Michael Berry

Lecture 1.

Title: Geometric phases old and new

Abstract: The waves that describe systems in quantum physics can carry information about how their environment has been altered, for example by forces acting on them. This effect is the geometric phase. It occurs in the optics of polarised light, where it goes back to the 1810s; it influences wave interference; and it provides insight into the spin-statistics relation for identical quantum particles. The underlying mathematics is geometric: parallel transport, explaining how falling cats turn, and how to park a car, and the quantum geometric tensor combining curvature and metric, with interesting recently calculated statistics. Incorporating the back-reaction of the geometric phase on the dynamics of the changing environment exposes an unsolved problem: how can a system be separated from a slowly-varying environment? A timeline of the tangled history of the concept will be provided.

Lecture 2.

Title: Chaos and quantum

Abstract: Although envisioned by Einstein in 1917, it was only in the 1970s that the implications for quantum mechanics of chaos in the classical limiting dynamics was recognised as a problem. The solution emerged from several directions. There is no sharp quantum-classical boundary, but rather a rich borderland. For energy levels: semiclassical asymptotics, in the form of Gutzwiller’s trace formula, giving the quantum spectral density as a sum over classical periodic orbits, combined with the recognition that correlations between close-lying levels depend on long periodic orbits, which enjoy a universal phase space democracy, while short orbits give nonuniversal correlations between more distant levels. The universality leads to random-matrix level statistics, and nonuniversality leads to failure of random-matrix theory for distant correlations. A bonus was the discovery that the Riemann zeros share the same statistics. For wavefunctions: semiclassical asymptotics, implying gaussian random functions with a particular spatial correlation, occasionally decorated by scars from unstable periodic orbits. Many-body quantum chaos will be touched on, emphasising that large N will imply asymptotics additional to semiclassical, possibly clashing (cf Anderson’s ‘More is different’).

 

Martin Greiter

Title: Theory of Eigenstate Thermalization (I)

Title: Theory of Eigenstate Thermalization (II)

Abstract: If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is deterministic. The eigenstate thermalization hypothesis (ETH) of Deutsch and Srednicki suggests that this is possible because each eigenstate of the full quantum system acts as a thermal bath to its subsystems, such that the reduced density matrices of the subsytems resemble thermal density matrices. In these lectures, I will use the observation that the eigenvalue distribution of interacting quantum systems is a Gaussian under very general circumstances, and Dyson Brownian motion random matrix theory, to derive the ETH and thereby elevate it from hypothesis to theory. The analysis provides a derivation of statistical mechanics which neither requires the concepts of ergodicity or typicality, nor that of entropy. Thermodynamic equilibrium follows solely from the applicability of quantum mechanics to large systems and the absence of integrability.

The lectures will be self contained and neither assume previous knowledge about eigenstate thermalization nor about random matrix theory.

 

Biao Huang

Title: Shielding and steering a Schrödinger's cat with cat-scar enforced discrete time crystals

Abstract :

Part I: Phenomena and applications in superconducting qubits

Greenberger-Horne-Zeiling (GHZ) state is the qubit-analogue of the famous Schrödinger's cat. These states possess maximal entanglement, making them valuable in quantum technologies, but for a long time, their applications have been limited by their extreme fragility. Here I will discuss a new perspective of the time crystals, originally conceptualized by Frank Wilczek to concretize the spontaneous breaking of time translation symmetries, as an entanglement stabilizer. I will characterize the cat eigenstates hosted by these time crystals, and show that they serve as robust storage medium to protect the fragile GHZ states and lead to time crystalline dynamics of the GHZ states. Further, I would compare the cat eigenstates possibly hosted in time crystals obtained in different ways, i.e. many-body localization, prethermalization, and scarring the Hilbert space with rare Schrödinger's scar eigenstates. Then, I will show that a recent experiment on superconducting qubit put these ideas into practice using the on-demand designed scarring scheme. 

