Formation of Bright Matter-Wave Solitons during the Collapse of Attractive Bose-Einstein Condensates

We observe bright matter-wave solitons form during the collapse of ${}^{85}\mathrm{Rb}$ condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.

Figure 1

Dependence of the number of condensate atoms surviving the collapse on the magnitude of the negative scattering length, $a_{\mathrm{collapse}}$ (where $a_0=0.0529\mathrm{nm}$ is the Bohr radius). The data are expressed as the ratio of the number of remnant condensate atoms to the critical number calculated according to Eq. (1). Results are shown for three different initial numbers of condensate atoms; $N_0=15000$ (●), 10 000 (◇), and 5000 (▲). The dashed line shows the critical number. The error bars represent the statistical spread in the data only.

Figure 2

Observation of solitons oscillating in the magnetic trap following the collapse at $a_{\mathrm{collapse}}=-11.4a_0$ of condensates initially containing approximately 8000 atoms. (a) The evolution of the axial (horizontal) FWHM of the remnant condensate obtained from a single Gaussian fit to the images. Above the resolution limit of the imaging system, the remnant condensate is observed to separate into two solitons as shown in the images taken at (b) 210 ms, (c) 1140 ms, and (d) 3110 ms. Each image is $77\times 129\mu \mathrm{m}$. The error bars represent the statistical spread in the data only.

Figure 3

Images and cross sections of remnant condensates. (a) When the magnitude of $a_{\mathrm{collapse}}$ is sufficiently small a single remnant condensate containing less than the critical number is observed to survive the collapse. When the magnitude of $a_{\mathrm{collapse}}$ is larger and/or larger initial condensates are used, the remnant condensate is observed to split into a number of solitons determined by the conditions of the collapse (b)–(d). Each image is $77\times 129\mu \mathrm{m}$.

Figure 4

(a) The modal number of solitons (□) observed after 200 ms of evolution at the collapse field as a function of the magnitude of the negative scattering ($a_{\mathrm{collapse}}$). The ratio of the number of remnant condensate atoms to the critical number (●) is also plotted on the right axis (note the two $y$ axes have the same scale). The initial condensate contained approximately 8000 atoms. (b) The ratio of the number of remnant condensate atoms to the critical number is plotted against the mean number of observed solitons to show that each soliton contains less than the critical number of atoms defined by Eq. (1) and is therefore expected to be stable. The error bars represent the statistical spread in the data only.