Attosecond angular streaking and tunnelling time in atomic hydrogen

Abstract: Tunnelling, one of the key features of quantum mechanics, ignited an ongoing debate about the value, meaning and interpretation of 'tunnelling time'. Until recently the debate was purely theoretical, with the process considered to be instantaneous for all practical purposes. This changed with the development of ultrafast lasers and in particular, the 'attoclock' technique that is used to probe the attosecond dynamics of electrons. Although the initial attoclock measurements hinted at instantaneous tunnelling, later experiments contradicted those findings, claiming to have measured finite tunnelling times. In each case these measurements were performed with multi-electron atoms. Atomic hydrogen (H), the simplest atomic system with a single electron, can be 'exactly' (subject only to numerical limitations) modelled using numerical solutions of the 3D-TDSE with measured experimental parameters and acts as a convenient benchmark for both accurate experimental measurements and calculations. Here we report the first attoclock experiment performed on H and find that our experimentally determined offset angles are in excellent agreement with accurate 3D-TDSE simulations performed using our experimental pulse parameters. The same simulations with a short-range Yukawa potential result in zero offset angles for all intensities. We conclude that the offset angle measured in the attoclock experiments originates entirely from electron scattering by the long-range Coulomb potential with no contribution from tunnelling time delay. That conclusion is supported by empirical observation that the electron offset angles follow closely the simple formula for the deflection angle of electrons undergoing classical Rutherford scattering by the Coulomb potential. Thus we confirm that, in H, tunnelling is instantaneous (with an upperbound of 1.8 as) within our experimental and numerical uncertainty.

• The paper establishes that tunnelling in atomic hydrogen is effectively instantaneous, with an upper delay limit of 1.8 attoseconds.
• It employs attosecond angular streaking combined with REMI measurements and precise 3D-TDSE simulations to validate experimental findings.
• Simulations replacing the Coulomb potential with a Yukawa model confirm that the observed angular offsets arise solely from Coulomb influences.

Insights into Attosecond Angular Streaking and Tunnelling Time in Atomic Hydrogen

The research paper under consideration presents a comprehensive study on the contentious issue of tunnelling time in quantum mechanics, particularly focusing on the attoclock experiment performed on atomic hydrogen (H). The authors employ a combination of advanced experimental techniques and precise numerical simulations to address the prominent question of whether a tunnelling quantum particle consumes a finite, measurable amount of time under a potential barrier.

Key Experimental and Theoretical Framework

The paper utilizes the attosecond angular streaking (attoclock) method, which leverages circularly-polarized infrared pulses to map time to angle in the polarization plane. The atomic hydrogen system functions as a benchmark due to its simplicity, allowing exact numerical modelling using the three-dimensional time-dependent Schrödinger equation (3D-TDSE). The research involves precise measurements using a Reaction Microscope (REMI) and 770 nm laser pulses with peak varying intensities, corroborated with high-fidelity ab-initio simulations.

A unique feature of the experimental set-up is the usage of slightly elliptically-polarized light pulses to mitigate complications introduced by carrier-envelope phase (CEP) instabilities, allowing for the determination of electron ejection angles more precisely.

Major Findings

The investigation reveals two critical outcomes:

1. Coulomb Potential Influence: The experiments and simulations indicate that the experimentally determined angular offsets of the photoelectrons align well with the 3D-TDSE simulations incorporating the Coulomb potential. When replaced with a short-range Yukawa potential in simulations, the angular offsets consistently reduce to zero across intensities, negating any contribution from tunneling delay.
2. Instantaneous Tunnelling: The alignment between experimental data and theoretical predictions leads to the conclusion that tunnelling in atomic hydrogen occurs instantaneously within the experimental and numerical uncertainties, with an upper limit for any tunnelling delay set at 1.8 attoseconds. This rules out all existing theoretical tunnelling times as the period spent by an electron beneath the potential barrier.

Implications and Future Directions

The findings critically impact the theoretical understanding of quantum tunnelling, suggesting that tunnelling processes in atomic hydrogen might be as instantaneous as quantum mechanics allows. This debunks previous assertions of finite tunnelling times and challenges widely used theoretical models in various quantum phenomena, including Keldysh and Eisenbud-Wigner times, among others.

The work opens avenues for further high-precision experimental research on more complex multi-electron atoms and molecules, potentially unveiling deeper insights into electron dynamics and interactions. Additionally, the prospects of exploring even finer time scales into the zeptosecond domain could offer unprecedented understanding into quantum processes and possibly unfold aspects of wave function collapse, challenging long-held interpretations within quantum mechanics.

Conclusion

This paper significantly contributes to the field of quantum optics and atomic physics by providing compelling evidence and analysis that advocates for the instantaneous nature of tunnelling in atomic hydrogen. This work not only reconciles experimental observations with theoretical simulations but also provides a robust platform for future explorations into the ultrafast electron dynamics of more complex atomic and molecular systems.