An Optical Vortex-Based Azimuthal Lattice for Rotating a
Bose-Einstein Condensate
Azure Hansen, Pierre Cladé, Mikkel Andersen, Changhyun Ryu, Vasant Natarajan, Kristian Helmerson, William D. Phillips
National Institute of Standards & Technology, Atomic Physics Division, Laser Cooling Group
Many properties of Bose-Einstein condensates, including band structure, momentum distribution, and atomic interactions, have been studied in linear optical lattices produced by the interference of two counter-propagating laser beams. We propose to instead use an azimuthal lattice created by the interference of off-resonance co-propagating Laguerre-Gaussian laser beams of opposite helicity. This new ring-shaped lattice provides a uniform atom density, and periodic boundary conditions that approximate an infinite lattice. Variation of the rate of rotation of the lattice imparts angular momentum to its trapped atoms, the same way that accelerating a linear lattice by chirping one beam's frequency accelerates atoms.
Laguerre-Gaussian (LG) beams, the optical vortex mode, have a spiral phase distribution and therefore a characteristic region of undefined phase on the axis of the beam where the amplitude is necessarily zero. The interference between two vortices of equal and opposite helicity has resembles dark and bright beads regularly spaced on a ring. The trapping potential of the lattice comes from the optical dipole force, which depends on the intensity of the light and its detuning from atomic resonance. We create LG beams using a computer-generated hologram (CGH) implemented in either a phase plate or a spatial light modulator (SLM). A CGH is the calculated interference between a plane wave and Laguerre-Gaussian mode. The result has a "fork" discontinuity that introduces the vortex singularity when used as a diffraction grating.
The azimuthal lattice is rotated by introducing a phase shift in one of the two LG beams that compose the interferogram. If the LG beams are created using the SLM, this phase change can easily be programmed into the CGH code. However, in testing this method we found that the maximum rotation rate that can be achieved is too slow for our application. Therefore, we have developed and tested another system that has the desired time response, spatial resolution and stability. Vortices produced by a "fork" phase plate are interfered in a modified Mach-Zehnder interferometer in which a computer-controlled screw tilts a glass plate in one arm. Varying the tilt changes the optical path length and rotates the interferogram. This interferometer will soon be incorporated in our sodium BEC apparatus using a 532 nm laser.
|