Tunnelling is one of the key features of quantum mechanics. A related debate, ongoing since the inception of quantum theory, is about the value, meaning and interpretation of 'tunnelling time' 1-5 . Simply put, the question is whether a tunnelling quantum particle spends a finite and measurable time under a potential barrier. 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 attosecond metrology 6 , which gave physicists experimental access to the attosecond (1 as = 10 -18 s) domain. It is at this time scale

We present a detailed experimental and theoretical study on the relativistic non-dipole effects in strong-field atomic ionisation by near-infrared linearly-polarised few-cycle laser pulses in the intensity range 10 14 -10 15 W/cm 2 . We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly ab-initio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counter-intuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between experimental results and theoretical predictions.

Dissociation of diatomic molecules with odd number of electrons always causes the unpaired electron to localize on one of the two resulting atomic fragments. In the simplest diatomic molecule H2+ dissociation yields a hydrogen atom and a proton with the sole electron ending up on one of the two nuclei. That is equivalent to breaking of a chemical bond—the most fundamental chemical process. Here we observe such electron localization in real time by performing a pump–probe experiment. We demonstrate that in H2+ electron localization is complete in just 15 fs when the molecule’s internuclear distance reaches 8 atomic units. The measurement is supported by a theoretical simulation based on numerical solution of the time-dependent Schrödinger equation. This observation advances our understanding of detailed dynamics of molecular dissociation.