## Quantized circular motion of a trapped Bose-Einstein condensate in laser beams: coherent rotation and vortices |

Phys. Rev. A.

One can understand that no vortex is created in a harmonic
potential by realizing that the energy interval E_{n+1} - E_{n}
between two energy eigenstates (both the ground state and vortex states
are eigenstates of the Hamiltonian) is constant. Therefore, if the transition
between the ground state and the first vortex state is resonant, soon higher
vortex states will be populated, too. A pure vortex state can never be
achieved! The corresponding superposition of vortex states is equivalent
to the circular motion shown on the previous page.

In an anharmonic trapping potential the energy interval
E_{n+1} - E_{n} is not constant and depends on n. Hence,
if the transition between the ground state and the first vortex state is
in resonance this will not be the case for the transition to higher vortex
states. We therefore examined whether a rotating force can create a vortex
state in an r^{4 }potential. Our results demonstrate that this
is the case. You may see the creation process in the
following movie which is based on a numerical simulation.

Click here if you cannot see the applet.

Tips for viewing the movie:

- Press the "Load Movie" button to read the numerical data. Since their size is about 400 kB this may take a while (between 10 seconds if you have a good connection to the internet and 5 Minutes if you are using a modem).
- Vary the speed of the movie with the scroll bar on the right side.
- Increase the brightness of your monitor to see the full condensate.
- You can also view the movie externally by downloading a zipped .flc file. Available are the modulus of the wavefunction (630 kB) and the phase of the wavefunction (930 kB). In this case you need a .fli/.flc player. For Windows you can use AAview (140 kB).