Evaluation of the geometric phase of a two-level atom manipulated on the Bloch sphere using a time-domain atom interferometer

The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant π pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation