Abstract
In quantum electrodynamics with charged fermions, a background electric field is the source of the chiral anomaly which creates a chirally imbalanced state of fermions. This chiral state is realized through the production of entangled pairs of right-moving fermions and left-moving antifermions (or vice versa, depending on the orientation of the electric field). Here we show that the statistical Gibbs entropy associated with these pairs is equal to the entropy of entanglement between the right-moving particles and left-moving antiparticles. We then derive an asymptotic expansion for the entanglement entropy in terms of the cumulants of the multiplicity distribution of produced particles and explain how to re-sum this asymptotic expansion. Finally, we study the time dependence of the entanglement entropy in a specific time-dependent pulsed background electric field, the so-called "Sauter pulse", and illustrate how our resummation method works in this specific case. We also find that short pulses (such as the ones created by high energy collisions) result in an approximately thermal distribution for the produced particles.
Highlights
The notion of entanglement played a key role in the development [1] and validation [2] of quantum mechanics
We derive an explicit relation between the entanglement entropy and the multiplicity distribution of created particles and show how it can be used in practice to reconstruct the entanglement entropy from the knowledge of the cumulants of the multiplicity distribution
The asymptotic expansion we find is the same as the one previously derived in the context of shot noise in quantum point contacts (“full counting statistics”) [28]
Summary
The notion of entanglement played a key role in the development [1] and validation [2] of quantum mechanics. We show that the statistical Gibbs entropy associated with the created pairs is equal to the entanglement entropy between right and left movers (we refer to this as “chiral entanglement”) This result elucidates the microscopic quantum origin of the statistical entropy of the produced state. We derive an explicit relation between the entanglement entropy and the multiplicity distribution of created particles and show how it can be used in practice to reconstruct the entanglement entropy from the knowledge of the (few) cumulants of the multiplicity distribution
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