Fig. 2: Closed and open trajectories of free electrons.

a The displacement of a free electron coupled to a coherent state for various initial moments of the interaction t0, calculated using Newton’s equations of motion. Each trajectory corresponds to a different initial time t0, with the trajectories offset for visibility and their respective y-axes marked with a horizontal gray line. The electric field is depicted in blue. b The excess width of a free electron driven by squeezed vacuum for various initial moments, calculated by numerical time evolution of a Gaussian wavepacket driven by squeezed vacuum (SI section II). Similarly to (a), each trajectory corresponds to a different initial time t0, with the trajectories offset for visibility and their respective y-axes marked with a horizontal gray line. The variance of the electric field is depicted in blue. Both observables (a, b) exhibits “closed” trajectories for initial times t0 between 0 and 0.25 T (solid lines), and open trajectories between 0.25 T and 0.5 T (dashed lines)