Universal spatiotemporal dynamics of spontaneous superfluidity breakdown in the presence of synthetic gauge fields

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 results 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. Furthermore, the critical exponents are numerically extracted from the critical spatiotemporal 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.

Figure 1

(a) Schematic diagram for a bosonic ladder in a uniform magnetic field, where $J$ and $K$ are respectively the intra- and interleg tunneling strengthes, $g$ is the interaction strength, and $\varphi$ is the magnetic flux per plaquette. (b) The chiral current $j_c$ versus the ratio $K/J$. There are three typical phases: (I) the vortex phase, (II) the biased ladder phase (BLP), and (III) the Meissner phase. The thickness and length of the arrows denote the current strength, which is normalized to the maximum current for the chosen $K/J$. The two dash-dotted lines label the two critical points between different phases. The dispersion relations $\varepsilon \left(k\right)$ for three typical phases are shown in the insets. The parameters are chosen as $N=5\times {10}^4, L=200, J=1, g\overline{n}/J=0.2$, and $\varphi =\pi /2$.

Figure 2

(a) The Landau critical velocity $v_L$ versus $K/K_c$. Inset: the critical region of the Landau critical velocity. (b) The inverse critical velocity $v_L^{-1}$ versus $\left|\epsilon \right|=\left|K\left(t\right)-K_c\right|/K_c$. The open triangles and circles correspond to the Meissner phase and the biased ladder phase, respectively. Here, to minimize finite-size effects, we choose $L=50000$ and the other parameters are the same as the ones for Fig. 1.

Figure 3

The universal scaling of the averaged bifurcation delay $\overline{b_d}$. The error bars denote the standard deviation. Inset: The chiral current $j_c$ versus $K\left(t\right)/K_c$ for different ${\tau }_Q$. All parameters are chosen the same as the ones for Fig. 1.

Figure 4

The universal scaling of the averaged vortex number $\overline{N_v}$ counted at the time where $\delta j_c=\left|(j_c\left(t\right)-j_c^{\text{max}})/j_c^{\text{max}}\right|=0.005$. The error bars denote the standard deviation. All parameters are chosen the same as the ones for Fig. 1.