Quantum filaments in dipolar Bose-Einstein condensates

Collapse in dipolar Bose-Einstein condensates may be arrested by quantum fluctuations. Due to the anisotropy of the dipole-dipole interactions, the dipole-driven collapse induced by soft excitations is compensated by the repulsive Lee-Huang-Yang contribution resulting from quantum fluctuations of hard excitations, in a similar mechanism as that recently proposed for Bose-Bose mixtures. The arrested collapse results in self-bound filamentlike droplets, providing an explanation for the intriguing results of recent dysprosium experiments. Arrested instability and droplet formation are general features directly linked to the nature of the dipole-dipole interactions, and should hence play an important role in all future experiments with strongly dipolar gases.

Figure 1

Crystal-like droplet arrangements of $n_{XY}(x,y)/N$, with $n_{XY}(x,y)=\int dzn\left(\mathbf{r}\right)$, for a BEC of (a) $N=7500$ atoms and (b) 15 000 atoms, initially formed with $a=120a_B$, 20 ms after a quench to $a=70a_B$.

Figure 2

Droplet energy per particle $E_D$ [in units of $\hslash \tilde{\omega }$, with $\tilde{\omega }={\left({\omega }_x{\omega }_y{\omega }_z\right)}^{1/3}]$ as a function of the number of particles in the droplet $N_D$ for $a=70a_B$; for $N_D<N_{\text{min}}\simeq 900$ no stable droplet is found. Droplets with $E_D>0$ occur for $N_D\lesssim 1500$. In the inset, we show the density profile (solid line with crosses) of a droplet with $N_D=1000$ at the trap center for the cut $x=y=0$. At the droplet center, $n(0,0,z)\propto {(1-z^2/Z^2)}^{2/3}$ (dotted curve).

Figure 3

(a) Droplet number as a function of the initial atom number $N$, 20 ms after a quench from $a=120a_B$ to $70a_B$. Inset: Atom number per droplet as a function of $N$ under the same conditions. In both cases the average is denoted by a blue cross, and the variance by the error bar. (b) Histogram of the atom number per droplet for the same conditions evaluated from a sample of 260 droplets.

Figure 4

Atom number (blue dotted) and spectral weight (red solid) as a function of the time after a quench from $a=120a_B$ to $70a_B$ for a BEC with initially $10000$ atoms.