Part II: Theories of Fock space localization

With the phenomenology illustrated in the first set of lectures, we will delve more deeply into the underlying mechanisms, and illustrate a useful Fock space perspective in characterizing many-body physics. In the Fock space, each “site” is made of a bit-string pattern of all physical qubits, while the Hamiltonian terms make extensive connections among these sites. I will discuss in more detail how to analytically quantify the characters of the cat eigenstates, which is crucial to benchmark contemporary quantum computing devices that usually have system sizes far beyond what classical computers can simulate. Further, with the Fock space picture, we would proceed to discuss an ongoing experiment on superconducting qubits measuring wave packet propagation in Fock space outside the cat scar subspace, and illustrate the unusual prethermalization behaviors due to local domain wall constraints. 

Reading materials
Theory: Phys. Rev. B 108, 104309 (2023)
Experiment: Nat. Commun. 15, 8823 (2024)
Analytical framework: PRL 129, 133001 (2022)
Fock space perspective: Phys. Rev. B 104, 024202 (2021)

 

Qingdong Jiang

Title: The Power of Quantum Fluctuations: From Forces to Spectra to Many-Body Physics

Abstract: tba

Lecture 1: A general tour towards Casimir effect and cavity quantum materials

This opening lecture introduces the profound role of vacuum quantum fluctuations in physics. Beginning with the fundamentals of the Casimir effect, I will provide an overview of its physical significance and extend the discussion to recent breakthroughs in cavity quantum materials, offering a preview of the power of quantum fluctuations.

Lecture 2: Casimir physics: force, torque, and friction

In the second lecture, I will guide the audience through a rigorous, step-by-step derivation of key phenomena within the Casimir family, including Casimir forces, torques, and friction. Additionally, I will explain how the diversity and richness of these effects can be understood from a symmetry-breaking perspective.

Lecture 3: Quantum atmosphere: Quantum fluctuations induced anomalous specra

In the third lecture, I will explore how a material’s symmetry breaking imprints its signature onto the surrounding vacuum, a zone referred to as the material's quantum atmosphere. Through illustrative examples, I will demonstrate the manifestations of these effects and their profound implications.

Lecture 4:  Cavity quantum materials: band structure,topology, and magnetism

In the final lecture, I will emphasize the important impact of symmetry-breaking quantum fluctuations on material properties. These fluctuations reshape band structures, amplify interactions, and drive the emergence or destruction of topological phases, such as chiral spin liquids and quantum Hall effect.

 

Lin Li

Title: Quantum photonics and quantum computing with Rydberg atoms

Abstract: Highly excited Rydberg atoms exhibit strong and long-range interactions, opening new possibilities for scalable quantum information processing. Rydberg atom array is high programmable and scalable, features excellent connectivity and allows high-fidelity quantum operations, making it an excellent candidate for large-scale quantum computers. Moreover, the interactions between Rydberg atoms and its matter-light quantum interface provide a new avenue for deterministic control of photonic quantum states. In this lecture, I will discuss the important properties of Rydberg atoms, recent developments in quantum photonics with Rydberg superatoms, and quantum computing based on Rydberg atom arrays.

Part I. Properties of Rydberg atoms

We will begin by exploring the fundamental characteristics of Rydberg atoms, including their enhanced dipole moments, extended lifetimes, response to external fields, and tunable interactions. These unique properties make Rydberg atoms particularly well-suited for applications in quantum photonics, quantum simulation, and quantum computing, enabling the exploration of complex quantum phenomena and the development of advanced quantum technologies.

Part II. Quantum photonics with Rydberg atoms

The lecture will then address recent advancements in quantum photonics using Rydberg superatoms. We will explore how collective excitations in Rydberg atom ensembles can form superatoms, which serve as powerful tools for studying quantum optics. These superatoms enable the creation of efficient quantum interfaces between light and matter, facilitating precise control of photonic quantum states. We will discuss their applications in various quantum optical processes, including quantum memory, single-photon sources, single photon switch and transistors, photonic quantum logic gates, entanglement filters, and quantum nonlinear optics at the single-photon level.

Part III. Quantum computing with Rydberg atoms

We will discuss the rapidly developing field of quantum computing based on Rydberg atom arrays. The lecture will cover the implementation of high-fidelity single-qubit gates through precise laser control, and two-qubit gates leveraging the strong, tunable interactions between Rydberg atoms. We will also explore recent advancement in using Rydberg atom arrays for quantum simulations of complex many-body systems. Additionally, we will examine distributed quantum computing using Rydberg atoms.

 

Allan MacDonald

Titles:  

1. Emergent Models of Moire Materials

2. Twisted Graphene Multilayer Moire Materials

3. Transition Metal Dichalcogenide Moire Materials

4. Equilibrium Electron-hole Fluids in van der Waals materials

Abstract: tba

 

Antti Niemi

Title: Hamiltonian time crystals: From cold atom BEC to molecular motors (I)

Title: Hamiltonian time crystals: From cold atom BEC to molecular motors (II)

Abstract: These lectures provide a theoretical and computational introduction to autonomous, energy-conserving time crystals, with real-world applications to cold atom Bose-Einstein condensates and biomolecular motors. They offer both theoretical insights and practical tools to understand and explore non-driven, autonomous time crystals and related phenomena. The lectures begin with an overview of the mathematical foundation, focusing on the Lagrange Multiplier Theorem in the context of a Hamiltonian system with conditions. Building on the two-dimensional harmonic oscillator as a simple pedagogical example, we highlight how the approach differs from the more familiar use of Lagrange multipliers in constrained systems. Next, we explore the Gross-Pitaevskii equation as a model for cold atom Bose-Einstein condensates, analyzing the topological structure of its vortices through tools like the Brouwer degree and the Poincaré-Hopf index theorem. Connections are drawn to the well-known Kosterlitz-Thouless topological phase transition. The lectures then extend to molecular systems, examining piecewise linear molecular chains and demonstrating how the Lagrange Multiplier Theorem reveals time-crystalline dynamics in one-dimensional, closed molecular chains. We also discuss the interplay between rotational motion and angular momentum in deformable bodies. Finally, the lectures conclude with a short introduction to the computational design of molecular motors at the level of all-atom modeling, using amino acids as the building blocks.

 

Jian-Wei Pan

Title: A Brief Introduction to Quantum Information and Experiments (I)

Title: A Brief Introduction to Quantum Information and Experiments (II)

Abstract: tba

 

Yannis Semertzidis

Titles: Exploring Frontiers in Fundamental Physics

Abstract: Modern physics thrives on the interplay between theoretical breakthroughs and experimental ingenuity. My lectures at the Winter School will offer a journey through transformative ideas and cutting-edge experiments in fundamental physics. From the quest to unravel the mysteries of dark matter to practical lessons on choosing a scientific path, these sessions reflect decades of pioneering work. They also draw upon chapters from my upcoming book, where I share experiences and insights gained from building world-class institutions and advancing the frontiers of science.

1. 1. Building a World-Class Axion Dark Matter Institute in Less Than 10 Years

2. Creating a top-tier research facility is a daunting task, but strategic vision, interdisciplinary collaboration, and a relentless drive can make it possible. This lecture shares the blueprint behind building the IBS-CAPP, now a global leader in axion research.

2. Axion Dark Matter Searches: Status and Prospects

Axions are among the most promising candidates for dark matter. This lecture will provide a detailed overview of the experimental landscape, highlighting breakthroughs and challenges in the field.

3. New Ideas Toward the Next Sensitivity Frontier in Axion Dark Matter Research

Pushing the boundaries of detection requires innovative methodologies. Here, we will explore novel approaches and technologies that promise to redefine sensitivity benchmarks in axion research.

4. The Muon g-2 Experiment and Its History

The muon g-2 anomaly has sparked renewed interest in precision measurements. This lecture traces the experiment's evolution, its scientific implications, and its potential to unveil new physics.

5.Electric Dipole Moments in Storage Rings and Elsewhere

Electric Dipole Moments (EDMs) are powerful probes of CP violation. This session explores into the design and execution of storage ring EDM experiments, their implications for the Standard Model, and their role in probing new physics.

6.1 Basic Science in the Service of Humanity

The pursuit of basic science often leads to unforeseen societal benefits. This lecture reflects on how fundamental research serves humanity, from fostering innovation to addressing global challenges. It goes, however, much deeper than that and we will explore some aspects of it that are rarely discussed.

6.2 How to Choose Your Supervisor

Navigating the early stages of a scientific career can be daunting. This practical session offers insights on selecting a mentor, a decision that shapes not only your research but also your growth as a scientist.

These lectures aim to inspire and empower attendees, blending the rigor of physics with practical wisdom to drive the next generation of discoveries.

 

Frank Wilczek

Title：Lagrangians that Support Time Crystals，and Their Quantization

Title：Lagrangians and Quantization

Abstract:The theme of these lectures is spontaneous breaking of time translation symmetry, a concept that is conveyed in the phrase “time crystals”.   My focus will be on broad principles and simple models, but I’ll also survey recent work and provide references.  Four lectures have been prepared. They are of unequal (and possibly excessive) length, so this description might not correspond neatly to the four sessions.

Lecture 1

Title：Introduction and Survey

Abstract: A very brief historical reminiscence, followed by a description of the 2012 breakthrough experiments on discrete time crystals, followed by a broad overview of recent work on discrete and continuous time crystals.

Lecture 2

Title：Perspectives on Symmetry Breaking

Abstract:A detailed discussion of the Mott-Heisenberg problem (which I’ll define) as an example of spontaneous symmetry breaking by the process of measurement in quantum theory.  Then a perspective on cooperative symmetry breaking, emphasizing its deep commonality.  Finally, a discussion of rigidity and sensitivity as phenomenological hallmarks of spontaneous symmetry breaking, extending the concept of “soft modes” or “Nambu-Goldstone bosons” to temporal and discrete contexts.

Lecture 3

Title： Lagrangians, Hamiltonians, and Quantization

Abstract: A review of how extending the Landau-Ginzburg philosophy to the time domain directs us to smooth Lagrangians whose Hamiltonians are on the cusp of pathology.  How physically sensible models, including quantum models, emerge.  Discussion of paradigmatic examples, including the AC Josephson effect.

Lecture 4

Title：Considerations on Angular Motion

Abstract: Extension of our Mott-Heisenberg analysis to the angular domain.  Motion induced by magnetic fields as a paradigmatic example.  Observability of fractional angular momentum.  Description of very recent work (with Maxim Chernodub) on enhancement of condensation by rotation, leading to a mechanism for substantially increasing the transition temperature of superconducting thin films.

Here is a short list of interesting papers (and a book) related to the lectures:

Shapere and F. Wilczek, Branched Quantization, Phys. Rev. Lett. 192, 200402 (2012).

K. Sacha, Time Crystals (Springer, 2020).

N. Zheludev, Time Crystals for Photonics and Timetronics ; Nature Photonics 18, 1123-1125 (November 2024).

M. Zalatel et al., Colloquium: Quantum and Classical Discrete Time Crystals, Rev. Mod. Phys. 95, 031001 (2023),

M. Chernodub and F. Wilczek, Enhanced Condensation Through Rotation, new on the arXiv

 

Wang Yao

Title: 2D semiconductor moiré superlattices: (I) excitons and valley optics; (II) quantum geometric properties and topological transport

Abstract: 

