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 95% can be generated by a longitudinally (transversely) spin-polarized electron beam, with a photon flux 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, and laboratory astrophysics.

The interaction of an unpolarized electron beam with a counterpropagating ultraintense linearly polarized laser pulse is investigated in the quantum radiation-dominated regime. We employ a semiclassical Monte Carlo method to describe spin-resolved electron dynamics, photon emissions and polarization, and pair production. Abundant high-energy linearly polarized $\gamma$ photons are generated intermediately during this interaction via nonlinear Compton scattering, with an average polarization degree of more than 50%, further interacting with the laser fields to produce electron-positron pairs due to the nonlinear Breit-Wheeler process. The photon polarization is shown to significantly affect the pair yield by a factor of more than 10%. The considered signature of the photon polarization in the pair's yield can be experimentally identified in a prospective two-stage setup. Moreover, with currently achievable laser facilities the signature can serve also for the polarimetry of high-energy high-flux $\gamma$ photons.

Vortex $\gamma$ photons with intrinsic orbital angular momenta possess a wealth of applications in various fields—e.g., strong-laser physics, nuclear physics, particle physics, and astrophysics—yet their generation remains unsettled. In this work, we investigate the generation of vortex $\gamma$ photons via nonlinear Compton scattering of ultrarelativistic electrons in a circularly polarized laser pulse. We develop a quantum electrodynamics scattering theory that explicitly addresses the multiphoton absorption and the angular momentum transfer mechanism. In pulsed laser fields, we unveil the vortex phase structure of the scattering matrix element, discuss how the vortex phase could be transferred to the radiated photon, and derive the radiation rate of the vortex $\gamma$ photon. We numerically examine the energy spectra and beam characteristics of the radiation, while also investigating the influence of finite laser pulses on the angular momentum and energy distribution of the emitted vortex $\gamma$ photons.

We put forward a novel method for producing ultrarelativistic high-density high-polarization positrons through a single-shot interaction of a strong laser with a tilted solid foil. In our method, the driving laser ionizes the target, and the emitted electrons are accelerated and subsequently generate abundant $\gamma$ photons via the nonlinear Compton scattering, dominated by the laser. These $\gamma$ photons then generate polarized positrons via the nonlinear Breit-Wheeler process, dominated by a strong self-generated quasistatic magnetic field ${\mathbf{B}}^{\mathrm{S}}$. We find that placing the foil at an appropriate angle can result in a directional orientation of ${\mathbf{B}}^{\mathrm{S}}$, thereby polarizing positrons. Manipulating the laser polarization direction can control the angle between the $\gamma$ photon polarization and ${\mathbf{B}}^{\mathrm{S}}$, significantly enhancing the positron polarization degree. Our spin-resolved quantum electrodynamics particle-in-cell simulations demonstrate that employing a laser with a peak intensity of about ${10}^{23}\mathrm{W}/{\mathrm{cm}}^2$ can obtain dense ($\gtrsim {10}^{18}{\mathrm{cm}}^{-3}$) polarized positrons with an average polarization degree of about 70% and a yield of above 0.1 nC per shot. Moreover, our method is feasible using currently available or upcoming laser facilities and robust with respect to the laser and target parameters. Such high-density high-polarization positrons hold great significance in laboratory astrophysics, high-energy physics, and new physics beyond the standard model.

The polarization characteristics of the linear Breit-Wheeler (LBW) pair-production process in polarized $\gamma \gamma$ colliders have been investigated via our developed spin-resolved binary collision simulation method. We find that the polarization of $\gamma$-photons modifies the kinematics of scattering particles and induces the correlated energy-angle shift of LBW pairs, and the latter’s polarization characteristic depends on the helicity configures of scattering particles. We confirm that the polarized $\gamma \gamma$ collider with an asymmetric setup can be performed with currently achievable laser-driven high-density x rays and high-brilliance $\gamma$-photon beams to produce abundant polarized LBW pairs, fulfilling the detection power of polarimetries. Our method and results on the polarized LBW process have plenty of significant applications in strong-field physics, high-energy physics and astrophysics, such as calibrating and monitoring the polarized $\gamma \gamma$ collider and challenging the current understanding of astrophysical objects through enhancing the opacity of $\gamma$-photons to exacerbate the inconsistency between some observations and standard models.