Ebook: Quantum Fluids of Light and Matter

The primary goal of the School was to familiarize the emerging generation of young researchers with the fundamental concepts across all key disciplines integral to the realm of quantum fluids of light and matter. The aim was to contribute to their education by instilling the distinctive interdisciplinary mindset essential for engaging in this cutting-edge field of research. Accordingly, lecturers were carefully selected to encompass a broad spectrum of subjects. The lecture notes encapsulated in this book offer an introductory panorama of the principal topics explored throughout the School, providing a foundational understanding for those venturing into the multifaceted landscape of quantum fluids of light.

The lecture by Luigi A. Lugiato provided an historical overview, tracing the evolution from the perspective of nonlinear optics and pattern formation in nonlinear dynamical systems, up to their modern applications in laser and quantum optics devices, such as twin photons generation and quantum imaging. The lectures by Steven Girvin provide an introductory overview of circuit QED and its promise as a platform for the simulation of correlated quantum matter and lattice gauge theories. The lectures by Tomoki Ozawa offer a comprehensive summary of fundamental concepts in topological physics, focusing on the theory of topological bands, renowned topological models, and their recent implementations in atomic and optical platforms. In the lectures by Atac Imamoglu, an overview is provided on quantum photonics in solid-state devices utilizing 2D van der Waals materials. These materials undergo modifications in their optical properties due to the interaction of polaritons with the electron gas. Additionally, novel confinement strategies are explored with the aim of realizing strongly correlated fluids of light. The lectures by Victor Albert introduce bosonic or continuous-variable coding techniques. These methods leverage the intrinsic infinite-dimensionality of bosonic systems, such as electromagnetic signals or mechanical modes, for robust quantum information processing and communication. The focus lies on utilizing electromagnetic signals or mechanical modes for these purposes.

In addition to the lectures documented in this volume of proceedings, we would like to highlight the intriguing presentations by Nicolas Regnault on twisted bilayer graphene as well as the fantastic course on Rydberg atoms and their use as quantum simulators conducted by Hannes Bernien. Further seminars were delivered by the organizers on the physics of superfluidity, topological excitations and dark solitons in quantum fluids of light, on cavity-modified quantum Hall physics and high-impedance multi-mode circuit QED.

The organizers gratefully acknowledge Barbara Alzani and all the SIF staff for their efficient efforts during each stage of the organization of the school.

The school was partially supported by the Pitaevskii BEC Center of INO-CNR (Trento), the Provincia Autonoma di Trento, French ANR project TRIANGLE (ANR-20-CE47-0011) and FET FLAGSHIP Project PhoQuS (grant agreement 820392).

A. Bramati, I. Carusotto and C. Ciuti

We illustrate the rationale according to which the equation formulated in 1987 by Lugiato and Lefever was conceived and discuss the topic of Kerr frequency combs which is governed by such an equation. Some pertinent quantum aspects are finally outlined.

Circuit QED is the application of the language and ideas of quantum optics and cavity QED to superconducting microwave circuits. Microwave resonators play the role of Fabry-Perot cavities and Josephson junction circuits (superconducting qubits) play the role of artificial atoms strongly coupled to microwave photons. The circuit QED architecture is the leading platform for creation of quantum computers based on superconducting circuits. In these lectures we explore current and future applications of this platform to the simulation of correlated quantum matter and lattice gauge theories. The native bosonic modes in this platform make it especially powerful for quantum simulation of physical models containing bosons.

There is an increasing interest in the study of topological phases and topological band structures in the platforms of atomic, molecular, and optical physics (AMO physics), motivated both from the exploration of fundamental science and possibility for practical applications. This paper is intended to explain this exciting field assuming only basic knowledge on quantum mechanics and solid-state physics. After introducing atomic and optical settings where tight-binding lattice models can be realized, we explain basics of topological band structure, focusing on Chern insulators. We then explain how Chern insulators can be realized in the settings of AMO physics, concluding with unique topological phenomena that can be seen in AMO platforms.

These lectures focus on the properties of elementary optical excitations in two-dimensional degenerate electron or hole systems. Transition metal dichalcogenide monolayers and their van der Waals heterostructures constitute an ideal platform to explore this physics. After a brief review of the material system, we will develop a formalism for analyzing exciton-electron as well as polariton-electron interactions. We will then describe how external electric fields could be used to achieve tunable quantum confinement of excitons. When an electron-doped van der Waals heterostructure is embedded inside a microcavity, the interactions between exciton-polaritons could be enhanced, rendering this system of potential interest for exploring strongly correlated photonic systems.

Bosonic or continuous-variable coding is a field concerned with robust quantum information processing and communication with electromagnetic signals or mechanical modes. I review bosonic quantum memories, characterizing them as either bosonic stabilizer or bosonic Fock-state codes. I then enumerate various applications of bosonic encodings, four of which circumvent no-go theorems due to the intrinsic infinite-dimensionality of bosonic systems.