title: Tunneling Time and Weak Measurement in Strong Field Ionization.
abstract: Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.
authors.affiliation: Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland.|Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland.
authors.forename: Tomáš
authors.initials: T
authors.lastname: Zimmermann
authors.affiliation: Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland.
authors.forename: Siddhartha
authors.initials: S
authors.lastname: Mishra
authors.affiliation: Department of Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland.
authors.forename: Brent R
authors.initials: BR
authors.lastname: Doran
authors.affiliation: Radiation and Acceleration Physics Section, Naval Research Laboratory, Washington, D.C. 20375, USA.
authors.forename: Daniel F
authors.initials: DF
authors.lastname: Gordon
authors.affiliation: Seminar for Applied Mathematics, ETH Zurich, CH-8093 Zurich, Switzerland.|Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland.|Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany.
authors.forename: Alexandra S
authors.initials: AS
authors.lastname: Landsman