N+CPT clock resonance

Abstract

In a typical compact atomic time standard a current modulated semiconductor laser is used to create the optical fields that interrogate the atomic hyperfine transition. A pair of optical sidebands created by modulating the diode laser become the coherent population trapping (CPT) fields. At the same time, other pairs of optical sidebands may contribute to other multiphoton resonances, such as three-photon N-resonance [Phys. Rev. A65, 043817 (2002)]. We analyze the resulting joint CPT and N-resonance (hereafter N+CPT) analytically and numerically. Analytically we solve a four-level quantum optics model for this joint resonance and perturbatively include the leading ac Stark effects from the five largest optical fields in the laser's modulation comb. Numerically we use a truncated Floquet solving routine that first symbolically develops the optical Bloch equations to a prescribed order of perturbation theory before evaluating. This numerical approach has, as input, the complete physical details of the first two excited-state manifolds of Rb87. We test these theoretical approaches with experiments by characterizing the optimal clock operating regimes.