Relaxation and hysteresis near Shapiro resonances in a driven spinor condensate

TL;DR

This paper investigates the dynamics of a driven spin-1 Bose-Einstein condensate near Shapiro resonances, revealing relaxation to phase-locked states, the role of dissipation, and hysteresis effects, drawing parallels with superconducting Josephson junctions.

Contribution

It introduces a phenomenological model for the dissipative dynamics of driven spinor BECs and demonstrates hysteresis phenomena near Shapiro resonances.

Findings

Observation of relaxation to unstable asymptotic states with drive.

Identification of phase-locked stationary states analogous to superconducting junctions.

Demonstration of hysteresis when sweeping across Shapiro resonances.

Abstract

We study the coherent and dissipative aspects of a driven spin-1 Bose-Einstein condensate (BEC) when the Zeeman energy is modulated around a static bias value. Resonances appear when the bias energy matches an integer number of modulation quanta. They constitute the atomic counterpart of Shapiro resonances observed in microwave-driven superconducting Josephson junctions. The population dynamics near each resonance corresponds to slow and non-linear secular oscillations on top of a rapid `micromotion'. At long times and in a narrow window of modulation frequencies around each resonance, we observe a relaxation to asymptotic states that are unstable without drive. These stationary states correspond to phase-locked solutions of the Josephson equations generalized to include dissipation, and are analogous to the stationary states of driven superconducting junctions. We find that dissipation is essential to understand this long-time behavior, and we propose a phenomenological model to explain quantitatively the experimental results. Finally, we demonstrate hysteresis in the asymptotic state of the driven spinor BEC when sweeping the modulation frequency across a Shapiro resonance.