  The Kibble-Zurek mechanism provides a unified theory to describe the
universal scaling laws in the dynamics when a system is driven through a
second-order quantum phase transition. However, for first-order quantum phase
transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we
experimentally demonstrate and theoretically analyze a power-law scaling in the
dynamics of a spin-1 condensate across a first-order quantum phase transition
when a system is slowly driven from a polar phase to an antiferromagnetic
phase. We show that this power-law scaling can be described by a generalized
Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin
population, we show the power-law scaling of the temporal onset of spin
excitations with respect to the quench rate, which agrees well with our
numerical simulation results. Our results open the door for further exploring
the generalized Kibble-Zurek mechanism to understand the dynamics across
first-order quantum phase transitions.
