$d$-Wave Collapse and Explosion of a Dipolar Bose-Einstein Condensate

We investigate the collapse dynamics of a dipolar condensate of ${}^{52}\mathrm{Cr}$ atoms when the $s$-wave scattering length characterizing the contact interaction is reduced below a critical value. A complex dynamics, involving an anisotropic, $d$-wave symmetric explosion of the condensate, is observed. The atom number decreases abruptly during the collapse. We find good agreement between our experimental results and those of a numerical simulation of the three-dimensional Gross-Pitaevskii equation, including contact and dipolar interactions as well as three-body losses. The simulation indicates that the collapse induces the formation of two vortex rings with opposite circulations.

Figure 1

Collapse dynamics of the dipolar condensate. (a) Timing of the experiment. The red curve represents the time variation of the scattering length $a(t)$ one would have in the absence of eddy currents, while the blue curve is obtained by taking them into account (see text). (b) Sample absorption image of the collapsed condensate for $t_{\mathrm{hold}}=0.4\mathrm{ms}$, after 8 ms of time of flight, showing a “cloverleaf” pattern on top of a broad thermal cloud. This image was obtained by averaging 60 pictures taken under the same conditions. (c) Same image as (b) with the thermal cloud subtracted. In (b) and (c) the field of view is $270\mu \mathrm{m}$ by $270\mu \mathrm{m}$. The green arrow indicates the direction of the magnetic field. (d) Series of images of the condensate for different values of $t_{\mathrm{hold}}$ (upper row) and results of the numerical simulation without adjustable parameters (lower row); the field of view is $130\mu \mathrm{m}$ by $130\mu \mathrm{m}$.

Figure 2

In-trap column density obtained in the simulation, for different $t_{\mathrm{hold}}$. The field of view is $5\mu \mathrm{m}$ by $5\mu \mathrm{m}$. Because of the DDI, the condensate collapses radially, acquiring the shape of a very thin cigar elongated along $z$. At $t_{\mathrm{hold}}\simeq 0.5\mathrm{ms}$, the collapse occurs, and immediately after, the cloud starts to expand radially.

Figure 3

Atom losses during collapse. Blue circles: atom number $N_{\mathrm{BEC}}$ in the condensate as a function of $t_{\mathrm{hold}}$. The solid curve is the result of the simulation for $L_3=2\times {10}^{-40}{\mathrm{m}}^6/\mathrm{s}$, without any adjustable parameter. Inset: the atom number $N_{\mathrm{thermal}}$ in the thermal cloud (red squares) remains essentially constant during the collapse.

Figure 4

Vortex rings predicted by the numerical simulation. (a) Isodensity surface of an in-trap condensate at $t_{\mathrm{hold}}=0.8\mathrm{ms}$. The topological defects are shown by the red rings. (b) Velocity field of the atomic flow in the $x=0$ plane at $t_{\mathrm{hold}}=0.8\mathrm{ms}$. The field of view is $2.5\mu \mathrm{m}$ by $2.5\mu \mathrm{m}$; the color scale represents the velocity (red is faster).