Joint CPT and N resonance in compact atomic time standards

Currently development efforts towards small, low power atomic time standards use current-modulated VCSELs to generate phase-coherent optical sidebands that interrogate the hyperfine structure of alkali atoms such as rubidium. We describe and use a modified four-level quantum optics model to study the optimal operating regime of the joint CPT- and N-resonance clock. Resonant and non-resonant light shifts as well as modulation comb detuning effects play a key role in determining the optimal operating point of such clocks. We further show that our model is in good agreement with experimental tests performed using Rb-87 vapor cells.