Derivation and demonstration of four- and six-photon stimulated Raman transitions*

We demonstrate direct coupling between electronic angular momentum states with a difference in magnetic quantum number ∆mJ ≥ 2 driven by resonant four- and six-photon stimulated Raman transitions. By extending the standard treatment of the two-photon Raman process, we provide derivations of 4- and 6-photon transition Rabi frequencies by reducing the problem to a two-state system via adiabatic elimination of non-resonantly coupled intermediate states. We present experimental results that demonstrate the expected super-linear scaling of the Rabi frequencies with drive beam intensity. Finally, we discuss pathways to increase the presented multi-photon transition fidelities, enabling high-fidelity connectivity between states with ∆mJ > 2.