Markus Aspelmeyer

Lecture 1. Quantum Optomechanics I: Bringing Massive Mechanical Objects into the Quantum Regime
Lecture 2. Quantum Optomechanics II: Quantum Controlled Solids as Quantum Sources of Gravity
Lecture 3. Probing the Quantum Nature of Gravity I: What Can We Learn (or not) about Quantum Gravity from Experiments?   
Lecture 4. Probing the Quantum Nature of Gravity II: Towards a “Quantum Cavendish” Experiment

 

Pavel Belov

Lecture 1. History of Metamaterials

The lecture will include history of metamaterials and overview of various metamaterials including their properties and related applications. Such phenomena as negative refraction, backward waves and artificial magnetism will be described in detail.

Lecture 2. Subwavelength Imaging by Means of Metamaterials
The use of metamaterials makes possible to overcome diffraction limit for resolution inherent to conventional imaging systems. In the lecture we will discuss various physical mechanisms of imaging with subwavelength resolution and various designs of metamaterial-based super-lenses which allows transmission and manipulation of near-field distributions with resolution much smaller than wavelength of light.

Lecture 3. Wire Metamaterials: Theory and Applications
The metamaterials made of parallel arrays of metallic wires feature plasma-like behavior at frequencies which can be tuned by varying distances between wires and their radii. Also, the wire metamaterials support transmission-line modes featuring dispersion-less propagation. These properties of wire metamaterials make them attractive candidates for creation of various devices enhancing performance of magnetic resonance imaging, wireless power transfer and even haloscopes for dark matter search.

Lecture 4. All-Dielectric Nanophotonics
A resonant magnetic response of dielectric nanoparticles is an interesting alternative to plasmonic resonance of metallic nanoparticles. This phenomenon, also known as magnetic light, makes possible to create many nanophotonic devices including nano-antennae, nano-waveguides and functional all-dielectric metasurfaces.

 

Maxim Chernodub

Title: Quantum Matter in Non-Inertial Frames

Abstract:  Interacting systems can exhibit a rich thermodynamic behaviors when pushed away from the standard "textbook" conditions. In the series of four lectures, we concentrate on quantum field theories in non-inertial settings of rotation and acceleration. As a physically appealing example, we discuss the properties of quark-gluon plasma, which is believed to have been the first primordial ocean that once filled the early universe during the first few microseconds after the Big Bang. Nowadays, closely related conditions can be recreated experimentally: relativistic heavy-ion collisions at modern collider facilities routinely produce short-lived, finite-size droplets of this strongly interacting matter.

In noncentral heavy-ion collisions, the droplets of quark-gluon plasma carry large angular momentum that can also experience strong local accelerations. What makes the subject more exciting from an academical perspective is that the recent experimental and theoretical results reveal puzzling, sometimes controversial, properties of this non-inertial, strongly interacting matter. These developments sparked intense and steadily growing activity in the field.

The first part of lectures is devoted to a formal question of how to extend the statistical-mechanics approach to systems that reside in global thermodynamic equilibrium under non-inertial conditions. In this setting, equilibrium is most cleanly formulated geometrically: the state exhibits stationarity with respect to a timelike flow and satisfies an appropriate covariant Kubo-Martin-Schwinger condition. We highlight the constraints imposed by causality and the global structure of the system, such as the light-cylinder bound in rigid rotation and the role of the Rindler horizon in accelerated frames.

Then, we describe the Barnett effect ("Magnetization of matter by rotation") discovered experimentally in a slowly rotating iron cylinder in 1915. We show how this century-old experiment allows us to learn the properties of the most vortical fluid ever created by humans, the rapidly spinning quark-gluon plasma. We describe in detail the academic bridge between these phenomena provided by the measurements of the spin polarization of hadrons produced by the fireballs of quark-gluon plasma.

On the theoretical side, we argue that quark-gluon plasma possessing high angular momentum can also be modeled in global thermal equilibrium in a controlled setting of numerical Monte Carlo simulations. We review the results of these "numerical experiments" and show that the apparently straightforward and routine first-principle approaches reveal several remarkable and seemingly unrelated thermodynamic properties of (quark)-gluon plasma that cannot be understood even at an intuitive level.

We show that the apparent puzzles observed in numerical simulations are related to the surprising violation of the (also century-old) Tolman-Ehrenfest picture of thermodynamics in curved spacetime backgrounds (the question, "What is the weight of heat?" was first asked in 1930). In a parallel line of reasoning, we present an introduction to gravitational anomalies and illustrate how they affect the "weight" and transport of heat that can, possibly, explain these puzzles. A low-dimensional and explicitly solvable model is elaborated in detail as an academic example of the anomalous breaking of the Tolman-Ehrenfest (also known as Luttinger) relation in stationary gravitational backgrounds.

