Phase-space description of photon emission

Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making "snapshots" of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.