Higher order geometric phase for qubits in a bichromatic field

The geometric phase in the dynamics of a spin qubit driven by transverse microwave (MW) and longitudinal radio frequency (RF) fields is studied. The phase acquired by the qubit during the full period of the 'slow' RF field manifests in the shift of Rabi frequency ω1 of a spin qubit in the MW field. We find out that, for a linearly polarized RF field, this shift does not vanish at the second and higher even orders in the adiabaticity parameter ωrf/ω1, where ωrf is the RF frequency. As a result, the adiabatic (Berry) phases for the rotating and counter-rotating RF components compensate each other, and only the higher order geometric phase is observed. We experimentally identify that phase in the frequency shift of the Rabi oscillations detected by a time-resolved electron paramagnetic resonance.