Instability of Rotationally Tuned Dipolar Bose-Einstein Condensates

The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the stationary states in the Thomas-Fermi limit, in the corotating frame, as well as direct numerical simulations in the Thomas-Fermi regime, explicitly accounting for the rotating polarization. The condensate is found to be inherently unstable due to the dynamical instability of collective modes. This ultimately prevents the realization of robust and long-lived rotationally tuned states. Our findings have major implications for experimentally accessing this regime.

Figure 1

Stationary solutions, as characterized by $\alpha$, as a function of $\mathrm{\Omega }$: (a) and (b) $\gamma =1$ and various ${\epsilon }_{\mathrm{dd}}$; (c) and (d) ${\epsilon }_{\mathrm{dd}}=0.4$ and various $\gamma$. In (b), the $\gamma =1$, ${\epsilon }_{\mathrm{dd}}=0$ branch has $\alpha =0$.

Figure 2

Comparison of the solutions for the rapid-rotating dipoles and time-averaged DDI formalisms. Shown is ${\kappa }_{\perp }$ (lines) evaluated at $\mathrm{\Omega }=50{\omega }_{\perp }$ and ${\kappa }_{\parallel }$ (markers), with ${\epsilon }_{\mathrm{dd}}\to -{\epsilon }_{\mathrm{dd}}/2$, as a function of ${\epsilon }_{\mathrm{dd}}$ and for various trap aspect ratios.

Figure 3

Simulation of a dipolar BEC during an adiabatic ramp-up of ${\epsilon }_{\mathrm{dd}}$, with $N={10}^5$, $\gamma =1$, and $\mathrm{\Omega }=3{\omega }_{\perp }$: cross sections at $z=0$ of density (first row) and phase (second row) at $t=50{\omega }_{\perp }^{-1}$ (first column), $t=150{\omega }_{\perp }^{-1}$ (second column), and $t=200{\omega }_{\perp }^{-1}$ (third column), scaled by $l_{\perp }=\sqrt{\hslash /(m{\omega }_{\perp })}$. The density is normalized to $n_0=N/l_{\perp }^3$.

Figure 4

Comparison between the numerical simulation and the TF solutions: $\alpha$ as a function of ${\epsilon }_{\mathrm{dd}}$ at $\mathrm{\Omega }=3{\omega }_{\perp }$ and $\gamma =1$, determined via Eqs. (7)–(9) (dashed line) and numerical simulation for $N={10}^5$ (solid line).

Figure 5

Dynamical instability of the TF stationary states: $\sqrt[4]{{\lambda }_0}$ as a function of $\mathrm{\Omega }$ and ${\epsilon }_{\mathrm{dd}}$ with $\gamma =1$ and $N_{\max }=13$. The prevalence of real, positive eigenvalues for ${\epsilon }_{\mathrm{dd}}>0$ indicates the existence of a dynamical instability. Note that black corresponds to $\sqrt[4]{{\lambda }_0}=0$. The inset takes a cross section at $\mathrm{\Omega }=3{\omega }_{\perp }$, corresponding to Figs. 3 and 4, and plots ${\lambda }_0$, showing that ${\lambda }_0>0\forall {\epsilon }_{\mathrm{dd}}>0$.