Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

TL;DR

This paper investigates the resonant spin-wave growth in a driven spin-1 Bose-Einstein condensate, revealing non-uniform excitations and nonlinear effects beyond previous single-mode approximations.

Contribution

It extends the analysis of Shapiro resonances in spinor BECs beyond the single-mode approximation using Floquet theory and numerical simulations.

Findings

Spin waves with finite wavenumbers can be excited at resonance.

Nonlinear effects cause growth of nonresonant hydrodynamic variables.

Resonant dynamics involve non-uniform, spatially varying excitations.

Abstract

We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein condensate periodically driven by a quadratic Zeeman coupling. This phenomenon is closely related to the Shapiro steps in superconducting Josephson junctions, and the previous experimental work [Evrard $et al.,$ Phys. Rev. A 100, 023604 (2019)] for a spin-1 bosonic system observed the resonant dynamics and then called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii equation, we study the Shapiro resonance beyond the single-mode approximation used in the previous work, which assumes that all components of the spinor wavefunction have the same spatial configuration. Considering resonant dynamics starting from a polar state, we analytically calculate the Floquet-Lyapunov exponents featuring an onset of the resonance under a linear analysis and find that spin waves with finite wavenumbers can be excited. This kind of non-uniform excitation cannot be described by the single-mode approximation. Furthermore, to study the long-time resonant dynamics beyond the linear analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii equation, finding that the nonresonant hydrodynamic variables also grow at wavelengths of even multiples of the resonant one due to the nonlinear effect.