Plasmonics

Several delay times have been proposed: the phase time (stationary phase approximation), the dwell time, the local Larmor time, the Büttiker-Landauer (LB) traversal time [1]. We will first introduce the subject by discussing the difference of these times focusing mainly on the phase time and the LB traversal times who have a “simple” interpretation. After this introduction, we will present our measurement realized in a metallic tunnel junction. In this experiment, by combining optical and electronic measurements, we estimate this traversal time at around 1.1 femtosecond in agreament with the LB theoretical prediction. Measuring this traversal time requires current measurements at optical frequencies and remains challenging. However, it has been known for more than 40 years that as soon as the bias voltage exceeds one volt, the junction emits infrared radiation as an electrically driven optical antenna [2]. We demonstrate here that the photon emission results from the fluctuations of the current inside the tunneling barrier. Photon detection is then equivalent to a measurement of the current fluctuations at optical frequencies, allowing to probe the tunneling time. Based on this idea, we perform optical spectroscopy and electronic current fluctuation measurements in the far from equilibrium regime. Our experimental data are in very good agreement with theoretical predictions based on the Landauer-Büttiker scattering formalism. By combining the optics and the electronics, we directly estimate the so-called traversal time [3]. Finally, we will talk about recent results concerning the measurement of tunnel time in atomic hydrogen [4]. The system is totally different and it puts an upper limit of 1.8 attoseconds on possible delays due to tunneling. The author confirm that, in atomic H, tunnelling is instantaneous within their experimental and numerical uncertainty. The difference between these two recent experimental results shows how much this old subject is still relevant.

[1] R. Landauer & T. Martin. Barrier interaction time in tunneling. Review of Modern Physics. 66, 217 (1994).

[2] J. Lambe & S. L. McCarthy. Light emission from inelastic electron tunneling. Physical Review Letter. 37, 923 (1976).

[3] P. Février & J. Gabelli. Nature Communications, 9, 4940 (2018).

[4] U. Satya Sainadh et al. Attosecond angular streaking and tunnelling time in atomic hydrogen. Nature 568, 75–77 (2019).