Time-of-flight expansion dynamics of a circulating ring BEC

We have studied the effect of non--zero circulation on the time--of--flight expansion dynamics of a ring--shaped BEC, under conditions matching recent experiments at the Joint Quantum Institute/NIST in Maryland. We modeled the dynamics of the condensate by first solving the time--independent Gross--Pitaevskii equation (GPE) to obtain the initial condensate wavefunction, with the (quantized) circulation set by imprinting an azimuthal phase gradient. This state was then propagated using the time--dependent GPE in real time, with the trapping potential turned off. In the absence of circulation, the BEC expands and closes the central hole in a few milliseconds, eventually resulting in a density profile with a central peak surrounded by a pedestal modulated by weak concentric fringes. When the ring BEC is circulating, the central hole initially decreases in size but never closes due to the phase singularity. In the long--time limit, the size of the central hole scales nearly linearly with the winding number of the circulation state, in good agreement with the NIST experimental results.