As we explore non-inertial thermodynamics further, we also pose a simple yet closely related question: how does uniform acceleration affect the phase structure of thermal matter? Can the acceleration be accounted for as a thermal property inspired by the Unruh effect? Does the acceleration heat the matter up, cool it down, or not affect it at all?

We conclude the lectures by posing the provocative question of whether a closed system can possess a negative moment of inertia and, if true, how this system might be related to time crystals made of quark-gluon plasma.

Hong Ding

Title: Probing Novel Quasiparticles in Solid Universes

Maxim Gorlach

Lecture 1. Introduction to Quantum Brachistochrone Method

Ancient brachistochrone problem posed in XVII century by J. Bernoulli aimed to find a curve of the quickest descent between the two points and gave birth to the variational calculus. Nowadays analogous problems arise in many other contexts including quantum physics. Recently emerged quantum brachistochrone method addresses a similar question: how one should vary the Hamiltonian of a quantum system in order to transfer it from the given initial to the desired final state within the minimal possible time given the prescribed constraints on the Hamiltonian. This lecture will introduce the methodology, derive the governing equations and present several simple but instructive examples.

Lecture 2. Applications of Quantum Brachistochrone to Quantum Optimal Control Problems

This lecture will introduce further applications of quantum brachistochrone technique to the multi-qubit systems. Despite the large number of degrees of freedom involved, we will demonstrate that numerical solutions are available unlocking routes to time-optimal manipulation of large-scale quantum systems.

Lecture 3. Crafting Axion Responses in Metamaterials

Artificially structured media allow one to realize tailored and exotic electromagnetic properties. In this lecture, I will introduce axion metamaterials governed by the equations of axion electrodynamics and discuss associated physical phenomena.

Lecture 4. Dual Nature of Axion Response in Photonics and Condensed Matter

This lecture will introduce recently predicted dual axion response arising in photonic and condensed matter structures. Similar to the conventional axion response, it is manifested only at the boundaries of the material and features the same coupling to the incident plane waves. However, the response to the external sources introduced inside is profoundly different. The lecture will introduce the governing equations and representative examples of such structures.

 

Hans Hansson

Title: Quantum Field Theory Anomalies — Some Basics

Abstract:  The two first lectures will cover the basics of anomalies in continuous symmetries. What they are, why they are important and how they are computed. I will illustrate with a couple of examples from high energy physics and condensed matter physics. The last two lectures will be about global anomalies. What they are and why they are important in a condensed matter context. I will illustrate mainly on time-reversal invariant topological insulators, and if there is time, also on topological superconductors and some recent works on the quantum Hall effect. 

 

Qihang Liu

Title: Symmetry Theory of Magnetism

Lecture 1. Spin Group Theory

Abstract: The physical properties in magnetic-ordered materials were ultimately believed to rely on the symmetry theory of magnetic groups. Recently, it has come to light that a more comprehensive group, known as spin (crystallographic) group, which combines separate spin and spatial operations, is necessary to fully characterize the geometry and underlying properties of magnetic-ordered materials. In this lecture, we introduce the recent developments of spin group theory, including extensive enumeration of over 100000 spin space groups, identification of spin groups for collinear, coplanar, and noncoplanar configurations, and irreducible co-representations in momentum space leading to more energy degeneracies that are disallowed by magnetic groups.

Lecture 2. Application of Spin Group Theory and Unconventional Magnetism

Abstract:  With the advancement of antiferromagnetic (AFM) spintronics, magnetic materials with diverse magnetic structures have garnered widespread attention. Of particular interest are “unconventional magnets”, which simultaneously exhibit AFM configurations while displaying properties reminiscent of ferromagnets (FMs). In this lecture, we start with the application of spin group theory on the classification of magnetic order and the homemade online program, FINDSPINGROUP (https://findspingroup.com/), which is applied to diagnose the physical properties of magnetic materials. We then discuss different facets of unconventional magnetism, including spin splitting (altermagnets), anomalous Hall effect, quantum geometry, topological magnons, and multiferroicity.

