Entanglement generation in relativistic quantum fields

TL;DR

This paper develops an analytic method to calculate entanglement generated between modes of bosonic quantum fields via Bogoliubov transformations, applicable in quantum optics and curved spacetime scenarios.

Contribution

It provides a general recipe for quantifying entanglement in Gaussian states resulting from Bogoliubov transformations, including a specific example involving accelerated cavities.

Findings

Entanglement can be enhanced by initial single-mode squeezing.

The method applies to all Gaussian states and Bogoliubov transformations.

Potential applications include quantum fields in curved spacetime.

Abstract

We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.