Particle number fractionalization of an atomic Fermi-Dirac gas in an optical lattice

We show that a dilute two-species gas of Fermi-Dirac alkali-metal atoms in a periodic optical lattice may exhibit fractionalization of the particle number when the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. This results in fractional eigenvalues of the spin operator with vanishing fluctuations. The fractional part can be accurately controlled by modifying the effective detuning of the electromagnetic field.