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Tunneling time and weak measurement in strong field ionisation

by T. Zimmermann and S. Mishra and B. Doran and D. Gordon and A. Landsman

(Report number 2015-39)

Abstract
Tunnelling delays is 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 average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment. We demonstrate a big discrepancy in strong field ionization between the Bohmian and the weak measurement values of tunneling time, and suggest this arises because the tunneling time is calculated for a small probability post-selected ensemble of electrons. Our results have important implications for interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.

Keywords: strong field ionization, time-independent Schroedinger equation, Bohmian dynamics, hydrogen, helium, quantum mechanical tunneling

@Techreport{ZMDGL15_629,
  author = {T. Zimmermann and S. Mishra and B. Doran and D. Gordon and A. Landsman},
  title = {Tunneling time and weak measurement in strong field ionisation
},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-39},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-39.pdf },
  year = {2015}
}

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