Revealing the Berry phase under the tunneling barrier

In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the Hall effect, orbital magnetism, and polarization. Resolving the quantum nature of these processes commonly requires sensitive quantum techniques, as tunneling, being the dominant mechanism in STM microscopy and tunneling transport devices. In this study, we integrate these two phenomena - geometrical phases and tunneling - and observe a complex-valued Berry phase via strong field light matter interactions in condensed matter systems. By manipulating the tunneling barrier, with attoseconds precision, we measure the imaginary Berry phase accumulated as the electron tunnels during a fraction of the optical cycle. Our work opens new theoretical and experimental directions in geometrical phases physics and their realization in condensed matter systems, expanding solid state strong field light metrology to study topological quantum phenomena.