Simulation of interactions of cesium atoms with an rf cavity mode for measurement of the nuclear anapole moment

We report simulations of a cesium, ¹³³Cs, atomic beam interacting with an rf field. The rf field will drive a weak electric dipole interaction between the hyperfine components of the ground state of cesium (6s²S_1/2 F=3→ 6s²S_1/2 F=4), which is weakly allowed due to the nuclear anapole moment. We use detailed numerical calculations of the rf field modes in a cavity and numerical integration of the equations of motion of the state amplitudes to calculate the expected magnitude of precession of the Bloch vector. We show sinusoidal modulation of the relative population of the two ground states with the phase of the rf field, relative to the phase of the initial superposition state. The magnitude of this modulation is ∼5 x 10^-6, which we show to be measurable in the laboratory.