Electron-positron pair creation in a supercritical static asymmetric potential well

TL;DR

This work addresses vacuum electron-positron pair creation in a static, supercritical asymmetric potential well formed by a subcritical and a supercritical region. It develops an analytical bound-state condition for subcritical asymmetric wells, then extends it to supercritical wells via (i) fitting the $E$–$V_1$ relation for large $V_1$ and (ii) analytic continuation to complex energies, with validation against 1D CQFT showing sub-0.2% accuracy. The discrete peaks in the positron spectrum are tied to resonant states from bound-continuum overlap, and the imaginary part of the complex energy yields the pair-creation rate. The results demonstrate that adjusting the subcritical height can tailor electron energy concentration and that combining a symmetric well with a supercritical step can enhance pair yield beyond the sum of individual contributions, suggesting practical routes to observe vacuum pair production.

Abstract

The electron-positron pair creation in a supercritical static asymmetric potential well, which is composed of a subcritical and a supercritical potential separated by a fixed distance, is investigated using computational quantum field theory. To explain the discrete peaks in the positron energy spectrum, an analytical formula for determining the positions of bound states in a subcritical asymmetric potential well is derived and extended to the supercritical asymmetric potential well in two ways. One of the two methods can not only predict the positions of bound states, but also offer the pair creation rate. This study also reveals that the subcritical potential height can optimize the energy spread of created electrons, providing a new way to produce high-energy electron beams with concentrated energy in experiments. Moreover, it is found that the pair creation rate in a supercritical asymmetric potential well, composed of a subcritical symmetric potential well and a supercritical Sauter potential, exceeds the sum of the pair creation rates produced by each potential individually. This finding suggests a potential method for enhancing pair yield.

Figures (7)

• Figure 1: Sketch of energy levels for an asymmetric potential well (thick red line). The resonant state energy levels (green bar) are shown in the potential well. I, II, and III represent there regions divided by the potential. The parameters of a typical potential are $V_1=2.5c^2$ and $V_2=0.25c^2$.
• Figure 2: The variation of bound state energy with the potential height $V_1$ calculated according to Eq. (\ref{['eqn:bsel']}). Other potential parameters are $V_2=0.25c^2$, $w\rightarrow0$, and $d=\,0.2\mathrm{a.u.}$.
• Figure 3: Energy spectra of created electrons (a) and positrons (b) at $t=0.03\,\mathrm{a.u.}$ for $V_2=0,\,0.1,\,0.25,\,0.4,\,0.5c^2$. Each line is marked with the value of $V_2$. Other potential parameters are $V_1=2.5c^2, w=0.3/c, d=0.2\,\mathrm{a.u.}, N_z=8192, L=16\,\mathrm{a.u.}$.
• Figure 4: Time evolution of the number of positrons created in the step potential with $V_1=3.54c^2, V_2=0$ (black solid line), the asymmetric potential well with $V_1=3.54c^2, V_2=0.95c^2$ (red dashed line), the overlap region between the positive and negative continuum in the asymmetric potential well (blue dotted line), and the overlap region between bound sates and the negative continuum in the asymmetric potential well (green dash-dotted line). Other parameters are $w=0.3/c, d=0.2\,\mathrm{a.u.}, N_z=2048, L=8\, \mathrm{a.u.}$.
• Figure 5: Energy spectra of created positrons at different times. (a) shows the comparison of energy spectra for the asymmetric potential well ($V_1=3.54c^2, V_2=0.95c^2$) and the step potential ($V_1=3.54c^2, V_2=0$) at $t=4.5\times10^{-4}\,\mathrm{a.u.}$. (b) shows the energy spectra for the asymmetric potential well at $t=0.45,\,1.8,\,3.6,\,5.4,\,7.2,\,9.0\times10^{-3}\,\mathrm{a.u.}$ (corresponding to red points in Fig.\ref{['fig:Evolution-Nt']}). The time values are marked on the lines. Other parameters are the same as in Fig.\ref{['fig:Evolution-Nt']}.