Chaoyang Lu

Title: Quantum Computing with Photons and Atoms

Abstract:  I will go through our recent efforts using photons and atoms to build increasingly large-scale quantum computers and, in turn, how these early quantum computers can already be used for studies of fundamental problems in mathematics, quantum physics, and condensed matter physics. We start from generating deterministic single and entangled photons from solid state in a cavity QED system (Wang et al. PRL 2019, Ding et al. Nature Photonics 2019, 2025), and use it for interfering with sunlight (Deng et al. PRL 2019) and showing intensity squeezing (Wang et al. PRL 2020). We use the protocol of Gaussian boson sampling to demonstrate quantum computational advantage, with up to 3050 detected photons (Zhong et al. Science 2020, PRL 2021, Deng et al. PRL 2023). In addition, we also show the unconditional quantum metrological advantage and quantum teleportational advantage. We develop an AI-enabled constant-time-overhead rearrangement protocol to prepare a 2024 defect-free atomic array (Lin et al. 2024). Using a single atom trapped in an optical tweezer and cooled to the motional ground state in three dimensions, we faithfully realize the Einstein-Bohr recoiling-slit gedankenexperiment tunable at the quantum limit (Zhang et al. 2025). Based on a bottom-up quantum engineering approach, we experimentally created the fractional quantum Hall state using strongly interacting photons (Wang et al. Science 2024). We further use the quantum computing platform to rule out a real-value description of standard formalism of quantum theory (Chen et al. PRL 2022), and other applications based on Jiuzhang, such as graph problems (Deng et al. 2023), image recognition (Gong et al. 2025) and cryptographic one-way encryption.

 

Mairi Sakellariadou

Title: Gravitational Waves

Abstract:  Gravitational waves, a fundamental prediction of Einstein’s theory of General Relativity, provide a unique observational window into some of the most energetic and otherwise inaccessible processes in the Universe. In these , lectures, we begin with a concise overview of the theoretical foundations of gravitational waves within General Relativity, including their generation, propagation, and classification, as well as a summary of the detection techniques. We then discuss gravitational-wave transients and the gravitational-wave background. Finally, we illustrate how gravitational waves constitute a powerful and novel probe of the early Universe, particle physics beyond the Standard Model, and theories of gravity.

 

Jörg Schmiedmayer

Title: What Can We Know About a Quantum Many-Body System?

Abstract:  Quantum many-body systems form the backbone of modern quantum simulation, yet their complete microscopic description is generically inaccessible for non-trivial strongly correlated systems. For these systems we are not limited by the experimental data but by the computational complexity of the data analysis. A central challenge is therefore to understand what information about a many-body system is experimentally accessible, how this information is structured, and how it can be reliably extracted or manipulated.

In this lecture series, I will discuss complementary approaches to characterizing quantum many-body systems. One route, rooted in quantum field theory, exploits correlation functions, which encode the experimentally accessible structure of quantum fields and their collective excitations, and allow effective low-energy descriptions either directly or through Hamiltonian learning-based inference methods.

A different approach is quantum many-body tomography, which enables access to quantities such as von Neumann entropies and mutual information, and has allowed experimental verification of information-theoretic concepts such as area laws in extended quantum systems. However, present schemes are restricted to Gaussian effective models.

Moreover, many of these analysis techniques are inherently model dependent, relying on prior assumptions about effective Hamiltonians. While powerful, such approaches restrict what can be learned to what is already built into the assumed model. In contrast, our recent work pursues genuinely model-agnostic strategies: we aim to learn the structure and information content of the quantum simulator directly from experimental data, with minimal theoretical bias. This not only opens access to strongly correlated and topological many-body systems beyond Gaussian or perturbative descriptions in and out of equilibrium, but also gives a new way to ‘verify’ quantum simulators and explore their validity.

Beyond static correlations and entropies, transport provides a powerful probe of emergent dynamics. I will present our recent experimental work on measuring Drude weights in a one-dimensional quantum gas, which directly quantifies ballistic transport and dissipationless currents in an interacting many-body system at finite temperature. These experiments combine controlled non-equilibrium protocols with generalized hydrodynamics and physics-informed machine-learning techniques to reconstruct particle and energy currents from sparse experimental data, illustrating how ML can become an integral tool for quantitative analysis of quantum simulators.

Finally, I will address the thermodynamic cost of information processing in many-body systems and discuss experiments probing Landauer’s principle in the quantum many-body regime.

Together, these examples illustrate how correlations, transport coefficients, entropy, and machine-learning-assisted inference form a coherent framework for understanding what can—and cannot—be known about complex quantum systems.

 

Steven Simon

Title 1: Introduction to Anyons and Quantum Information

Title 2: Introduction to Quantum Hall Effects

 

Ye Wang

Title: Trapped-ion Based Quantum Network and Quantum Computing

Abstract:  Trapped ions are among the leading platforms for quantum information processing, offering long coherence times and high-fidelity quantum control. In this lecture, I will briefly introduce the basic principles of trapped-ion systems and review recent progress in trapped-ion–based quantum computing and quantum networks. Key advances in scalable architectures, high-fidelity gate operations, and remote entanglement between ions will be discussed. I will conclude with an overview of the main challenges and future prospects for trapped-ion platforms in large-scale quantum computing and quantum communication.

 

Frank Wilczek

Title: Axions: Fundamentals to Frontiers

Lecture 1. T Symmetry and θ Parameter
Lecture 2. PQ Symmetry, Axion Lagrangian, Laboratory and Astrophysical Constraints
Lecture 3. Axion Cosmology
Lecture 4. Looking for the Cosmic Axion Background