Odd-petal states and persistent flows in spin-orbit-coupled Bose-Einstein condensates

We study the phase diagram of a Rashba spin-orbit-coupled Bose-Einstein condensate confined in a two-dimensional toroidal trap. In the immiscible regime we find an azimuthally periodic density distribution, with the periodicity highly tuneable as a function of the spin-orbit coupling strength and which favours an odd number of petals in each component. This allows for a wide range of states that can be created. We further show that in the miscible regime, both components possess states with persistent flows with a unit winding number difference between them and with the absolute values of these winding numbers depending on the spin-orbit coupling strength. All features of the odd-petal and the persistent flow states can be explained using a simple but effective model.