Phase evolution in spatial dark states

Adiabatic techniques using multilevel systems have recently been generalized from the optical case to settings in atom optics, solid state physics, and even classical electrodynamics. The most well known example of these is the so-called stimulated Raman adiabatic passage (STIRAP) process, which allows transfer of a particle between different states with large fidelity. Here we generalize and examine this process for an atomic center-of-mass state with a nontrivial phase distribution and show that even though dark state dynamics can be achieved for the atomic density, the phase dynamics will still have to be considered as a dynamical process. In particular we show that the combination of adiabatic and nonadiabatic behavior can be used to engineer phase superposition states.