Angular momentum transfer in multiphoton pair production

Abstract

We propose a method to accurately calculate the momentum distributions and the phase distributions of the probability amplitude for both boson and fermion pair production in a spatially homogeneous and time-dependent electric field. Applying this method to multiphoton pair production in a circularly polarized electric field rotating around the $z$-axis, we clarify that the topological charge appearing in the phase distribution of the probability amplitude for pair production reflects the orbital angular momentum (OAM) of the produced pairs rather than that of individual particles. On this basis, we demonstrate that, within the semiclassical framework, the $z$-component of the total angular momentum of the field and the particles is conserved, whereas the conservation of total angular momentum cannot be verified. The results also reveal that the pair production is also constrained by $C$-parity conservation, and that pairs with smaller OAM are produced more favorably. These findings provide deeper insight into angular momentum transfer in pair production.

Figures (4)

• Figure 1: Schematic diagram of the four possible transition modes for a negative-energy electron to the positive-energy continuum under an external field. For the four spin configurations, the $z$-components of the spin angular momentum of the produced electron-positron pairs are $0$, $1$, $-1$, and $0$, respectively.
• Figure 2: The momentum distributions (first column) and the phase distributions of the probability amplitude (second column) for produced bosons. The first and second rows correspond to $q_z=0$ and $q_z=0.2m$, respectively. The electric field parameters are $E_0=0.05E_{\mathrm{cr}}$, $\Omega=0.7m$, $\tau=20$, and $\delta=+1$.
• Figure 3: A comparison between the computational results from our method (second row) and those obtained using the DHW formalism (first row). The left and right columns correspond to spin-up and spin-down particles, respectively. The momentum $q_z$ equals $0.2m$. The electric field parameters are $E_0=0.05E_{\mathrm{cr}}$, $\Omega=0.7m$, $\tau=20$, and $\delta=+1$.
• Figure 4: The four spin-resolved momentum distribution functions $f_{s,s^{\prime}}$ (first row) and the phase distributions of the probability amplitude $\phi _{s,s^{\prime}}$ (second row) for produced electron-positron pairs. Here, $s$ (or $s^{\prime}$) equals $1$ and $2$, representing spin up and spin down, respectively. The momentum $q_z$ is $0.2m$. The electric field parameters are $E_0=0.05E_{\mathrm{cr}}$, $\Omega=0.7m$, $\tau=20$, and $\delta=+1$.