# Is it possible to determine timescales of electron dynamics from the natural linewidth of an electronic transition?

A lot of work has been done recently on electron dynamics using attosecond pump-probe techniques; for instance in this paper. In this particular paper, the authors photoionized the neutral tetrapeptide $\mathrm{TrpLeu}_3$ to the cation and observed the repopulation from the HOMO-1 to the HOMO (highest-occupied molecular orbital) of the cation in a time-resolved manner.

Here's my question: Since Heisenberg's uncertainty principle guarantees that the natural linewidth of a energy measurement will be greater than or equal to the inverse of the state's lifetime times $\hbar$, i.e.

$\Delta E \geq \frac{\hbar}{\Delta t}$,

could you just measure the natural linewidth of the photons emitted by the transition between the transient state and the final state and deduce the lifetime of the transient state? Or would the broadening be too large for subfemtosecond states to accurately determine the natural linewidth? Or, would other effects such as Doppler broadening be too large to get a reasonable measurement of the natural linewidth?

Note: I'm a long way out of my field of specialty (computational chemistry) in this question, so I apologize in advance if this makes no sense whatsoever (please tell me why, though, in your answer if this is the case). Also, obviously this would only yield an upper bound for the lifetime; my question is more along the lines of if it would yield an upper bound worth obtaining.

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This is a standard technique for particle physics (where the lifetimes are short and the energy widths therefore large), but for relatively long lifetimes it becomes constrained by questions of energy resolution. I've seen a number of atto-second physics colloquia, but I have no grasp of their energy resolution. – dmckee Dec 2 '10 at 1:44
@dmckee: Thanks for the informative comment. Could you point me to a journal article where this technique is used? I'd try and find it myself, but I'm not even sure what to look for, since I don't know the formal name of the technique. – David Hollman Dec 2 '10 at 14:53
Uhm...Okay, this is kinda embarrassing: I'd have to go hunting. Because this is so common that (as far as I know) it doesn't have a name. Every particle physicist simple knows that lifetimes are found by measuring line widths... A grad school buddy of mine bashed over the $J/\Psi$ and $\Psi'$ peaks for Fermilab's e866 and rediscovering the lifetime was an early validation step for his analysis. – dmckee Dec 2 '10 at 19:10

I don't know a great deal about attosecond spectroscopy, but my inclination is to say that it would be extremely difficult to get a lifetime from a linewidth in this manner. The energy width due to a femtosecond lifetime of the intermediate state would be about 2/3 of an eV, which is a sizable fraction of the energy of a photon of the base laser wavelength (usually they start with something like a YAG or Ti:Sapph, so in the 800-1000nm kind of range, which is between 1 and 1.5 eV photon energy). That means you'd be looking for a spread of frequencies that was almost as big as the excitation frequency, and it's kind of a hassle to extract a linewidth from that sort of thing.

That's the real attraction of the attosecond pump-probe sort of experiments: when you've got that kind of timing resolution, you don't need to try to back time dependence out of broad-band spectroscopic features. You can just measure it directly by stroboscopically following the transition. They can watch electrons redistributing themselves in the molecules directly, by doing an initial excitation, then probing the state at a series of short time steps after the excitation. They can basically make movies of the evolution of the electron wavefunction directly, which is just awesome.

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Thanks for a great answer. It sounds like the idea would work in theory, but in practice the broadening would just be too much for the energy scale of electronic transitions if the time scale is attoseconds or a few femtoseconds. Maybe it would be possible for a small subset of electronic transitions that lasted, say, on the order of 3-5 femtoseconds and had energies on the order of 30-50 keV (but very few interesting things fit this build). I understand the draw of attosecond pump-probe experiments, but I also understand the drawback: they're really expensive – David Hollman Dec 2 '10 at 14:47
@David: with 30 keV, you're already in the hard X-ray region. I don't think there are electronic transition at this energy scale. Maybe for highly ionized atoms ? – Frédéric Grosshans Dec 2 '10 at 15:43
@Frédéric: Deep shell electron from heavy neutral atoms can have ionization energies in the tens of keV range. If you look in the particle data book chapter on the passage of particles through matter (PDF link) there is a graph that shows the edges quite clearly in terms of absorption length as a function of photon energy. – dmckee Dec 3 '10 at 16:12