Dark states and the Morris-Shore transformation
Prof. Dr. Bruce Shore (Lawrence Livermore National Laboratory, University of California)

The two-state quantum system, interacting with radiation, is the basic idealization that underlies much of contemporary physics, for example selective laser excitation and quantum information processing. In simplest form it dates from notions of Einstein, who proposed, a century ago, simple rate equations to describe absorption, stimulated and spontaneous emission. For laser-induced interactions the relevant equations are derived from the time-dependent Schroedinger equation, in the form of two coupled ordinary differential equations for probability amplitudes, whose solutions offer possibilities of Rabi oscillations of excitation probabilities. When the transitions involve degenerate energy states, it is possible that there occur a specific superposition quantum state that is not affected by coherent (laser) radiation: an atom in such a state does not undergo excitation nor subsequent fluorescence -- it is in a dark state. Such states have been important in the recent development of state-selective excitation (e.g. stimulated Raman adiabatic passage or STIRAP) and quantum optics. Within the last few years it has been rediscoverd that generalizations of the elementary two-state superpositions are possible and that these have a number of interesting properties and applications: under appropriate conditions the complicated linkage patterns of transitions between degenerate sublevels can be reduced to a set of independent two-state transitions, together with unaffected spectator states. The construction of these bright and dark states is by means of a transformation of Hilbert-space basis states now termed the Morris-Shore transformation. I will describe the background of dark states and the M-S transformation, as well as noting some applications.