Amplitude and phase control of a coherent superposition of degenerate states. I. Theory

Abstract

We present the theory for a technique, based on multistate variants of the stimulated Raman adiabatic passage (STIRAP) process, that allows efficient and robust preparation of a preselected superposition of two or three degenerate states (magnetic sublevels of an atom) and the measurement of their relative amplitudes and phases. Because the preparation utilizes adiabatic passage it is robust against small fluctuations of the Rabi frequencies and temporal shapes of the coupling fields. We here describe and, in the following companion paper we demonstrate, an approach to the experimental characterization of the superposition state, i.e., the measurement of the relative phases and the ratios of amplitudes of the components. That technique, termed phase-to-population mapping, is applicable to the characterization of a stream of identically prepared atoms and is based on laser-induced fluorescence after the atoms have undergone optical pumping cycles induced by an additional laser. The optical pumping process maps the phase into populations of a subset of levels by means of a filtering laser field, and is robust against variations in the intensity and detuning of that field. We describe four linkage patterns appropriate to the creation of superpositions of two or three degenerate states of angular momentum $J=2$, starting from $J=0$. We offer an interpretation, from three different perspectives, of the subsequent characterization procedure.