Entanglement dynamics of second quantized quantum fields

TL;DR

This paper investigates how entanglement evolves in coupled quantum fields, demonstrating that linear couplings only transfer entanglement, while non-interacting modes can still become entangled through indirect interactions, with applications to specific models.

Contribution

It provides a theoretical analysis of entanglement dynamics in quadratic Hamiltonian systems and explores entanglement generation in models without direct mode interactions.

Findings

Entanglement is transferred but not created in linear coupling systems.

Particles in different modes can become entangled without direct interaction.

Photon polarization entanglement increases linearly with photon number in the Jaynes-Cummings model.

Abstract

We study the entanglement dynamics in the system of coupled quantum fields. We prove that if the coupling is linear, that is if the total Hamiltonian is a quadratic form of field operators, entanglement can only be transferred between the fields. We show that entanglement is produced in the model of the two-mode self-interacting boson field with the characteristic Gaussian decay of coherence in the limit of high number of particles. The interesting feature of this system is that the particles in different modes become entangled even if there is no direct interaction between the modes. We apply these results for analysis of the entanglement dynamics in the two-mode Jaynes-Cummings model in the limit of large number of photons. While the photon-atom interaction is assumed to conserve helicity the photons with different polarizations still get entangled due to an effective interaction mediated by the atom with the characteristic entanglement time linearly increasing with the number of photons.