Control of Valence Electron Motion in Xe Cation Using Stimulated Raman Adiabatic Passage Technique

TL;DR

The paper extends STIRAP from population transfer to controlling the mixing of states in an existing quantum superposition via a generalized fractional STIRAP (f-STIRAP) framework. It develops analytic and approximate pulse schemes, including fitted Gaussians and two identical-Gaussian-pulse protocols, to robustly steer superpositions while minimizing population of the intermediate state. The authors apply these methods to Xe$^+$, demonstrating ultrafast charge migration control using either low-lying valence or core-excited intermediates and monitoring outcomes with attosecond transient absorption spectroscopy (ATAS). The work outlines experimental routes using high-harmonic generation for XUV and free-electron laser sources for X-ray pulses, signaling practical pathways for observing and exploiting controlled electron dynamics in complex atoms. Overall, the study provides a foundation for robust, experimentally feasible coherent control of ultrafast electronic motion in multi-level systems.

Abstract

This work theoretically investigates possibilities of using the Stimulated Raman Adiabatic Passage (STIRAP) and its variants to control a coherent superposition of quantum states. We present a generalization of the so-called fractional STIRAP (f-STIRAP), demonstrating precise control over the mixing ratio of quantum states in the wave packet. In contrast to conventional f-STIRAP, designed to drive a system from an eigenstate into a coherent superposition, our scheme enables arbitrary control over the composition of an already existing superposition state. We demonstrate that an approximate version of this technique -- where analytically designed laser pulses with composite envelopes are replaced by simple Gaussian pulses -- achieves comparable performance in controlling the dynamics of the wave packet. A limiting case of this scheme, utilizing two pulses with identical Gaussians envelopes and tuned delay and relative phase, is also explored, revealing experimentally accessible pathways for manipulating quantum coherence. We apply our developed techniques to control the ultrafast charge migration in the spin-orbit split ground electronic states of xenon cation via intermediate valence- and core-excited states. Finally, we propose concrete experimental realizations of the developed control schemes in combination with attosecond transient absorption spectroscopy as a method to probe the system.

Figures (7)

• Figure 1: Example of the generalized f-STIRAP in a three-level system where a coherent mixture of two lowest eigenstates is controlled by the population transfer via an intermediate state. Three panels indicate: (a) time dependences of the Rabi frequencies for the pump $\Omega_P(t)$ and Stokes $\Omega_S(t)$ pulses; (b) populations on the field free states; (c) populations of the adiabatic states in the rotating frame. It is seen that the system is driven from a coherent superposition of states $\ket{1}$ (25%) and $\ket{3}$ (75%) to an equal superposition of those states.
• Figure 2: Comparison of the analytic generalized f-STIRAP (solid lines) and its approximate version with fitted Gaussian pulses (dashed lines) in controlling a coherent mixture of two lowest eigenstates via an intermediate state in a three-level system. Four panels indicate: (a) Rabi frequencies for the pump $\Omega_P(t)$ and Stokes $\Omega_S(t)$ pulses; (b) populations on the field free states; (c) populations of the adiabatic states in the rotating frame; (d) angle $\Theta(t) = \arctan[\Omega_P(t)/\Omega_S(t)]$ quantifying the difference between the pump and Stokes pulses. It is seen that the system, driven from an equal superposition of states to a single eigenstate, is efficiently controlled by both the analytic and fitted versions of the applied laser fields.
• Figure 3: Landscapes showing final populations in states $\ket 1$ (top panel) and $\ket 3$ (bottom panel) evolved from an initial coherent superposition of the same states with various mixing angle $\alpha$ (horizontal axis). The population transfer is driven via an intermediate state $\ket 2$ by two Gaussian pulses with identical envelopes, fixed relative phase $\phi = 1.14 \pi$, and controlled relative delays (vertical axis, negative values indicate that the pump pulse precedes the Stokes pulse). It is seen that the system ends up almost entirely in superposition of states $\ket 1$ and $\ket 3$ with only minor amount of population lost in the intermediate state $\ket 2$.
• Figure 4: Final populations in states $\ket 1$ and $\ket 3$ for different values of the initial mixing angle $\alpha$ and the relative phase $\phi$ of the pump and Stokes pulses with identical Gaussian envelopes delayed by $12.75$ fs from each other. See the caption of Fig. \ref{['fig:delphase']} for a detailed description.
• Figure 5: Schematic representation of the relevant energy levels, couplings, and the applied laser fields for studying and controlling the charge migration dynamics in Xe$^+$. Following ionization, a linear combination (represented by the ellipsoids) of the two lowest spin-orbit split ionic states is created. Appropriately tuned "pump" and "Stokes" laser pulses are applied to the system in order to redistribute populations between the initial states using a variant of the Stimulated Raman Adiabatic Passage (STIRAP) technique. Depending on the frequency of the utilized control pulses, the intermediate state for the population transfer can either be (A) one of the low-lying valence electronic states of the cation, or (B) energetically deep core ionic state. The electron dynamics and the influence of the control fields on the system are quantified by measuring the transmission of weak extreme ultraviolet (XUV) probe pulses as a function of time delay.