We demonstrate the feasibility of generation of bright ultrashort gamma-ray pulses and the signatures of stochastic photon emission via the interaction of a relativistic electron bunch with a counterpropagating tightly-focused superstrong laser beam in the quantum-radiation-dominated regime. We consider the electron-laser interaction at near-reflection conditions when pronounced high-energy gamma-ray bursts arise in the backward-emission direction with respect to the initial motion of the electrons. The Compton scattering spectra of gamma-radiation are investigated using a semiclassical description for the electron dynamics in the laser field and a quantum electrodynamical description for the photon emission. We demonstrate the feasibility of ultrashort gamma-ray bursts of hundreds of attoseconds and of dozens of megaelectronvolt photon energies in the near-backwards direction of the initial electron motion. The tightly focused laser field structure and radiation reaction are shown to be responsible for such short gamma-ray bursts, which are independent of the durations of the electron bunch and of the laser pulse. Moreover, the quantum stochastic nature of the gamma-photon emission is exhibited in the angular distributions of the radiation and explained in an intuitive picture. Although, the visibility of the stochasticity signatures depends on the laser and electron beam parameters, the signatures are of a qualitative nature and robust. The stochasticity, a fundamental quantum property of photon emission, should thus be measurable rather straightforwardly with laser technology available in near future.
Several signatures of quantum radiation reaction are investigated in the interaction of an electron beam with superstrong focused laser pulses in the radiation dominated regime. Analytic expressions for the electromagnetic fields of an ultrashort, tightly focused, laser pulse in vacuum are derived from scalar and vector potentials, using on equal footing two small parameters connected with the waist size of the laser beam and its duration. Due to the combined effect of the laser focusing and radiation reaction the angular spread of the main photon-emission region has a prominent maximum at an intermediate pulse duration and decreases along the further increase of the pulse duration, and the spectral bandwidth monotonically decreases with rising pulse duration. Those signatures can be used to distinguish the quantum radiation reaction with the classic radiation reaction and are measurable with currently available laser systems.