Bragg Spectroscopy of Vortex Lattices

Raman Lab Research Projects

 
 

    We have measured the velocity field of a vortex lattice within a sodium Bose-Einstein condensate using Bragg scattering. The idea is to use the Doppler (velocity) sensitivity of the Bragg technique to extract spatial information about the lattice. Our results show that a combination of spectral and spatial information yields a complete description of the coarse-grained superfluid flow, including a direct measurement of its sense of rotation.

 

    This technique allows for a direct and intuitive spatial mapping of the velocity field of the atoms. For instance, in the limit of large number of vortices, one can clearly observe the mechanical effect of rigid-body rotation manifesting itself in a macroscopic quantum sample.

How We Make It

    Also, an animation (Quicktime movie) of the collected data shows the center of mass displacement of the diffracted cloud, as function of Bragg frequency:

 


The figure at right shows the spatial mapping of the velocity field of a vortex lattice.  Measuring the center-of-mass locations of the right and left diffracted atoms (XR, YR) and (XL, YL) in the x-y plane allows us to reconstruct the velocity profile of the rotating cloud.  For negative detuning, as in (a) where (d - d0) = -10 kHz, we observe YL > 0 and YR < 0.  For positive detuning, the opposite happens, as in (b) where (d - d0) = +10 kHz. 

The difference (XR - XL) is mapped as a function of frequency in (c), while   (YR - YL) is plotted in (d).  Finally, in (e), we have plotted (YR - YL) vs (XR - XL).  The data in (e) is a direct map of the position (Y-coordinate) versus velocity (X-coordinate) distribution within the vortex lattice, and shows a linear relationship consistent with rigid body rotation. 

 

    The figure shows vortices probed by Bragg scattering.  Outcoupled atoms (to the far right and left of each image) showed no particular structure for non-rotating clouds (a), whereas from vortices (b) and (c), the outcoupled atoms were tilted according to the direction of rotation. Images (a-c) were taken at 10 ms TOF.  The tilt angle increases with respect to time of flight, as shown in (e). Each pair of Bragg frequencies is resonant with a thin strip of atoms parallel to the x-axis, as illustrated in (d). All images were taken at d = 102 kHz.

       The tilting observed in the diffracted cloud is a clear signature of the rigid-body rotation of the superfluid.