Multiple-quantum-coherence dynamics of spin-1 Bose-Einstein condensate during quantum phase transitions

Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose-Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.