Quantum Dynamics - Fundamentals and Realizations

In recent years superconducting qubits have become one of the leading platforms for quantum computation and simulation. In 2019, the google team demonstrated that a quantum processor could perform certain computational tasks exponentially faster than a classical computer [1]. Going beyond this milestone, we utilize these Noisy Intermediate Scale Quantum (NISQ) processors to study nonequilibrium quantum dynamics and simulate quantum phases of matter. After introducing these processors, I will present some of our recent works in studying robustness of bound states of photons[2], universality classes of dynamics in the 1D Heisenberg chain [3], and measurement-induced quantum information phases [4]. The aim of the talk is to provide a sense of what NISQ discoveries to anticipate and a time scale for them. [1] Nature 574, 505–510 (2019) [2] Nature 612, 240–245 (2022) [3] Arxiv.org/abs/2306.09333 [4] Arxiv.org/abs/2303.04792

One of the most paradigmatic outstanding problems in condensed matter physics is the mechanism behind unconventional superconductivity, as for example exhibited in the cuprate materials. The interplay between spin and charge degrees of freedom in these systems enables a rich phenomenology, but also renders theoretical predictions challenging. In this talk, I will focus mainly on a single hole in an antiferromagnet and present different approaches to tackle the question of its dynamical properties, reaching from numerical approaches and their limitations, to semi-analytical descriptions and the corresponding approximations, and quantum simulation experiments using cold atoms in optical lattices.

When charged particles are placed in a magnetic field, the single-particle energy states form discrete, highly-degenerate Landau levels. Since all states within a Landau level have the same energy, the behaviour of the system is completely determined by the interparticle interactions and strongly-correlated behaviour such as the fractional quantum Hall effect occurs. Here, we present recent experiments from MIT on the microscopy of a rapidly-rotating Bose-Einstein condensate, in which the Coriolis force felt by a massive particle in a rotating frame plays the role of the Lorentz force felt by a charged particle in a magnetic field. In a magnetic field the X and Y coordinates of a particle do not commute, leading to a Heisenberg uncertainty relation between spatial coordinates. We exploit the ability to squeeze non-commuting variables to dynamically create a Bose-Einstein condensate occupying a single Landau gauge wavefunction, and investigate its purely interaction-driven dynamics in the lowest Landau level. We reveal a spontaneous crystallization of the fluid, driven by the interplay of interactions and the magnetic field; increasing the cloud density smoothly connects this quantum behavior to a classical Kelvin-Helmholtz-type hydrodynamic instability, driven by the sheared superfluid flow profile arising from the vector potential. Finally, we project a sharp optical boundary onto our system and demonstrate controllable injection of its associated chiral edge states, quantifying their speed, excitation energy, and dependence upon wall structure.

Understanding quantum mechanical systems of many particles at a microscopic level is one of the grand challenges of modern physics. In 1982, Feynman addressed this issue by formulating his vision that one can use well-controlled quantum systems to simulate and understand other quantum systems. Single atoms trapped in individual optical traps coupled to Rydberg states have recently emerged as a versatile experimental platform geared towards realizing Feynman's vision. In this talk, I will focus on the basics of this platform. First, I will describe how individual atoms are loaded, detected, and manipulated in optical tweezers. Afterwards, I will explain how strong, switchable interactions between highly excited atomic Rydberg states emerge, and how they can be induced and controlled by lasers. This will set the stage for highlighting the accessible many-body models for quantum simulation and the potential of the platform for quantum computation and a brief discussion of recent experimental breakthroughs in the field.

This lecture will introduce some of the exciting research underway using Rydberg atoms - highly excited atoms in which one or more electrons has been promoted to a very high principal quantum number - as well as some of the core concepts used to understand their behavior and properties. We will discuss quantum defect theory used to analytically describe individual Rydberg atoms, derive the different ways in which Rydberg atoms can interact, and develop some basic applications of Rydberg atoms in quantum science.

Quantum computers hold the promise to outperform their classical counterparts in certain computational tasks. Among others, the simulation of quantum many-body systems in and out of equilibrium attracts considerable attention. For this purpose, Trotterization is commonly used to discretize the continuous time evolution with a small Trotter step size. In this talk, I will introduce some basic concepts in digital quantum simulation and a simple Trotterization algorithm. An advanced quantum algorithm that can adaptively update the Trotter step size will also be briefly discussed.

