Scaling characteristics of a discontinuous quantum phase transition in a spinor Bose-Einstein condensate

Driving a system across a symmetry-breaking quantum phase transition can lead to the production of topological defects or domain walls. Across a wide range of physical systems, these exhibit universal scaling laws described by the Kibble-Zurek mechanism when the transition is second order. We propose a spinor Bose-Einstein condensate as a testbed system where critical scaling behavior in a first-order quantum phase transition can be understood from generic properties. Generalizing the Kibble-Zurek description, we derive critical exponents describing both the short-time onset of decay of the metastable state as well as the number of domains as the condensate is driven across the discontinuous quantum critical point between the broken-axisymmetry and ferromagnetic phases. We show that numerical mean-field simulations give excellent agreement with predictions. Together our results suggest that the spinor Bose-Einstein condensate provides a paradigm for studying the decay of persisting states in experimentally accessible systems.