Benasque Lectures on Gaussian Bosonic Systems and Analogue Gravity

TL;DR

This paper provides a comprehensive Gaussian phase-space framework for linear bosonic quantum systems, with applications to quantum optics, quantum information, and analogue gravity, including black hole phenomena.

Contribution

It introduces a unified, platform-independent Gaussian formalism for bosonic systems, connecting quantum optics with semi-classical black hole physics and analogue gravity models.

Findings

Formalism covers harmonic dynamics, Gaussian transformations, and state characterization.

Application to Hawking radiation and superradiance in black holes.

Laboratory models simulate black hole phenomena.

Abstract

These notes are adapted from six lectures that I delivered at Analogue Gravity in Benasque 2023. They present the unified Gaussian (phase-space) framework to describe linear bosonic quantum systems, the standard tool in quantum optics and continuous-variable quantum information, emphasizing its simplicity and platform independence, with applications to semi-classical black holes and analogue gravity. Parts (I-III) develop the formalism: from harmonic dynamics and Gaussian transformations to state characterization via moments, Wigner functions, and entanglement measures. Part (IV) applies these tools to semi-classical black holes, discussing Hawking radiation and quantum superradiance in rotating black holes, and laboratory analogues in light-matter systems via toy models.