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The problem of achieving population inversion adiabatically in an N-level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The SU (N) coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the (N^2-1) -dimensional SU (N) space contains an (N-1) --dimensional steady-state subspace (t) whose orthonormal basis vectors {}₁, , {}₍-₁ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of S about. Multilevel adiabatic following occurs when the angle (t) between the coherence vector S and its projection onto is very small. The multiple dimension of is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving N-1 simple equations for the directional cosines of S on {}₈. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.
Oreg et al. (Wed,) studied this question.