Measurement protocol for non-adiabatic geometric phases of Floquet states

Periodically time-dependent quantum systems have Floquet solutions. They consist of a phase factor and a Floquet mode which shares the periodicity of the driving. Consequently, any such solution possesses a non adiabatic geometric phase known as the Aharonov-Anandan (AA) phase. It is gauge-invariant and, therefore, is experimentally accessible. We propose a protocol for the measurement of AA phases based on the adiabatic change of the phase of the non-adiabatic driving. We argue that the experimental requirements of the protocol are those of previous measurements of adiabatic phases.