Comparison of the Rabi and Ramsey pulling in an optically pumped caesium-beam standard

We present an evaluation of the frequency shifts in an optically pumped caesium-beam frequency standard caused by the neighbouring transitions. We analyse the shifts caused by the Rabi and Ramsey pulling effects and find a well-known result for the Rabi pulling but a new result for the Ramsey pulling. The revised Ramsey shift is found to be proportional to not the imaginary but the real part of the ground-state atomic coherence. The value of the Ramsey shift is proportional to the first power of the Rabi frequency defined by a small orthogonal component of the microwave field and the inverse value of the Zeeman splitting. We compare the shifts caused by the neighbouring transitions and show that the relative contributions of the Rabi and Ramsey pulling effects crucially depend on the quality of optical pumping. We estimate that the Rabi shift for the KRISS-1 caesium-bearn frequency standard is at a relative level of 10(-14) while the Ramsey shift is at a relative level of 10(-12).