Pulse-train control of multiphoton transitions in anharmonic progressions: Resonance loci and resonance ridges

The properties of pulse-train induced multiphoton excitation in anharmonic progressions and the accumulation of population in a specific rung state are investigated by means of numerical simulations. It is shown how and under which conditions resonant π-pulses and multiple-π pulses can be split into trains of fractional π-pulses driving the same transition. Standardized train forms are considered with sub-pulses of equal (gaussian) shapes and equal, but tunable pulse-to-pulse delays and pulse-to-pulse phase shifts. The increased number of tuning parameters together with the handle on the number of sub-pulses gives rise to a remarkable variability in the control of state-specific population transfer, where simple zero-order estimates assist the determination of the parameters. Each π- or multiple-π pulse is replaced by a resonance locus in parameter space representing an infinite set of π-trains. The loci span extended frequency ranges that increase with increasing sub-pulse number. Their projection onto the frequency-field strength plane gives rise to elliptically shaped closed curves, termed resonance ridges, which replace the singular points mapped out by simple π- and multiple-π pulses. In the subspace of pulse-to-pulse delays and pulse-to-pulse phase shifts the resonance loci are characterized by phase recurrence relations, whose number and complexity increases with increasing numbers of sub-pulses. Our results indicate that pulse trains may be a powerful tool for the control of parallel or branching multiphoton transitions and for the elimination of background and intruder state population.