We present a general formalism for describing stimulated Raman adiabatic passage in a multi-level atom. The atom is assumed to have two ground state manifolds a and b and an excited state manifold e, and the adiabatic passage is carried out by resonantly driving the a-e and b-e transitions with time-dependent fields. Our formalism gives a complete description of the adiabatic passage process, and can be applied to systems with arbitrary numbers of degenerate states in each manifold and arbitrary couplings of the a-e and b-e transitions. We illustrate the formalism by applying it to both a simple toy model and to adiabatic passage in the Cesium atom.
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