  According to the famous Kibble-Zurek mechanism (KZM), the universality of
spontaneous defect generation in continuous phase transitions (CPTs) can be
understood by the critical slowing down. In most CPTs of atomic Bose-Einstein
condensates (BECs), the universality of spontaneous defect generations has been
explained by the divergent relaxation time associated with the nontrivial
gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge
fields, their spontaneous superfluidity breakdown is resulted from the
divergent correlation length associated with the zero Landau critical velocity.
Here, by considering an atomic BEC ladder subjected to a synthetic magnetic
field, we reveal that the spontaneous superfluidity breakdown obeys the KZM.
The Kibble-Zurek scalings are derived from the Landau critical velocity which
determines the correlation length. In further, the critical exponents are
numerically extracted from the critical spatial-temporal dynamics of the
bifurcation delay and the spontaneous vortex generation. Our study provides a
general way to explore and understand the spontaneous superfluidity breakdown
in CPTs from a single-well dispersion to a double-well one, such as, BECs in
synthetic gauge fields, spin-orbit coupled BECs, and BECs in shaken optical
lattices.
