Attosecond angular streaking and tunnelling time in atomic hydrogen.

Abstract

The tunnelling of a particle through a potential barrier is a key feature of quantum mechanics that goes to the core of wave-particle duality. The phenomenon has no counterpart in classical physics, and there are no well constructed dynamical observables that could be used to determine 'tunnelling times'. The resulting debate^1-5 about whether a tunnelling quantum particle spends a finite and measurable time under a potential barrier was reignited in recent years by the advent of ultrafast lasers and attosecond metrology⁶. Particularly important is the attosecond angular streaking ('attoclock') technique⁷, which can time the release of electrons in strong-field ionization with a precision of a few attoseconds. Initial measurements^7-10 confirmed the prevailing view that tunnelling is instantaneous, but later studies^11,12 involving multi-electron atoms-which cannot be accurately modelled, complicating interpretation of the ionization dynamics-claimed evidence for finite tunnelling times. By contrast, the simplicity of the hydrogen atom enables precise experimental measurements and calculations^13-15 and makes it a convenient benchmark. Here we report attoclock and momentum-space imaging¹⁶ experiments on atomic hydrogen and compare these results with accurate simulations based on the three-dimensional time-dependent Schrödinger equation and our experimental laser pulse parameters. We find excellent agreement between measured and simulated data, confirming the conclusions of an earlier theoretical study¹⁷ of the attoclock technique in atomic hydrogen that presented a compelling argument for instantaneous tunnelling. In addition, we identify the Coulomb potential as the sole cause of the measured angle between the directions of electron emission and peak electric field: this angle had been attributed^11,12 to finite tunnelling times. We put an upper limit of 1.8 attoseconds on any tunnelling delay, in agreement with recent theoretical findings¹⁸ and ruling out the interpretation of all commonly used 'tunnelling times'¹⁹ as 'time spent by an electron under the potential barrier'²⁰.