quantum droplets under Gaussian-modified harmonic confinement, highlighting new mechanisms for oscillation tuning.

Findings

Gaussian potential amplitude affects oscillation frequency.

Time-dependent Gaussian induces nonlinear frequency mixing.

Wigner analysis reveals hidden phase dynamics.

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.