Tunable frequency stabilization to Zeeman sublevel transitions between an intermediate state and Rydberg states

We demonstrate a robust method of direct laser frequency locking on the Zeeman sublevel transitions between an intermediate state and Rydberg states, with continuously tunable frequency range from  −35 MHz to  +35 MHz, which is based on electromagnetically induced transparency (EIT) spectra of nondegenerate Zeeman sublevels in a Rydberg cascade system. With a small axial magnetic field, the EIT spectrum will split into two individual sub-peaks due to the Zeeman Effect of three energy levels, including the ¹³³Cs 6S_1/2, 6P_3/2 and nl Rydberg states which form the cascade system. It is shown that the coupling field, corresponding to the transitions between the Zeeman sublevels of the intermediate state and Rydberg state, can be locked arbitrarily on any one of the two EIT sub-peaks. The frequency stability of locked lasers is bounded by 0.81 MHz. The root of Allan variance of the frequency reaches a minimum of $2.06\times {10}^{-8}$ for an averaging time of 512 s. (paper)