Vacuum polarization current in presence of intense Sauter field

The spontaneous creation of particle-antiparticle pairs from vacuum fluctuations under strong electromagnetic fields - known as the Sauter-Schwinger effect - represents one of quantum electrodynamics’ most profound nonperturbative predictions. A well-known difficulty, however, is that the time-dependent particle number defined via Bogoliubov transformations lacks an unambiguous physical meaning during the field’s evolution, becoming well-defined only once the external field is switched off. This raises the need for alternative observables that remain physically meaningful at all times. Here, we demonstrate that the vacuum polarization current provides such an observable. Focusing on scalar QED in $$(1+1)$$ ( 1 + 1 ) dimensions with a time-dependent Sauter field, we compute the polarization current and analyze its relation to the particle correlation function. We find that the current, unlike the particle number, does not saturate at late times but instead exhibits persistent oscillations around zero–a distinctive signature of scalar systems. Remarkably, this current is shown to be largely unaffected by the choice of adiabatic basis, underscoring its robustness as a probe of pair-creation dynamics.