Stable Quantum Vortices in Lee-Huang-Yang Dipolar Superfluids

TL;DR

This work investigates vortex nucleation and dynamics in a rotating quasi-2D dipolar BEC where beyond-mean-field Lee-Huang-Yang (LHY) corrections can dominate the nonlinearity. By formulating a reduced 2D Gross-Pitaevskii model including contact, dipole-dipole interactions (DDI), and LHY terms, and by exploring both mixed and purely LHY regimes, the authors map how rotation drives vortex formation and how the angular momentum per particle tracks the vortex count. A key finding is that, under MF cancellation (tuning of contact and DDI), the system can realize a robust pure-LHY superfluid that supports vortices, with the single-vortex threshold around $\Omega_c \approx 0.6401$ and even-numbered vortex states being particularly stable, up to $N_v \approx 20$ at high rotation. These results illuminate how quantum fluctuations can stabilize and structure vortices in dipolar quantum fluids, offering practical pathways to realize and control LHY-dominated vortices via Feshbach tuning and dipole orientation in experiments.

Abstract

The nucleation and dynamics of vortices in the quasi-two-dimensional rotating dipolar Bose-Einstein condensate are explored by taking into account the Lee-Huang-Yang (LHY) correction to the mean-field (MF) theory. Assuming approximate cancellation of the MF interactions, we focus on the formation of a pure LHY superfluid. The effect of rotational frequency $Ω$ is investigated numerically by determining the corresponding number of stable vortices in the superfluid, together with the respective energy per particle $E$ and chemical potential $μ$. The LHY superfluid provides a deep minimum of $E$ and $μ$, indicating that it is a remarkably robust state of quantum matter. By fixing the LHY interaction strength, an exact single-vortex critical frequency is found, along with the respective chemical potential. A notable feature, observed when creating the LHY superfluid with fewer than five vortices, which is understood as being due to the superfluid's nonlinearity and trapping aspect ratio, is the large frequency ranges admitting the production of two and four vortices, as compared to the small frequency ranges to obtain one and three vortices.

Figures (11)

• Figure 1: The representation of DDIs in the dipolar quasi-2D BEC in the coordinate space. Angle between vector $\mathbf{r}_{2}\mathbf{-r}_{1}$ and the $z$ axis is $\theta _{d}\approx 90^{\mathrm{o}}$. The variation of angle $\varphi$ between the magnetic dipoles and the $z$ axis alters the strength and sign of DDI, from repulsive to attractive.
• Figure 2: (Color online) Density profiles $|\psi |^{2}$ projected onto the 2D plane, displaying vortex lattices with the nonlinearity represented solely by the MF contact interactions with $g=100$. The rotation frequences $\Omega$ (in units of $\omega _{\perp }$) are indicated in the panels, with the density levels coded by the by color bars. The $x$ and $y$ coordinates (in units of $\ell _{\perp }$) cover the interval $[-10,+10]$.
• Figure 3: (Color online) Density profiles $|\psi |^{2}$ projected onto the 2D plane, displaying vortex lattices with the nonlinearity represented solely by DDI with $g_{\mathrm{dd}}=100$. The rotation frequencies $\Omega$ are indicated in the panels, with the density levels coded by the color bars. The spatial domain and units are the same as in Fig. \ref{['fig02']}.
• Figure 4: (Color online) Density profiles $|\psi |^{2}$ projected onto the 2D plane, displaying vortex lattices with nonlinearity provided by contact and LHY interactions, with $g=100$ and $\eta=200$. The frequencies are indicated inside the panels, with the respective density levels given by color bars. The spatial domain and units are the same as in Fig. \ref{['fig02']}.
• Figure 5: (Color online) Density profiles $|\psi |^{2}$ projected onto the 2D plane, displaying vortex lattices with nonlinearity provided by contact, dipolar and LHY interactions, with $g=100$, $g_{dd}=100$, and $\eta=200$. The frequencies are indicated inside the panels, with the respective density levels given by color bars. The spatial domain and units are the same as in Fig. \ref{['fig02']}.