Pathway dynamics in the optimal quantum control of rubidium: Cooperation and competition

摘要: The dynamics that take place in the optimal quantum control of atomic rubidium upon population transfer from state 5${S}_{1/2}$ to 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}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${P}_{3/2}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${D}_{3/2}$ (pathway 1) and 5${S}_{1/2}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${P}_{1/2}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${D}_{3/2}$ 2), govern process. Pathway 1 has larger transition dipoles than pathway 2. However, 5${P}_{3/2}$ along may also be excited an undesired 5${D}_{5/2}$, which can result ``leakage.'' Thus, pathways either cooperate or compete each other various dynamical regimes. An important feature case cooperation is ratio between amplitudes 2 oscillates over time a frequency equal detuning transitions 5${S}_{1/2}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${P}_{3/2}$ 5${P}_{3/2}$$\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}$5${D}_{3/2}$. We study regime dominates when no longer compensate for its leakage. overall analysis illustrates utility HE-OD as tool reveal mechanism.