Entanglement in the Schwinger effect

TL;DR

This paper investigates how entanglement is generated in the Schwinger effect within quantum electrodynamics, revealing how thermal fluctuations and electric fields influence quantum correlations for bosons and fermions, with implications for laboratory tests.

Contribution

It provides a mode-by-mode analysis of entanglement in the Schwinger effect for scalar and spinor QED, deriving explicit formulas and identifying conditions for observable quantum correlations.

Findings

Thermal fluctuations enhance particle production but suppress entanglement for bosons.

Fermionic entanglement persists at finite temperature and exhibits a non-monotonic dependence on electric field.

Quantitative estimates suggest feasible experimental regimes to observe quantum effects of the Schwinger process.

Abstract

We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature $T_c$. At fixed $T$, entanglement appears only above a critical field $E_{\text{entang}}$. For fermions, we observe a qualitatively different pattern: the fermionic logarithmic negativity is non-vanishing at finite temperature, and is monotonically suppressed by thermal noise. As a function of the electric field, it is non-monotonic, featuring a temperature-independent optimal field strength $E_*$ and decreasing on both sides of the maximum. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.