Tunneling delay time

2019 Attoclock revisited on tunnelling time

This is the latest update on the electron tunneling time measured with the attoclock technique. Quantum tunneling time is a highly debated topic – we explain why. We discuss the attoclock technique to extract tunneling delays with regards to the typical approximations such as the dipole approximation, non-adiabatic effects, photoelectron momenta at the tunnel exit, electron correlation and exit coordinate. We can confirm that the He attoclock measurement is in agreement with finite tunneling time models. However, the adiabatic approximation gives the wrong field strength calibration which effectively increases the tunnel barrier width (Fig. 13 in Ref. [456] below). Unresolved is the issue of the starting time of the tunneling process. Some results indicate a starting time before the peak of the electric field which would increase the tunneling time shown in Fig. 12 and 13 in Ref. [456] below. Single active electron time-dependent Schrödinger equation (TDSE) calculations overlap with the non-adiabatic data (Fig. 6, in Ref. [456] below) - mostly within the error bars.

Reference:
Ref. [456] C. Hofmann, A. S. Landsman, U. Keller, Invited Paper
Download"Attoclock revisited on electron tunneling time" (PDF, 4 MB)
Journal of Modern Optics, vol. 66, No. 10, pp. 1052-1070 (2019)

Link to News:
https://ulp.ethz.ch/news/ulp-news/2019/04/quantum-tunneling-time-is-a-highly-debated-topic--we-explain-why.html

2014: Attoclock predicts a real tunneling delay time

The attoclock was used to address the fundamental question how long a tunneling particle spends inside the barrier region which has remained an unresolved question since the early days of quantum mechanics. The main theoretical contenders, such as the Buttiker-Landauer, the Eisenbud-Wigner, and the Larmor time give contradictory answers.

Refined attoclock measurements revealed a real tunneling delay time over a large intensity regime. Only two theoretical predictions are compatible within the experimental error: the Larmor time, and the probability distribution of tunneling times constructed using a Feynman Path Integral (FPI) formulation. The latter better predicts a broad tunneling time distribution with a long tail. The implication of such a probability distribution of tunneling times, as opposed to a distinct tunneling time, would imply that one must account for a significant, though bounded and measurable, uncertainty as to when the hole dynamics begin to evolve.

Reference:
Ref. [378] A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, U. Keller
Download"Ultrafast resolution of tunneling delay time" (PDF, 1.7 MB)
Optica, vol. 1, No. 5, pp. 343-349, 2014

Ref. [383] A. S. Landsman, U. Keller - Invited Paper
Download"Attosecond science and the tunneling time problem" (PDF, 2.5 MB)
Physics Reports, vol. 547, pp. 1-24, 2015 (published online 28. Sep. 2014)

2008: An upper limit in electron tunnelling time

It is typically assumed that electrons can escape from atoms through tunneling when exposed to strong laser fields, but the timing of the process has been controversial, and far too rapid to probe in detail. We have used the attoclock to place an upper limit of 34 attoseconds and an intensity-averaged upper limit of 12 attoseconds on the tunneling delay time in strong field ionization of a helium atom in the non-adiabatic tunneling regime.

Attoclock settings:

"Time zero" = angular direction of maximum electric field within intense laser pulse
"Tunneling delay time" = direction of minute hand of accelerating electric field when electron exits the tunnel with respect to minute hand direction of "time zero"

This is the fastest process that has ever been measured directly in the time domain. Our experimental results give a strong indication that there is no real tunneling delay time, which is also confirmed with numerical simulations using the time-dependent Schrödinger equation.

References:
Ref. [279] P. Eckle, A. Pfeiffer, C. Cirelli, A. Staudte, R. Dörner, H. G. Muller, M. Büttiker, U. Keller
DownloadAttosecond ionization and tunneling delay time measurements in helium (PDF, 857 KB)
Science, vol. 322. Nr. 5907, pp. 1525-1529, 2008

Ref. [322] A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, U. Keller
DownloadTunneling time faster than a few tens of attoseconds – confirmed in both Helium and Argon over a large intensity range (PDF, 1.4 MB)
Nature Physics, vol. 8, pp. 76-80, 2012 (online 23. Oct. 2011)