  The adiabatic manipulation of quantum states is a powerful technique that has
opened up new directions in quantum engineering, enabling tests of fundamental
concepts such as the Berry phase and its nonabelian generalization, the
observation of topological transitions, and holds the promise of alternative
models of quantum computation. Here we benchmark the stimulated Raman adiabatic
passage process for circuit quantum electrodynamics, by using the first three
levels of a transmon qubit. We demonstrate a population transfer efficiency
above 80% between the ground state and the second excited state using two
adiabatic Gaussian-shaped control microwave pulses coupled to the first and
second transition. The advantage of this techniques is robustness against
errors in the timing of the control pulses. By doing quantum tomography at
successive moments during the Raman pulses, we investigate the transfer of the
population in time-domain. We also show that this protocol can be reversed by
applying a third adiabatic pulse on the first transition. Furthermore, we
demonstrate a hybrid adiabatic-nonadiabatic gate using a fast pulse followed by
the adiabatic Raman sequence, and we study experimentally the case of a
quasi-degenerate intermediate level.
