Polarized ultrashort brilliant multi-GeV $\gamma$-rays via single-shot laser-electron interaction.

Generation of circularly-polarized (CP) and linearly-polarized (LP) $\gamma$-rays via the single-shot interaction of an ultraintense laser pulse with a spin-polarized counterpropagating ultrarelativistic electron beam has been investigated in nonlinear Compton scattering in the quantum radiation-dominated regime. For the process simulation a Monte Carlo method is developed which employs the electron-spin-resolved probabilities for polarized photon emissions. We show efficient ways for the transfer of the electron polarization to the high-energy photon polarization. In particular, multi-GeV CP (LP) $\gamma$-rays with polarization of up to about 90\% (95\%) can be generated by a longitudinally (transversely) spin-polarized electron beam, with a photon flux at a single shot meeting the requirements of recent proposals for the vacuum birefringence measurement in ultrastrong laser fields. Such high-energy, high-brilliance, high-polarization $\gamma$-rays are also beneficial for other applications in high-energy physics, nuclear physics, and laboratory astrophysics.