Observation of Solitonic Vortices in Bose-Einstein Condensates

We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.

Figure 1

Integrated triaxial density distribution of a BEC after a time of flight of 120 ms in presence of a solitonic vortex aligned along $y$. For each condensate we report absorption images along the two radial directions, horizontal $y$ (left) and vertical $z$ (top), and the residuals of axial ($x$) imaging after subtracting the Thomas-Fermi profile fit. (a)–(b) Experimental snapshots of two condensates with opposite circulation. (c) Theoretical 3D calculation with clockwise circulation and a ${\mu }_{\text{theo}}\simeq {\mu }_{\exp }/3$ (white noise has been added in order to better compare the theoretical calculation to the experimental results). Arrows indicate the atomic flow. Other examples of solitonic vortices with different orientation and shape can be seen in the Supplemental Material [16].

Figure 2

Theoretical solutions of in situ density and phase profiles for (a) a vortex aligned along the axis of an axially symmetric potential, a solitonic vortex (b) and a soliton (c) oriented perpendicularly to the axis of an elongated axially symmetric trap. Arrows indicate the atomic flow.

Figure 3

(a) Time sequence for the two-pulse Bragg interferometer. After $t_1$ from the atoms release a first $\pi /2$ Bragg pulse splits the condensate in two parts, one at rest and the other moving at the Bragg velocity. After $t_2$ a second pulse further splits each condensate and imaging after a long $t_3$ allows for the separation of the two outputs and for the creation of the interference pattern. (b)–(c) Experimental images of the two interferometer outputs in the presence of a vortex with clockwise circulation. (d) Enlargement on the interference pattern showing the dislocation-antidislocation pair and a guide to the eye (e) sketching the interference pattern. (f) 2D numerical simulation of the experiment. (g)–(k) The same, but for an antivortex with counterclockwise circulation.

Figure 4

(a) Sketch of the evaporation ramp. (b) Number of total defects (squares) and of solitonic vortices (dotted circles) measured on average at different times during and after the evaporation ramp. Blue (solid) and red (dashed) points correspond to data sets with different final evaporation frequencies. Error bars are evaluated as $\sqrt{{\sigma }^2+1/N_m}$, where $\sigma$ is the standard deviation of the average counts and $N_m$ the number of measurements. (c) Ratio between averaged counted solitonic vortices and total defects.