The geometric phase in two-level atomic systems

We report the observation of the geometric phase in a closed two-level atomic system using stimulated photon echoes. The two-level system studied consists of the two-electronic energy levels (3H4 and 3H6) of Tm3+ doped in YAG crystal. When a two-level atom at an arbitrary superposition state is excited by a pair of specially designed laser pulses, the excited state component gains a relative phase with respect to the ground state component. We identified the phase shift to be of pure geometric nature. The dynamic phase associated to the driving Hamiltonian is unchanged. The experiment results of the phase change agree with the theory to the extent of the measurement limit.