ABSTRACT
Ever since its discovery1, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena2. However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.
ABSTRACT
We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and nonlocal operators. This leads to a new critical exponent related to the disorder (as in classical disorder). We show that the time coordinate is rescaled at each renormalization group step, leading to anisotropic spacetime scaling at critical points. We write a universal formula for the dynamical scaling exponent z for weak disorder.
