Rotating Binary Bose-Einstein Condensates and Vortex Clusters in Quantum Droplets

Quantum droplets may form out of a gaseous Bose-Einstein condensate, stabilized by quantum fluctuations beyond mean field. Determining the ground state of a rotating binary condensate, we show that multiple singly quantized vortices may form in these droplets at moderate angular momenta in two dimensions. Droplets carrying these precursors of an Abrikosov lattice remain self-bound for certain timescales after switching off an initial harmonic confinement. Intriguingly, we find evidence of a metastable persistent current in these new types of binary condensates. We discuss how this finding can be used to experimentally generate vortex-carrying quantum droplets.

Figure 1

Time evolution of various rotational ground state densities in a harmonic trap ($V_0=0$) at different rotation frequencies for $N=1000$, $\omega =0.04$, and $K_3=0$ (i.e., no three-body losses). The harmonic trap frequency is linearly decreased in time such that it is zero at $t=100$. See the Supplemental Material [54] for movies of the full time evolution of the densities.

Figure 2

Upper panel: Ground state energy in the rotating frame as a function of rotation frequency for $N=1000$ and $\omega =0.04$, in a harmonic trap ($V_0=0$, light blue) and with a Gaussian added at the center ($V_0=0.2$, dark blue). Both curves are plotted against the energy of their respective nonrotating ground state $E_0$. Lower panel: Angular momentum as a function of rotation frequency for the same parameters. Distinct kinks in the energy correspond to an increase in the number of singly quantized vortices (green numbers) displayed as steps in the angular momentum shown in the lower panel.

Figure 3

Energy as a function of angular momentum for $N=1000$ and $\omega =0.04$, in a harmonic trap ($V_0=0$, light blue) and with a Gaussian added at the trap center ($V_0=0.2$, dark blue), as in Fig. 2. Both curves are plotted against the energy of their respective nonrotating ground state $E_0$.

Figure 4

Phases and superimposed density contours of the time evolution of ground states with zero or one vortex in a harmonic trap with a Gaussian ($V_0=0.2$) for $N=1000$ and $\omega =0.04$. Rows one and three show evolutions without three-body losses $K_3=0$, and rows two and four with $K_3=0.01$. The harmonic trap frequency is linearly decreased in time such that it is zero at $t=100$ while leaving the Gaussian unchanged. See the Supplemental Material [54] for movies of the full time evolution of the densities.