Collective Oscillations of Bose-Einstein Condensates in a Synthetic Magnetic Field

TL;DR

This paper investigates the collective oscillations of spin-orbit-coupled Bose-Einstein condensates in synthetic magnetic fields, revealing complex mode couplings and sensitivities that could enhance quantum sensing techniques.

Contribution

It introduces a combined numerical and analytical study of quadrupole modes in spin-orbit-coupled BECs under synthetic magnetic fields, highlighting mode couplings and their dependence on system parameters.

Findings

Coupling of scissors mode with quadrupole modes causes beating effects.

Coupled $xz$ and $yz$ scissors modes produce Lissajous-like patterns.

Anisotropic interactions and magnetic field orientation affect oscillation characteristics.

Abstract

We study the collective oscillations of spin-orbit-coupled Bose-Einstein condensates in the presence of position-dependent detuning. Specifically, we explore the quadrupole modes of the system using both numerical and analytical approaches based on the Gross-Pitaevskii equation and hydrodynamic theory. Due to spin-orbit coupling and the synthetic magnetic field, {the $xy$ scissors mode couples with a superposition of the three diagonal quadrupole modes ($x^2$, $y^2$, and $z^2$),} resulting in the characteristic beating effect. {The remaining two scissors modes, $xz$ and $yz$, are coupled, giving rise to a Lissajous-like pattern that is highly sensitive to the excitation method and orientation of the synthetic magnetic field.} Furthermore, we find that anisotropic interactions as well as the direction of the synthetic magnetic field, can significantly influence the oscillation amplitude and frequency of the quadrupole modes. These findings highlight the potential of Bose-Einstein condensates under synthetic magnetic fields for quantum sensing applications, such as magnetic field {gradient} measurements, and provide a promising foundation for future experimental research and technological development.