Quantum control and pathway manipulation in rubidium

Abstract

There is an increasing interest in the extraction and control of the interfering quantum pathway amplitudes induced by control fields during laser-matter interactions. The Hamiltonian-encoding and observable-decoding (HE-OD) technique has been introduced for extracting the amplitudes of the pathways present in the dynamics and has recently been experimentally applied to the pathway manipulation of atomic rubidium. This paper theoretically explores various strategies for manipulating pathway amplitudes in the context of a laser field interacting with a multilevel system similar to atomic rubidium for both narrow-band and broadband ultrafast fields. In the perturbation regime, two second-order quantum pathways connecting the Rb states $5{S}_{1/2}$ and $5{D}_{3/2}$ dominate the dynamics, namely, $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 1) and $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{1/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 2). For narrow-band field control, the analysis is carried out in the time domain with the laser field including only four narrow-band envelope subpulses centered at the resonant frequencies. When the two pathways cooperate constructively, temporal oscillations appear in the ratio of the two pathway amplitudes, and we conclude in this case that the period corresponds to the detuning between transitions $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}$ and $5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$. For broadband field control, the dynamics are treated in the frequency domain with the laser field including both resonant and continuous nonresonant frequency components. Various control strategies based on manipulating the phase of selected spectral components are tested. Compared to the outcome from a transform limited pulse, a $\frac{\ensuremath{\pi}}{2}$ step scheme can increase the dynamic range of the ratio between the two pathway amplitudes by a factor of $\ensuremath{\sim}3$. A scheme that manipulates eight spectral blocks, in which the spectral boundaries depend on the resonant frequencies, can increase the ratio by several orders of magnitude. Numerical simulations show that further dividing the spectrum into hundreds of evenly spaced blocks does not significantly enhance the pathway ratio over the eight-block scheme. The quantum control of pathways investigated in this work provides valuable insights on how to incorporate known information about the structure of quantum systems for the effective reduction of quantum control complexity.