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Generation of arbitrarily spin-polarized lepton (here refer in particular toelectron and positron) beams has been investigated in the single-shotinteraction of high-energy polarized $\gamma$ photons with an ultraintenseasymmetric laser pulse via nonlinear Breit-Wheeler (BW) pair production. Wedevelop a fully spin-resolved semi-classical Monte Carlo method to describe thepair creation and polarization in the local constant field approximation. Innonlinear BW process the polarization of created pairs is simultaneouslydetermined by the polarization of parent $\gamma$ photons, the polarization andasymmetry of scattering laser field, due to the spin angular momentum transferand the asymmetric spin-dependent pair production probabilities, respectively.In considered all-optical method, dense GeV lepton beams with averagepolarization degree up to about $80\%$ (adjustable between the transverse andlongitudinal components) can be obtained with currently achievable laserfacilities, which could be used as injectors of the polarized $e^{+}e^{-}$collider to search for new physics beyond the Standard Model.

Generation of arbitrarily polarized GeV lepton beams via nonlinear Breit-Wheeler process