Saydanzad Group

Active · 2021 –

Ultrafast dynamics of molecular Rydberg states

A time-domain Fano model for autoionizing Rydberg states in molecules, applied to CO₂ and compared against pump–probe measurements.

Two panels. Left: an infrared and an XUV pulse separated by a delay t_d ionize a CO2 molecule, releasing an electron. Right: an energy level diagram running from the CO2 ground state up through the CO2+ X state at 13.78 eV to the B state at 18.08 eV and the infrared ionization threshold at 19.25 eV, showing the Henning sharp and diffuse Rydberg series, the direct-ionization and XUV-excitation pathways, and autoionization into the epsilon-p-pi-u continuum.
The two pathways that interfere. An XUV photon can ionize CO₂ directly into the continuum, or excite a Rydberg state below the \(B\,^2\Sigma_u^+\) threshold that then autoionizes into that same continuum. Because the final states are identical, the two routes interfere. The delay \(t_d\) to the infrared pulse resolves the process in time.
Molecular Rydberg statesAutoionizationTime-domain Fano theoryNonadiabatic dynamics

The question

A molecule excited into a Rydberg state above its ionization threshold is degenerate with the continuum and leaks into it. This is autoionization, and the interference between the direct and resonant paths to the same final state produces the asymmetric Fano lineshape described in 1961.

A Fano profile, however, is a spectrum: it is what remains after the process has finished, and it carries no direct record of the order in which things happened. In a molecule that matters, because the nuclei move while the electronic dynamics unfold. The state can predissociate as well as autoionize, electronic and nuclear motion are coupled, and the Born–Oppenheimer separation that makes molecular structure tractable is exactly what fails here.

Approach

We developed a general analytical model based on the Fano formalism, so that the interference is something that accumulates over a computable interval rather than a shape fitted after the fact. An XUV pulse prepares the Rydberg wave packet and a delayed near-infrared pulse ionizes it while it decays; scanning the delay resolves the decay as it happens.

CO₂ is the working case, because the relevant structure is well characterized and there are measurements to check against. Ground-state CO₂ is excited by an attosecond XUV pulse train into the \(nd\sigma_g\) Henning-sharp and \(ns\sigma_g\) Henning-diffuse Rydberg series, and a delayed near-infrared probe ionizes those states to the \(B\,^2\Sigma_u^+\) limit. Using Fano parameters and solving the time-dependent Schrödinger equation, we simulate the build-up and decay of the resonant states and the photoelectron yields measured as a function of delay.

Open problems

Beyond Born–Oppenheimer. The lifetimes of autoionizing states — and predissociative states especially — are comparable to nuclear motion timescales, so the nuclei cannot be treated as fixed. Extending the model to keep the nonadiabatic couplings would give access to nonadiabatic transitions, vibronically modified autoionization, and ultrafast predissociation, all of which are visible as distortions of the asymmetric Fano lineshape.

The inverse problem. Given a measured delay-dependent yield, how much of the underlying nuclear–electronic dynamics can actually be recovered, and how much is lost to the averaging the measurement performs? This is the same class of question as in the nanoparticle work, and the two projects tend to borrow methods from each other.

A manuscript on time-resolved Rydberg dynamics in molecules is in preparation.

Figures

A three-dimensional contour plot of photoelectron yield against electron energy from 3.2 to 4.2 eV and time up to 300 femtoseconds, with line-outs drawn at 60, 150 and 300 femtoseconds showing progressively sharper and more structured peaks.
Why the time domain is worth the trouble. The same autoionizing resonance is shown as it builds up over 60, 150 and 300 fs: the structure is not present from the start but sharpens as the interference accumulates. A frequency-domain Fano profile is the last of these curves only, with no record of the order in which it formed.

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