Stability of the quantized circulation of an attractive Bose-Einstein condensate in a rotating torus

We investigate rotational properties of a system of attractive bosons confined in a one-dimensional torus. Two kinds of ground states, uniform-density and bright soliton, are obtained analytically as functions of the strength of interaction and of the rotational frequency of the torus. The quantization of circulation appears in the uniform-density state, but disappears upon formation of the soliton. By comparing the results of exact diagonalization with those predicted by the Bogoliubov theory, we show that the Bogoliubov theory is valid at absolute zero over a wide range of parameters. At finite temperatures we employ the exact diagonalization method to examine how thermal fluctuations smear the plateaus of the quantized circulation. Finally, by rotating the system with an axisymmetry-breaking potential, we clarify the process by which the quantized circulation becomes thermodynamically stabilized.