Editing Tunnel ionization (section)

== Tunneling time ==
The question of how long a tunneling particle spends inside the barrier region has remained unresolved since the early days of quantum mechanics. It is sometimes suggested that the tunneling time is instantaneous because both the Keldysh and the closely related Buttiker-Landauer<ref>{{cite journal | last1=Büttiker | first1=M. | last2=Landauer | first2=R. | title=Traversal Time for Tunneling | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=49 | issue=23 | date=1982-12-06 | issn=0031-9007 | doi=10.1103/physrevlett.49.1739 | pages=1739–1742}}</ref> times are imaginary (corresponding to the decay of the wavefunction under the barrier). In a recent publication<ref>{{cite journal | last1=Landsman | first1=Alexandra S. | last2=Weger | first2=Matthias | last3=Maurer | first3=Jochen | last4=Boge | first4=Robert | last5=Ludwig | first5=André | last6=Heuser | first6=Sebastian | last7=Cirelli | first7=Claudio | last8=Gallmann | first8=Lukas | last9=Keller | first9=Ursula |display-authors=5| title=Ultrafast resolution of tunneling delay time | journal=Optica | publisher=The Optical Society | volume=1 | issue=5 | date=2014-11-14 | issn=2334-2536 | doi=10.1364/optica.1.000343 | page=343 |doi-access=free |arxiv=1301.2766 }}</ref> the main competing theories of tunneling time are compared against experimental measurements using the attoclock in strong laser field ionization of helium atoms. Refined [[Attosecond chronoscopy|attoclock measurements]] reveal a real and not instantaneous tunneling delay time over a large intensity regime.  It is found that the experimental results are compatible with the probability distribution of tunneling times constructed using a [[Feynman path integral]] (FPI) formulation.<ref>{{cite journal | last=Fertig | first=H. A. | title=Traversal-Time Distribution and the Uncertainty Principle in Quantum Tunneling | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=65 | issue=19 | date=1990-11-05 | issn=0031-9007 | doi=10.1103/physrevlett.65.2321 | pages=2321–2324| pmid=10042518 }}</ref><ref>{{cite journal | last=Yamada | first=Norifumi | title=Unified Derivation of Tunneling Times from Decoherence Functionals | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=93 | issue=17 | date=2004-10-18 | issn=0031-9007 | doi=10.1103/physrevlett.93.170401 | page=170401 | pmid=15525052 }}</ref> However, later work in atomic hydrogen has demonstrated that most of the tunneling time measured in the experiment is purely from the long-range Coulomb force exerted by the ion core on the outgoing electron.<ref>{{Cite journal |last1=Sainadh |first1=U. Satya |last2=Xu |first2=Han |last3=Wang |first3=Xiaoshan |last4=Atia-Tul-Noor |first4=A. |last5=Wallace |first5=William C. |last6=Douguet |first6=Nicolas |last7=Bray |first7=Alexander |last8=Ivanov |first8=Igor |last9=Bartschat |first9=Klaus |last10=Kheifets |first10=Anatoli |last11=Sang |first11=R. T. |last12=Litvinyuk |first12=I. V. |date=April 2019 |title=Attosecond angular streaking and tunnelling time in atomic hydrogen |url=https://www.nature.com/articles/s41586-019-1028-3 |journal=Nature |language=en |volume=568 |issue=7750 |pages=75–77 |doi=10.1038/s41586-019-1028-3 |pmid=30886392 |hdl=10072/387846 |s2cid=81977455 |issn=1476-4687|hdl-access=free }}</ref>