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Ongoing work aimed at developing highly efficient methods of populating achosen sublevel of an energy level highlights the need to understandoff-resonant effects in coherent excitation. This motivated us to re-examinesome aspects of the theory of coherent excitation in a three-state system witha view to obtaining algebraic expressions for off-resonant eigenvalues andeigenvectors. Earlier work gives simple closed-form expressions for theeigenvalues this system, expressions applying even when the system is not ontwo-photon resonance. We present here expressions of similar simplicity forthe components of the normalised eigenvectors. The analytic properties ofthese components explain the observed sensitivity of thestimulated-Raman-adiabatic-passage process (STIRAP) to the condition oftwo-photon resonance. None of the eigenstates is ‘trapped’ or‘dark’ unless the system is on two-photon resonance; offresonance, all states have nonzero projections on the unperturbed intermediatestate. A simple argument shows that no dressed state can be adiabaticallyconnected to both the unperturbed initial and final states when the system isoff two-photon resonance. That is, adiabatic transfer from initial to finalstate requires that these be degenerate before and after the STIRAP pulsesequence, and this implies zero two-photon detuning. However, substantialtransfer probabilities are observed experimentally for very small two-photondetunings. We show that such systems are characterised by very sharp avoidedcrossings of two eigenvalues, and that the observed population transfer can beunderstood as an effect of non adiabatic transitions occurring at the avoidedcrossings.

Coherent Population Transfer among Three States: Full Algebraic Solutions and the Relevance of Non Adiabatic Processes to Transfer by Delayed Pulses