Study of spin states in vacuum pair production via the Dirac-Heisenberg-Wigner formalism

TL;DR

This paper develops a general spin-resolved momentum distribution for electron-positron pairs produced from the QED vacuum under strong external fields by integrating the covariant spin projection operator with the Dirac-Heisenberg-Wigner (DHW) formalism. It shows that helicity-resolved distributions are a special case of the spin-resolved framework and provides explicit expressions for f_s^{±} in terms of DHW components, with special reductions when the field is spatially homogeneous. Numerical studies for a left-handed circularly polarized field reveal that with zero z-component of the spin direction, spin-up and spin-down densities are equal but their momentum distributions are anisotropic; when z-component is nonzero, large spin-density differences can arise due to angular-momentum transfer in multiphoton absorption, which decrease as field strength increases or frequency decreases. The work elucidates angular-momentum transfer from fields to matter in extreme environments, links spin asymmetry to production mechanisms (multiphoton vs tunneling), and extends the DHW-based spin analysis to general spin states and potentially to spatially inhomogeneous fields.

Abstract

A general spin-resolved momentum distribution of electron-positron pairs produced in strong external fields is derived by combining the covariant spin projection operator and the Dirac-Heisenberg-Wigner (DHW) formalism. The result shows that the spin-resolved and helicity-resolved momentum distributions given in previous literature are actually two special cases of it. For any spin-direction unit vector, numerical investigations demonstrate that when the $z$-component of the unit vector vanishes, the number density of produced spin-up and spin-down particles is equal, while their momentum distributions have some asymmetry. For a nonzero $z$-component of the unit vector, there is a difference of $1-3$ orders of magnitude in the number density of spin-up and spin-down particles induced by angular momentum transfer in multiphoton absorption. Moreover, as the electric field strength increases and/or the field frequency decreases, the asymmetry between the spin-up and spin-down particle number density decreases rapidly. These results offer an approach to study general spin states in vacuum pair production, and enhance our understanding of angular momentum transfer from fields to matter in extreme environments.

Figures (5)

• Figure 1: The spin-resolved momentum distribution functions and the spin asymmetry degree $\kappa$ of positrons for selecting $\mathbf{s}=(1/\sqrt{2}, 1/\sqrt{2}, 0)$. Panels (a) and (d) correspond to the spin-up case, while panels (b) and (e) correspond to the spin-down case. Panels (c) and (f) denote the spin asymmetry degree. The first and second rows correspond to the momentum planes $(q_x=0, q_y, q_z)$ and $(q_x, q_y=0, q_z)$, respectively. The electric field parameters are $E_0=0.5E_{\mathrm{cr}}$, $\Omega=0.5m$, and $\sigma=5$.
• Figure 2: The spin-resolved momentum distribution functions and the spin asymmetry degree $\kappa$ of positrons for choosing $\mathbf{s}=(1/\sqrt{2}, 0, 1/\sqrt{2})$. Panels (a), (d), and (g) correspond to the spin-up case, while (b), (e), and (h) represent the spin-down case. Panels (c), (f), and (i) denote the spin asymmetry degree. The first, second, and third rows correspond to the momentum planes $(q_x, q_y, q_z=0)$, $(q_x=0, q_y, q_z)$, and $(q_x, q_y=0, q_z)$, respectively. The electric field parameters are $E_0=0.5E_{\mathrm{cr}}$, $\Omega=0.5m$, and $\sigma=5$.
• Figure 3: The spin-up particle number density (left panel) and the spin-down particle number density (right panel) for any spin-direction unit vector $\mathbf{s}=\left( s_x, s_y, \sqrt{1-s_{x}^{2}-s_{y}^{2}} \right)$. The electric field parameters are $E_0=0.3\sqrt{2}E_{\mathrm{cr}}$, $\Omega=0.65m$, and $\sigma=13\sqrt{2}$.
• Figure 4: The spin asymmetry degree $\kappa_N$ as a function of the electric field amplitude $E=E_0/\sqrt{2}$ for the spin-direction unit vector $\mathbf{s}=(0, 0, 1)$. The solid gray line represents the fitted curve for $\kappa_N$. Other electric field parameters are $\sigma=10\sqrt{2}$ and $\Omega=0.5m$ for the upper panel, and $\sigma=13\sqrt{2}$ and $\Omega=0.65m$ for the lower panel.
• Figure 5: The spin asymmetry degree $\kappa_N$ as a function of the electric field frequency $\Omega$ for the spin-direction unit vector $\mathbf{s}=(0, 0, 1)$. The blue dashed line and red dotted line represent the results in the momentum planes $q_z=0$ and $q_z=0.3m$, respectively. Other electric field parameters are $E_0=0.1\sqrt{2}E_{\mathrm{cr}}$ and $\sigma=20\sqrt{2}\Omega/m$.