Historical research guide · 1017 · 2008
Attosecond light-pulse-induced photoassociation
Paula Rivière · Camilo Ruiz · Jan-Michael Rost
In one minute
Paula Rivière, Camilo Ruiz and Jan-Michael Rost propose a new use for the shortest light pulses anyone can make. The usual attosecond experiment tears an electron loose and watches it leave. Here the second pulse does the opposite — it puts the electron back. One attosecond pulse frees an electron from one proton, the electron travels, and a second attosecond pulse arriving just as the packet reaches a second proton some distance away drives it into a bound state there. The authors call it induced photoassociation, and their fully time-dependent quantum calculations for a stretched hydrogen molecular ion show the recapture probability peaking sharply at one particular delay between the pulses, which turns that delay into a ruler for the distance between the two nuclei. Because the bare process is weak they add two amplifiers: a weak infrared field whose phase speeds the travelling electron up or slows it down, and a train of attosecond pulses instead of a single pair. Together those lift the recapture by three orders of magnitude.
Connection
Chapter 5 treats an electron as a wave you can steer rather than a bullet you can only fire, and this is that idea at its sharpest: the arrival time of a wave packet, controlled to attoseconds, decides whether a nucleus captures it or not. Chapter 10 owns the control knob, because what does the steering here is the phase of the driving field rather than its energy — the weak infrared pulse adds almost no recapture on its own and changes the outcome by a factor of about eighteen hundred purely by when its crest arrives.
From the source
The paper introduces a process, not just a measurement: induced photoassociation, in which an attosecond probe pulse causes an ion to recapture a continuum electron that an earlier attosecond pump pulse had freed at a different atomic centre. It is stimulated photo-absorption triggered by the attosecond photon field, and the authors are explicit that its bare probability is low, because the window during which it can happen is only as long as the pulse.Abstract and Section I Introduction, arXiv preprint 0802.0122
The demonstration is a fully time-dependent quantum calculation, in one and in two spatial dimensions, for the simplest system that can show the effect: two fixed protons forty atomic units apart with one electron, the stretched hydrogen molecular ion. The fixed-nuclei approximation is justified rather than assumed — the protons move less than half an atomic unit during a typical pump-probe interval of about fifty atomic units.Section II, with equations 1 to 4, arXiv preprint 0802.0122
Recapture peaks at one specific delay, and the peak position can be predicted. A free-electron flight-time estimate works only for the most energetic case tested, a forty-nanometre pump; including the potential energy of the two nuclei in the electron’s classical trajectory predicts the optimum delay to within about eight to ten per cent at all three wavelengths tested in one dimension, and six to twelve per cent in two dimensions. Longer wavelengths predict the optimum less accurately but give higher absorption probabilities, which may suit an experiment better.Section III, equations 5 to 7 with Figures 2 and 4, arXiv preprint 0802.0122
There is a laboratory observable. Recapture at the far centre removes flux that would otherwise escape in that direction, so the forward-to-backward asymmetry of the outgoing electron flux along the polarisation axis peaks exactly where the recapture peaks, and the effect can be read from the outgoing proton or electron signal. The authors add the caveat that matters for a real experiment: the asymmetry is never zero, because the second well reflects part of the outgoing wave, so detection should key on the shape of the curve and not on its absolute value.Section III, equations 12 to 16 with Figure 3, arXiv preprint 0802.0122
Attosecond pulse trains come with their delay fixed by the infrared field that generates them, which would kill the delay-scanning scheme. The authors get the control back by moving a different knob: adding a synchronised infrared field of ten to the thirteenth watts per square centimetre and varying its carrier-envelope phase accelerates or decelerates the freed electron on its way across. At one phase the recapture probability is about fifty times larger than with no infrared field at all, and the contrast between the best and the worst phase is about eighteen hundred, while the infrared field alone produces negligible recapture. The phase, not the energy, is doing the work.Section IV, equation 17 with Figures 5, 6 and 7, arXiv preprint 0802.0122
The proposed recipe for making the effect large enough to see: use a train rather than a pair. With two, four and eight attosecond pulses in the train the enhancement at the optimal infrared phase rises from fifty to four hundred and eighty to fifteen hundred and thirty, and a simple population-transfer recursion, with the first pulse ionising about 3.64 per cent of the initial state, puts the maximum transfer at about twenty-nine pulses. Longer trains are also the easier thing to generate experimentally. The authors name the payoff: microscopic time-of-flight measurement of atomic distances in situations where static diffraction methods fail, such as a molecule whose ions are rapidly exploding or rearranging.Section V, equation 18 with Figure 8, and Section VI Conclusions and Outlook, arXiv preprint 0802.0122
The way in
https://doi.org/10.1103/physreva.77.033421How to cite it
Paula Rivière, Camilo Ruiz, Jan-Michael Rost (2008) Attosecond light-pulse-induced photoassociation doi:10.1103/physreva.77.033421