Critical Superfluid Velocity in a Trapped Dipolar Gas

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we estimate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system.

Figure 1

The density profiles of a DBEC with $D=124$ in a trap with aspect ratio $\lambda =20$ after a blue-detuned laser with axis $\widehat{z}$, beam waist ${\tilde{w}}_0=0.4a_{\rho }$, $z_0=1.24a_{\rho }$, and $U_0=2\hslash {\omega }_{\rho }$ has traveled through the DBEC with velocity (a) $v=0.3a_{\rho }{\omega }_{\rho }$, (b) $v=3.0a_{\rho }{\omega }_{\rho }$. In (a), there are no visual excitations present in the system while in (b), excitations are clearly present, indicating the presence of a critical velocity for the system. The $1/e^2$ contour of the laser is shown by the red dotted lines at the center of the condensates.

Figure 2

The discrete BdG quasiparticle dispersions for a DBEC in a trap with aspect ratio $\lambda =20$ for various values of $D$ showing $m=0$ ($\mathrm{\text{black}}+\mathrm{\text{sign}}$), $m=1$ (teal squares), and $m=2$ (pink circles) quasiparticles. As $D$ is increased, the dispersion develops a phononlike character at low momenta and a rotonlike character at intermediate momenta. The slopes of the black dotted lines represent the corresponding Landau critical velocities for each $D$.

Figure 3

The occupations of the quasiparticles excited from a DBEC with aspect ratio $\lambda =20$ by a blue-detuned laser moving with velocity $v$ (plotted on the horizontal axis) and with parameters ${\tilde{w}}_0=0.3a_{\rho }$, $U_0=0.4\hslash {\omega }_{\rho }$, and $z_0=0.7a_{\rho }$, for various values of $D$. At a critical $v$ (indicated by the arrows), the occupations increase suddenly, indicating that the laser has excited quasiparticles in the system and superfluidity has been broken.

Figure 4

The superfluid critical velocities $v_{\mathrm{crit}}$ for dissipation due to the excitation of quasiparticles in a DBEC as a function of $D$. The black dashed line represents the Landau critical velocity extracted from the discrete dispersion relations of the system. The teal circles represent the results of numerical simulation for a laser with parameters ${\tilde{w}}_0=0.3a_{\rho }$, $z_0=0.7a_{\rho }$, and $U_0=0.4\hslash {\omega }_{\rho }$ and the pink squares represent the results of numerical simulation for a laser with parameters ${\tilde{w}}_0=0.4a_{\rho }$, $z_0=1.24a_{\rho }$, and $U_0=2\hslash {\omega }_{\rho }$.