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

• Published in: Physical review research Vol. 3; no. 4; p. 043090
• Main Authors: Imaeda, Yuya, Fujimoto, Kazuya, Kawaguchi, Yuki
• Format: Journal Article
• Language: English
• Published: American Physical Society 29.10.2021
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.3.043090

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 [B. Evrard et al., Phys. Rev. A 100, 023604 (2019)2469-992610.1103/PhysRevA.100.023604] 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 wave function 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 wave numbers can be excited. This kind of nonuniform 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.