Van der Waals assembly of 2D atomic crystals has provided a radically new approach to tailor material properties. The resultant layered structures can exhibit customizable characteristics, beyond those of the individual building blocks. Particularly, a rotational misalignment or lattice constant mismatch can lead to the formation of moiré patterns at the interfaces, where interlayer couplings define a new landscape for low-energy carriers and elementary excitations, thereby dramatically modulating the electronic and optical properties. Moiré superlattice physics and twist control of electronic structures started in graphene, with abundant exciting discoveries including the superconductivity in magic-angle twisted bilayer graphene. An equally interesting and perhaps more versatile moiré platform is made possible with the building blocks of 2D semiconductors, i.e. monolayer group VIB transition metal dichalcogenides (TMDs) which feature visible frequency range direct band gap at spin-valley locked band edges. These building blocks display fascinating optical characteristics dominated by excitons formed at the degenerate valleys, whereas the variety of TMDs compounds with disparity in band gap, electron affinity, spin splitting, and modestly different lattice constant offer rich possibilities in designing moiré superlattices for exploring exciton optics as well as other frontier topics of interest. For instance, in TMDs heterobilayer, the band offset between different compounds typically confines the electrons and holes in opposite individual layers, while in homobilayer stackings, layer hybridization in the context of twisting leads to a new approach to tailor quantum geometric properties of carriers, underlying the emergence of nontrivial topology, as well as novel forms of Hall effects under the structural chirality introduced by twisting.

In these lectures, we will introduce the properties of monolayer TMDs and their moiré superlattices, with a focus on two aspects: (I) excitons and valley optics; (II) quantum geometric properties from layer degree of freedom.

Reading materials for part I:

Hongyi Yu, Xiaodong Xu, Wang Yao, Valley excitons: From monolayer semiconductors to moiré superlattices, Semiconductors and Semimetals, Volume 105, 2020, Pages 269-303, https://doi.org/10.1016/bs.semsem.2020.09.00

 

Xiao-Bo Zhu

Title: Superconducting Quantum Computing

Title: Superconducting Quantum Computing with Quantum Error Correction (given by Ke Liu)

Abstract : Quantum computing is widely regarded as the next generation of computing technology because of its overwhelming advantage over classical computers in the processing power of certain problems,so it has attracted widespread attention.Superconducting solutions are currently attracting attention due to their good scalability,and major companies are investing in this field.This report will focus on the current status of superconducting quantum computing and its short-term and medium-term goals,and introduce a series of progress we have made in this direction.  

 

Peter Zoller

Title: Quantum Noise in Quantum Optics: a quantum information perspective (I)

Title: Quantum Noise in Quantum Optics: a quantum information perspective (II)

Abstract: Quantum optical systems of atoms coupled to light represent leading platforms for implementing quantum information processing, which encompasses quantum computing, quantum simulation, quantum networks, and quantum metrology. This course begins with a brief overview of quantum optical model systems, as well as Hamiltonian and quantum entanglement engineering, specifically illustrated within the context of laser-controlled trapped ion systems. The core of the lectures focuses on quantum optical systems modeled as open quantum systems through the framework of a Quantum Markov Process. We will explore this unified approach using a Quantum Stochastic Schrödinger Equation that incorporates operator white noise, which describes the joint dynamics of quantum optical systems and their interaction with electromagnetic reservoirs. While solving the Quantum Stochastic Schrödinger Equation, we will examine scenarios where the system dynamics is continuously monitored through measurements, as well as cases where the system remains unobserved. This will allow us to derive the Stochastic Schrödinger Equation for photon counting (quantum jumps) and homodyne measurements, as well as the master equation for unobserved systems. Our derivations will also connect to concepts from quantum stochastic calculus and the Kraus operator formalism used in quantum information theory. Additionally, we will review a variety of examples, ranging from simple illustrations to discussions of quantum optical networks composed of cascaded quantum systems, and other examples motivated by applications in quantum information. 

Reading material:

Quantum Noise, Crispin Gardiner and Peter Zoller, Springer Series in Synergetics (2004) 

The Quantum World of Ultra-Cold Atoms and Light Book II: The Physics of Quantum-Optical Devices, Crispin Gardiner, and Peter Zoller, World Scientific Publishing Company (2015)