Quantum Ferrofluid Turbulence

We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly nonequilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low-density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of the vortex line length is enhanced, closely following a $t^{-3/2}$ behavior. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.

Figure 1

Turbulence in the quantum ferrofluid, for three values of ${ϵ}_{\mathrm{dd}}$. Vortices are shown through isosurfaces (red tubes) of the quasicondensate density at the $0.05⟨n_q⟩$ level (angled brackets denote an ergodic average). The walls of the box show 2D density profiles, corresponding to integrating the density $|\psi {|}^2$ over the dimension perpendicular to their face.

Figure 2

(a) Polarization of the vortex tangle over time, shown through the area ratio of vortices, $A_z/A_{\perp }$, for three ${ϵ}_{\mathrm{dd}}$ values. Lines and shaded regions represent the mean and one standard deviation over five realizations with different randomized initial conditions, respectively. (b) Snapshot of the area ratio over more detailed range of ${ϵ}_{\mathrm{dd}}$ at $t=750\tau$ [dotted line in (a)].

Figure 3

A representative snapshot (left, top view; right, angled view) for ${ϵ}_{\mathrm{dd}}=0.8$ ($t/\tau =1000$) highlighting the location of the high-density regions [blue isosurfaces, plotted at $0.8\max (⟨n_q⟩)$] and the vortices (red isosurfaces, plotted at $0.05⟨n_q⟩$).

Figure 4

Coupling between vortices and the dipolar-driven density fluctuations. One large loop spreads across two planar density regions, which act as pinning layers. The observed dynamics are indicative of simulations for relative dipolar strength ${ϵ}_{\mathrm{dd}}<0$, and the times of the images shown are $t/\tau =50$ apart from left to right. The phase is evaluated and displayed on the quasicondensate density at the $0.05⟨n_q⟩$ level; the back wall of the box shows the 2D density profiles, corresponding to integrating the density over the dimension perpendicular to its face.

Figure 5

Decay of the vortex tangles. Vortex line length $L$ for the three ${ϵ}_{\mathrm{dd}}$ values shown, averaged over five simulations. For reference, $t^{-1}$ and $t^{-3/2}$ lines are shown (dashed lines) where appropriate. The horizontal line shows when the average intervortex spacing $\ell =1/\sqrt{L}$ equals the box half-width, representing the level at which the number of vortices becomes of the order of unity.