In this talk, I will discuss how quantum many-body systems process and transport quantum information. Quantum many-body systems distribute localized information over many non-local degrees of freedom in the course of their time evolution, a process called information scrambling. Information scrambling is related to fundamental questions in quantum dynamics such as thermalization, quantum chaos, and entanglement spreading, and to the control of information dynamics in quantum computing platforms. I will discuss information scrambling through the lens of operator dynamics, introducing out-of-time-ordered correlators as a diagnostic tool. Specializing to random circuit models, I will derive the appearance of an emergent hydrodynamics governing the universal aspects of information transport. Finally, I will discuss exact and perturbative solutions shedding light on this universality in models with space- and time-translational symmetries.

Three dimensional magnetic systems promise significant opportunities for both fundamental physics, and technological applications, for example providing higher density devices and new functionalities associated with complex topology and greater degrees of freedom [1,2]. With recent advances in both characterization and nanofabrication techniques, the experimental investigation of three dimensional magnetic systems is now possible [3,4,5], opening the door to the elucidation of new physical properties, and representing the first steps towards higher dimensional magnetic devices. Harnessing these recent advances in X-ray magnetic tomographic imaging, we have been able to map both the static configuration [3,5], and dynamical behaviour [4,6], of topological magnetic structures [3-8]. Understanding these complex configurations is challenging: recent advances in analytical techniques [7] have provided new capabilities to locate and identify 3D magnetic solitons, leading to the first observation of nanoscale magnetic vortex rings [7,9]. As well as existing within bulk and thin film systems, 3D spin textures can be introduced via the patterning of complex 3D magnetic nanostructures [10]. Such textures are not limited to the magnetization: we have recently observed highly coupled curvilinear nanosystems leading to the formation of topological textures within the magnetic stray field [8]. These new experimental capabilities for 3D magnetic systems open the door to complex three-dimensional magnetic structures, and their dynamic behaviour. In this talk I will discuss these new experimental capabilities of X-ray magnetic tomography and nanofabrication, and how they open the door to the elucidation of complex three-dimensional magnetic structures, and their dynamic behaviour. References [1] Fernández-Pacheco et al., Nature Communications 8, 15756 (2017). [2] C. Donnelly and V. Scagnoli, J. Phys. D: Cond. Matt. 32, 213001 (2020). [3] C. Donnelly et al., Nature 547, 328 (2017). [4] C. Donnelly et al., Nature Nanotechnology 15, 356 (2020). [5] K. Witte, et al., Nano Letters 20, 1305 (2020). [6] S. Finizio et al., Nano Letters (2022) [7] C. Donnelly et al., Nat. Phys. 17, 316 (2020) [8] C. Donnelly et al., Nature Nanotechnology 17, 136 (2022) [9] N. Cooper, PRL. 82, 1554 (1999). [10] L. Skoric et al., Nano Letters 20, 184 (2020).

Electronic transport measurements guide the discovery and characterization of quantum materials. The Biot-Savart law dictates that the motion of electrons generates a stray magnetic field during such a transport experiment. I will show how imaging these magnetic fields with a scanning SQUID microscope allows us the determine the path that current takes through our devices. I will then describe two examples where this capability has provided surprising results. First, we used magnetic imaging to disentangle the effects of a spatially inhomogeneous strain field on superconducting devices fabricated from CeIrIn5. Next, I will show how we revised the conventional microscopic picture of the quantum anomalous Hall effect by demonstrating that a bulk current gives rise to a quantized Hall effect.

After a general introduction defining topological states of quantum matter from a viewpoint of local unitary transformations, the consequences of quantum dynamics on the classification of topological matter and their physical phenomenology will be discussed. In particular, the consequences of three different thermodynamic limits in space-time will be analyzed: The adiabatic limit (long time at finite size), the spatial thermodynamic limit (large size at finite time), and the space-time scaling limit (long time and large size diverging at fixed ratio). Finally, the consequences of (periodic) driving and open system dynamics on topological phenomena will be briefly outlined.

Motivated by recent experiments on Google's sycamore platform studying transport in quantum spin systems, we study a classical variant thereof by a combination of analytical and numerical means. After a brief introduction to the subjects of quantum and classical spin dynamics, and the relevant notions of hydrodynamic transport, we will show that the classical model reproduces the quantum results in exquisite detail: shedding some light on the question of when, and to what extent, classical treatments can account for \textit{a priori} complex quantum dynamics.

Understanding how thermal equilibrium and irreversibility arise from unitary quantum evolution is a theme as old as quantum mechanics. Nowadays, this is well understood via the Eigenstate-Thermmalization Hypothesis (ETH). This is a simple assumption on the structure of local observables in the energy eigenbasis, that has proved to be extremely successful in describing some dynamical properties of physical Hamiltonian systems, as I will introduce in the first part of the talk. However, if one is interested in correlations of multiple times (relevant beyond linear response or to account for chaos), it becomes clear that ETH as was known is incomplete. In the second part of the lecture, I will explain recent developments in the field, including the full version of ETH and the emergence of Free Probability as the right tool to describe it.

