Pairwise mode entanglement in Schwinger production of particle-antiparticle pairs in an electric field

Abstract

Quantum entanglement is the characteristic quantum correlation. Here we use this concept to analyze the quantum entanglement generated by Schwinger production of particle-antiparticle pairs in an electric field, as well as the change of mode entanglement as a consequence of the electric field effect on an entangled pair of particles. The system is partitioned by using momentum modes.Various kinds of pairwise mode entanglement are calculated as functions of the electric field. Both constant and pulsed electric fields are considered. The use of entanglement exposes information beyond that in particle number distributions.

Schwinger effect of Gaussian correlations in constant electric fields

“…The Schwinger effect of correlations of boson-boson fields has some different features compared with that of fermion-fermion fields. For example, in the case of bilateral Schwinger effect of fermion fields [11], there is no sudden death in the degradation of entanglement between the original fermion modes of particle-particle, and the entanglement between fermion modes of particle-antiparticle and antiparticle-antiparticle can be produced. Further, the entanglement and mutual information between the fermion modes of particle-antiparticle change non-monotonically with the increase of electric field.…”

“…Note that the authors in [11] studied the bilateral Schwinger effect of fermion-fermion fields by use of the first set of measures. We find three differences between the two settings: Firstly, in the degradation of entanglement between fermion modes (p, q), it would not take place entanglement sudden death, or even has nonzero asymptotical value when E 0 → ∞.…”

“…However the transformation coefficients have different structures in different effects, which may lead to different influences to the quantum correlations. The authors in references [11,12] revealed the influence of Schwinger effect to the pairwise quantum correlations of fermion-fermion system and qubit-boson systems respectively. For the sake of completeness, we here want to further study the Schwinger effect of quantum correlations of continuous-variable boson-boson systems.…”

State of a particle pair produced by the Schwinger effect is not necessarily a maximally entangled Bell state

“…This correlation is one of the reason why the Bell state is called a maximally entangled state. Even though it is intuitive to assume that a Schwinger pair's spin state is in one of the Bell states, the pair production is derived in a basis different from the spin basis [12,13]. We will see that the Schwinger pair is not in a Bell state after transforming it to the correct spin basis.…”

“…Since even virtual particle should conserve quantum numbers, they are assumed to be highly correlated or entangled. Especially, the pair's spin state is generally expected to be one of the maximally entangled Bell states [12,13,15] 1 √ 2 (|↑↓ ± |↓↑ ).…”