| dc.description.abstract | Quantum vortices in superfluid Bose Einstein condensates (BECs) are excellent candidates
for studying hydrodynamic phenomena, such as turbulence and chaos, due to the
quantization of vortex circulation and the absence of dissipation in BECs. Since the early
2000s, many experimental groups have successfully observed vortices in dilute atomic
BECs.
This work mainly focuses on creating quantum chaos with a few vortices in a twodimensional
BEC of Rubidium87. We use graphics processing unit (GPU) computing methods to simulate our BEC trapped inside a harmonic potential with tight trapping in one direction. The quantum vortices are created by rotating the condensate. After generating the ground state of the BEC with a small number of singly charged vortices with positive phase winding, we imprint a 4\pi phase winding on top of one vortex in the opposite orientation to that of the original vortex. This phase imprinting annihilates the preexisting vortex and creates a new singly-charged vortex with negative phase winding. Due to the high resolution of our system and an excellent vortex tracking algorithm, the location of phase imprinting can be delicately controlled.
Both the individual vortex dynamics and the dynamics of the entire system of vortices
after flipping a vortex have shown strong signs of chaos. This chaotic nature is
further confirmed both qualitatively and quantitatively by employing two chaos indicators
on our numerical results. These chaos indicators are the Lyapunov exponent spectrum
and the Smaller ALignment Index (SALI). The Lyapunov exponent remains positive and
converges to a positive value during an experimentally realistic time period, which is the
smoking gun for chaotic behaviour. | |
