Electric quadrupole shifts of the precession frequencies of 131Xe atoms in rectangular cells

We study an atomic comagnetometer design based on the spin precessions of Xe-129 and Xe-131 atoms in glass cells. The quadrupole splittings in the precession spectrum of Xe-131 are fully resolved, allowing a precise determination of the magnetic-dipole precession frequency. The transverse asymmetry of quadrupole interactions, due to both the geometry and surface properties of the cell, characterized by a nonzero asymmetry parameter eta, modifies the dependence of the quadrupole splittings on the relative orientation between the cell axes and the bias magnetic field and lead to additional corrections in the precession frequencies of Xe-131 atoms. We examine these effects both theoretically and experimentally and develop methods to quantify and control such shifts.