The dynamics that take place in the optimal quantum control of atomic rubidium upon population transfer from state 5$S_{1/2}$ to state 5$D_{3/2}$ are investigated with Hamiltonian-encoding–observable-decoding (HE-OD). For modest laser powers two second-order pathways, 5$S_{1/2}$$\to$5$P_{3/2}$$\to$5$D_{3/2}$ (pathway 1) and 5$S_{1/2}$$\to$5$P_{1/2}$$\to$5$D_{3/2}$ (pathway 2), govern the population transfer process. Pathway 1 has larger transition dipoles than pathway 2. However, state 5$P_{3/2}$ along pathway 1 may also be excited to an undesired state 5$D_{5/2}$, which can result in population “leakage.” Thus, the two pathways may either cooperate or compete with each other in various dynamical regimes. An important feature in the case of cooperation is that the ratio between the amplitudes of pathways 1 and 2 oscillates over time with a frequency equal to the detuning between transitions 5$S_{1/2}$$\to$5$P_{3/2}$ and 5$P_{3/2}$$\to$5$D_{3/2}$. We also study the regime in which pathway 2 dominates the dynamics when the larger transition dipoles of pathway 1 can no longer compensate for its population leakage. The overall analysis illustrates the utility of HE-OD as a tool to reveal the quantum control mechanism.

• Received 10 December 2013

DOI:https://doi.org/10.1103/PhysRevA.89.023416