Spatially Overlapped Partners in Quantum Field Theory

TL;DR

This paper explores the spatial overlap of partner modes in quantum field theory, revealing that partner modes generally share spatial regions with detected particle modes and demonstrating this in an expanding universe context.

Contribution

It provides a general formula for partner modes in free fields and shows that spatial overlap occurs naturally without fine-tuning of detectors.

Findings

Partner modes generally have spatial overlap with particle detection modes.

A general formula for partner modes in Gaussian states is derived.

Memory effects are demonstrated in an expanding universe model.

Abstract

In quantum field theory particles are physically defined as what Unruh-DeWitt particle detectors observe. By detecting a particle mode $A$, a reduced density operator for a quantum state of $A$ is constructed. Even if the entire quantum state of the quantum field is pure, the state of $A$ is not pure but mixed due to entanglement between other subsystems. The partner mode $B$ of the field is defined as a purification partner of $A$ such that the $AB$ system in a pure state. We show that, without any fine-tuning of the particle detector design of $A$, the weighting function of partner $B$ has spatial overlap of that of $A$. We show a general formula of partner $B$ associated with arbitrarily fixed $A$ of a free field in a general Gaussian state. We demonstrate an example of memory effects in an expanding Freedman-Roberson-Walker universe.