Benasque Lectures on Gaussian Bosonic Systems and Analogue Gravity

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.

💡 Research Summary

The manuscript “Benasque Lectures on Gaussian Bosonic Systems and Analogue Gravity” is a comprehensive set of lecture notes derived from six talks delivered at the Analogue Gravity workshop in Benasque in 2023. Its primary aim is to present the Gaussian (phase‑space) formalism for linear bosonic quantum systems—a framework that underlies quantum optics, continuous‑variable quantum information, and many-body physics—and to demonstrate how this formalism can be applied to semi‑classical black‑hole phenomena such as Hawking radiation and superradiance, as well as to laboratory analogues of curved‑spacetime effects.

The first part introduces the quantum harmonic oscillator in the familiar textbook language and then lifts the description to a real 2N‑dimensional phase space for N coupled modes. The canonical operators are collected into a vector (\hat r=(\hat q_1,\hat p_1,\dots,\hat q_N,\hat p_N)^T) satisfying the canonical commutation relations (