Sub-cycle metrology of bright quantum light
In quantum optics, quantization of the electromagnetic field typically occurs in a finite volume - a cavity - which results in discrete frequency modes where photons are created, annihilated and exchanged between such modes. As a result, evolution of quantum optical states is periodic in the carrier wave of the field, measurement protocols return cycle-averaged information, and any sub-cycle evolution that is foundational to many light-matter interactions, especially at high field strengths, remains hidden. Adapting an attosecond technique, here we capture the electric-field evolution of a quantum optical state, femtosecond bright squeezed vacuum, with sub-cycle precision. We find that it consists of many stochastic, time-localized bursts within each pump pulse whose phase randomly switches between two values. We exploit the random phase flips to generate quantum random bit sequences with a generation rate that can reach petahertz frequencies. In addition, the sub-cycle resolution allows us to measure coherence functions of the waveforms between any two times, which we explain with a superposition of time-limited modes. These results bridge attosecond metrology and quantum optics and pave the way to measuring quantum light-matter interactions as they evolve on a few-femtosecond time scale, and integrate quantum randomness in petahertz electronics.