Probing coherent electronic superpositions of singly- and doubly-excited states of krypton with attosecond four-wave mixing spectroscopy

TL;DR

The study addresses how to resolve and control coherent superpositions of singly- and doubly-excited autoionizing states in krypton using tunable attosecond four-wave mixing with XUV pulse trains and non-commensurate IR pulses. A minimal multichannel quantum defect theory model is developed to describe the XUV-induced wave packet and the IR-driven two-photon transitions, including intermediate dark states and multiple symmetry channels. The authors observe quantum beats in krypton that arise from interference between SE and DE states and show quantitative agreement between experiment and MQDT predictions, including energy- and IR-frequency dependencies. This work provides a practical metrology framework for probing and steering correlated electronic states in complex atomic systems and lays the groundwork for all-optical control of autoionizing wave packets.

Abstract

Radiative nonlinear four-wave mixing can monitor the evolution of electronic wave packets, providing access to lifetimes and quantifies the light induced couplings between excited states. We report the observation of quantum beats in an autoionizing electronic wavepacket in krypton, probed using this technique. Analysis of the signal reveals that these beats originate from the contribution of previously unassigned, doubly excited states interacting with singly excited ones. We introduce a minimal theoretical model, based on multichannel quantum defect theory, that quantitatively reproduces both the wavepacket dynamics and the static spectrum. This work combines a versatile, background-free experimental scheme with a tractable model, establishing a powerful approach for the metrology and control of complex, correlated electronic states.

Figures (7)

• Figure 1: Experimental setup for tunable FWM spectroscopy. The fundamental NIR pulse is split in two parts. One arm (red) is used to generate XUV APT (purple) through HHG. In second arm, it is converted into tunable IR pulses (green) using an OPA. Subsequently, these pulses drive and control FWM processes in krypton, which are monitored by the XUV spectrometer.
• Figure 2: Energy diagram for the four wave mixing process. Solid lines indicate the experimental value of the states, and the dashed lines indicate the position predicted by the MQDT model. The arrows indicate the induced couplings by the reference 17th Harmonic (cyan arrow and bell curve) which creates the initial wave packet. From here the pathways induced by the IR (red arrows) interfere in the final $J=1$ states from which emission is measured in the experiment.
• Figure 3: Reference photoabsorption and photoionization spectra of krypton in the 26.2--27.3 eV range. Our experimental photoabsorption data in vicinity of the 17th harmonic of the XUV pulse (purple-solid line). Adapted photoabsorption from CodlingMadden1972 (yellow-dashed line). Reference photoionization from White1983 (green-dotted line). The features observed correspond to the $4s^{-1}np$ SE (red markers) and the $4p^{4}n{\ell}n^{\prime}\ell^{\prime}$ DE (blue markers) states.
• Figure 4: Tunable FWM emissions in krypton. (a) Reference static photoabsorption spectrum from CodlingMadden1972 with the CM labeled states and the $4s4p^6 np$ series. Panels (b),(c) and (d) show the time dependent difference spectrum $\Delta S$, normalized to the maximum signal value, for different IR frequencies: $1348$ nm (b), $1442$ nm (c) and $1550$ nm (d). Notice the change in strength of the signal at different energies. To bring to a similar scale the transient absorption around the $6p$ state one needs a $\times 10$ factor, while the FWM signal needed to a $\times 20$ factor.
• Figure 5: Theoretical calculation of the population of states at different energies for different values for the IR frequencies. On top we show the time delay calculation and vertical lines indicating the position of the CM15(Red) and the $5p$ states (grey lines). The subsequent panels (b-f) show different frequencies of the IR and the produced oscillations.