  We investigate the one-dimensional Hubbard ring with attractive interaction
in the presence of imbalanced spin populations by using the exact
diagonalization method. The singlet pairing correlation function is found to
show spatial oscillations with power-law decay as expected in the
Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the
strong coupling regime, the system shows an anomalous flux quantization of
period h=4e, half of the superconducting flux quantum of h=2e, as recently
predicted by mean-field analysis, together with various flux quanta smaller
than h=4e. Notably, the observed flux quanta are determined by the difference
between the system size NL and electron number N_e as h=(N_L-N_e)e.
