  Impacts of quantum stochasticity on the dynamics of an ultra-relativistic
electron beam head-on colliding with a linearly polarized ultra-intense laser
pulse are theoretically investigated in a quasi-classical regime. Generally,
the angular distribution of the electron beam keeps symmetrically in transverse
directions in this regime, even under the ponderomotive force of the laser
pulse. Here we show that when the initial angular divergence $\Delta \theta_i
\lesssim 10^{-6} a_0^2$ with $a_0$ being the normalized laser field amplitude,
an asymmetric angular distribution of the electron beam arises due to the
quantum stochasticity effect, via simulations employing Landau-Lifshitz,
quantum-modified Landau-Lifshitz equations, and quantum stochastic radiation
reaction form to describe the radiative electron dynamics respectively. The
asymmetry is robust against a variety of laser and electron parameters,
providing an experimentally detectable signature for the nature of quantum
stochasticity of photon emission with laser and electron beams currently
available.