There has been significant recent interest in non-Ohmic electrical transport in ultra-clean conductors including mono- and bi-layer graphene, (Al,Ga)As heterostructures, and PdCoO2. I will give an introduction to the Ohmic, viscous, and ballistic transport regimes, as well as their experimental realizations in both mesoscopic DC transport [1] and AC electrodynamics [2]. I will tell the story of our evolving understanding of non-Ohmic physics in PdCoO2, including the discovery of novel effects coming from band structure anisotropy [3] and the ongoing debate as to the microscopic origin of a possible viscous regime [4]. [1] Moll et al, Science 351, 1061 (2016) [2] Baker et al, arXiv:2204.14239 (2022) [3] Bachmann, Sharpe et al, Nat. Phys. 18, 819 (2022) [4] Cook & Lucas, Phys. Rev. B 99 235148 (2019)

Magnetism is a rich source of new fundamental physics in condensed matter systems. This talk will be a tour of aspects of modern research into quantum magnetism at the interface between theory and experiment with an emphasis on how thinking about magnon band topology both sheds new light on old questions and points to new directions in the broader field.

Magnons are quanta of spin-wave excitations in magnetically ordered systems, promising for information transport and processing on mesoscopic scales. The magnon kinetics in magnetic insulators supporting long-distance magnon transport is therefore of particular interest. We develop a general theory to describe different transport regimes of magnons in a ferromagnetic thin film. Our result is consistent with the diffusive (ballistic) model for the length scale much larger (smaller) than the magnon mean free path, and provides a description for the intermediate regime. I will discuss the concept of spin chemical potential, the enhancement of spin conductivity in two dimensions, and the access of magnon transport regimes with quantum-impurity relaxometry.

In the rapidly evolving landscape of quantum computing, harnessing the principles of topological band theory has emerged as a promising path towards the realization of robust and fault-tolerant quantum processors. This talk will delve into the intricate world of topological band theory and reveal its implications for quantum computing.

Macroscopic properties of matter, such as superconductivity and magnetism, often originate from the collective behavior of the electrons in the solid. When a solid is driven out of equilibrium with ultrashort laser pulses, this collective behavior is entirely altered, and states which are usually linked to low temperatures may emerge under highly excited conditions. Femtosecond pulses have been used to dynamically control microscopic parameters such as the electronic structure and the interaction between charge, spin and lattice, and to switch solids to so-called hidden orders which can exclusively be reached along non-thermal excitation pathways. Simulating the behavior of correlated electrons out of equilibrium provides a challenge for theory: Even for simple model systems, the exponential scaling of the Hilbert space and the highly entangled nature of the many-body wave function restrict wave-function based simulations to small systems, or short times. An alternative are methods based on many-body perturbation theory and non-equilibrium Green’s functions. In this talk, I will give a brief guide to the theoretical developments in this field, as well as an overview over some important phenomena, from light-dressed states (Floquet states) to light-induced superconductivity in photo-doped Mott insulators.

Chirality is a very active field of research in organic chemistry, closely linked to the concept of symmetry. Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter [1,2]. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals, for example, exhibit chiral bulk states that have enabled the realization of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions [3-5]. Chiral topological crystals exhibit excellent chiral surface states [6,7] and different orbital angular momentum for the enantiomers, which can be advantageous in catalysis. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and the homochirality of life, brings topological materials to the fore [8]. References: [1] M. G. Vergniory, B. J. Wieder, L. Elcoro, S. S. P. Parkin, C. Felser, B. A. Bernevig, N. Regnault, Science 2022, 376, 6595. [2] P. Narang, C. A. C. Gracia and C. Felser, Nat. Mater. 2021, 20, 293. [3] J. Gooth et al., Nature 2017, 547, 324. [4] J. Gooth et al., Nature 2019, 575, 315. [5] D. M. Nenno, et al., Nat Rev Phys 2022, 2, 682. [6] B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava and B. A. Bernevig, Science 2016, 353, aaf5037. [7] N. B. M Schröter, et al., Science 2020, 369, 179. [8] C. Felser, J. Gooth, preprint arXiv:2205.05809

This talk will discuss what is meant by quantum magnetism and how the properties of quantum magnets differ from conventional magnets in terms of their ground states and excited states. The ingredients required to enhance the quantum properties of magnets will be reviewed with particular emphasis on frustrated magnetism. The realization of quantum magnets in real materials will then be discussed along with experimental techniques for studying them.

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In my lecture, I will provide a pedagogical introduction and discuss in detail the time-evolving block decimation (TEBD) algorithm that allows to efficiently simulate the dynamics of quantum many-body systems.