Adiabatic following in multilevel systems

Abstract

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 (N2-1)-dimensional SU(N) space contains an (N-1) - dimensional steady-state subspace (t) whose orthonormal basis vectors 1, N-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 i. 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. © 1984 The American Physical Society.