Figure 1

Examples of domain formation in the density of one hyperfine component for (a) a uniform system with ${\tau }_Q=63$ ms and $N={10}^5$ atoms and (b) a trapped system with similar parameters. The red dashed vertical lines indicate the time where $\Omega (t)={\Omega }_{\mathrm{cr}}$, while the solid green vertical lines indicate the end of the quench $\Omega (t)=0$. The density of the second component (not shown) is complementary to the density of the first component.Reuse & Permissions

Figure 2

Mean number of domains formed $N_d$ as a function of the quench time ${\tau }_Q$ for a BEC in a ring trap. Blue circles are for a spatially homogeneous quench, and the red diamonds are for a spatially inhomogeneous quench simulating a harmonically trapped system. The open symbols average over 100 trajectories, while the closed symbols average over 1000 trajectories and are used for fitting the scaling exponent $n$. The error bars indicate the standard error. The linear fits to the data yield a scaling exponent $n=0.341\pm 0.006$ for the homogeneous quench, and $n=0.497\pm 0.015$ for the inhomogeneous quench. Data for the inhomogeneous quench are shifted upwards by a multiplicative factor for clarity. The top right inset shows the same data on a linear scale. The bottom left inset shows the time evolution of the average number of domains for quenches with ${\tau }_Q\le 2$ ms, for which the mean number of domains is still decreasing at $t=600\mathrm{ms}$.Reuse & Permissions

Figure 3

Mean number of domains formed $N_d$ versus quench time ${\tau }_Q$ for a harmonically trapped BEC. The different colors (symbols) correspond to different domain-counting threshold densities $\gamma ={\rho }_{\mathrm{cut}}/\rho (0)$ (see text). Filled symbols represent ensembles of 1000 trajectories used for estimating the scaling exponent $n$. The left inset shows the value of the exponent $n$ as a function of the density threshold $\gamma$. The dashed (dot-dashed) line indicates the value of $n$ obtained from a simulation of a homogeneous (inhomogeneous) coupling quench in a ring trap as in Fig. 2 (see text). The shaded region in the right inset illustrates the counting region in the BEC density. The flattening of the domain number at long quench times for $\gamma =0.1$ and $\gamma =0.2$ is due to the unavoidable miscounting of density fluctuations as domains.Reuse & Permissions