Revealing quantum-control mechanisms through Hamiltonian encoding in different representations

The Hamiltonian encoding is a means for revealing the mechanism of controlled quantum dynamics. In this context, the mechanism is defined by the dominant quantum pathways starting from the initial state and proceeding through a set of intermediate states to end at the final state. The nature and interpretation of the mechanism depends on the choice of the states to represent the dynamics. Alternative representations may provide distinct insights into the system mechanism, and representations producing fewer pathways are especially interesting. In addition, a suitable choice of representation may highlight the role of certain couplings in a system that would normally be masked by other, higher magnitude couplings. A simple three-level system is chosen for illustration, where different values for the Rabi frequencies lead to mechanistic analyses that are best described in terms of particular representations. As an examlple, the role of the nonadiabatic terms in stimulated Raman adiabatic passage dynamics is analyzed through the Hamiltonian encoding.