Axial current as the origin of quantum intrinsic orbital angular momentum

Abstract

We show that the axial current density is the physical origin (generator) of quantum intrinsic orbital angular momentum (IOAM). Without the axial current, the IOAM of particles vanishes. Broadly speaking, we argue that the spiral or interference characteristics of the axial current density determine the occurrence of nonlinear or tunneling effects in any spacetime-dependent quantum systems. Our findings offer a comprehensive theoretical framework that addresses the limitations of Keldysh's ionization theory and provides new insights into the angular momentum properties of quantum systems, particularly in tunneling-dominated regimes. Using Wigner function methods, fermionic generalized two-level model, and Berry phase simulations, we predict that IOAM effect can persist even in pure quantum tunneling processes. These results open the door for experimental verification of IOAM effects in future high-intensity QED experiments, such as those using X-ray free electron lasers.

Figures (2)

• Figure 1: Electron momentum distribution function $f_{\mathbf{q}}(+\infty)$ (a--f), intrinsic orbital angular momentum probability density $\mathcal{L}_{\text{IOAM}}$ (g--l), and phase $\arg\left[c_{\mathbf{q}}^{(2)}(+\infty)\right]$ (m--r) are shown in the first, second, and third columns, respectively. Each row corresponds to a different number of photons absorbed by the electron-positron pair: from 1 (first row) to 6 (sixth row). The laser frequencies $\omega_0$ are $2m$, $m$, $0.8m$, $0.5m$, $0.4m$, and $0.3m$, respectively. In the colorbar for $\mathcal{L}_{\text{IOAM}}$, positive (negative) values indicate alignment (opposition) of the angular momentum direction with respect to the $q_z$-axis. Other parameters: $\varepsilon_0 = 0.1$, $q_z = 0$, $N = 6$.
• Figure 2: First row: electron momentum distribution function $f_{\mathbf{q}}(+\infty)$ (a--c); second row: intrinsic orbital angular momentum probability density $\mathcal{L}_{\text{IOAM}}$ (d--f); third row: phase $\arg\left[c_{\mathbf{q}}^{(2)}(+\infty)\right]$ (g--i). Columns correspond to different pair-production regimes: multiphoton-dominated (a, d, g), mixed-mechanism (b, e, h), and tunneling-dominated (c, f, i). The laser frequencies are $\omega_0 = m$, $0.1m$, and $0.02m$, respectively. In the colorbar for $\mathcal{L}_{\text{IOAM}}$, positive (negative) values indicate alignment (opposition) of the angular momentum with the $q_z$-axis. Other parameters: $\varepsilon_0 = 0.1$, $q_z = 0$, $N = 6$.