Wave-function analysis of dynamic cancellation of ac Stark shifts in optical lattice clocks by use of pulsed Raman and electromagnetically-induced- transparency techniques

We study analytically the dynamic cancellation of ac Stark shift in the recently proposed pulsed electromagnetically-induced-transparency (EIT-)Raman optical lattice clock based on the wave-function formalism. An explicit expression for the time evolution operator corresponding to the effective two-level interaction Hamiltonian has been obtained in order to explain the atomic phase shift cancellation due to the ac Stark shift induced by the time-separated laser pulses. We present how to determine an optimum value of the common detuning of the driving fields at which the atomic phase shift cancels completely with the parameters for the practical realization of the EIT-Raman optical lattice clock with alkaline-earth-metal atoms.