In this talk, I will discuss the applications of cavity electrodynamics for controlling many-body electron systems. The focus will be on achieving strong coupling between cavities and collective excitations of interacting electrons at Terahertz and IR frequencies. As a specific example I will consider a cavity platform based on a two dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. I will also discuss how metallic mirrors sandwiching a paraelectric material can modify the transition into the ferroelectric state. Finally, I will review a general question of theoretically describing ultrastrong coupling waveguide QED. I will present a novel approach to this problem based on a non-perturbative unitary transformation that entangles photons and matter excitations. In this new frame of reference, the factorization between light and matter becomes exact for infinite interaction strength and an accurate effective model can be derived for all interaction strengths.

String theory was originally constructed as a unification of the quantum field theory of elementary particles with Einstein's theory of gravitation. Unexpectedly, it has led to the discovery of new "dualities" which have given us a new perspective on quantum field theories not coupled to gravity. Some of the latter theories are relevant to the strongly-interacting quantum many body problems of condensed matter physics. I will survey some of the challenging open problems associated with condensed matter experiments, and discuss the insights gained from string theory.

“With four parameters I can fit an elephant; with five I can make it wag its tail.” Systems biology models of the cell have an enormous number of reactions between proteins, RNA, and DNA whose rates (parameters) are hard to measure. Models of climate change, ecosystems, and macroeconomics also have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? Multiparameter fits are sloppy; the parameters can vary over enormous ranges and still agree with past experiments. Nonetheless, they can often make useful predictions about future experiments, even allowing for these huge parameter uncertainties: a few stiff combinations of parameters govern the behavior. Third, these sloppy models all appear strikingly similar to one another – for example, the stiffnesses in every case we’ve studied are spread roughly uniformly over a range of over a million. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. Finally, we shall show that models in physics are also sloppy – that sloppiness makes science possible.

A combination of ideas originating from Condensed Matter physics, Supersymmetric Field Theory, and AdS/CFT has led to a detailed web of conjectured dualities. These relate the long distance behavior of different short distance theories. These dualities clarify a large number of confusing and controversial issues in Condensed Matter physics and in the study of 2+1 dimensional quantum field theory.

This talk will present an overview of recent progress towards a solution of one of the grand-challenges of modern science: understanding the properties of interacting electrons in molecules and solids. After an introduction to the physics I will argue our theoretical understanding of a basic model system, the two dimensional Hubbard model, has reached the level that we can say with confidence that its superconducting properties capture key aspect of the high-Tc superconductivity in copper-oxide materials. I will then summarize the current status of our extension of the methods to fully physically realistic systems, emphasizing the areas of theoretical uncertainty and the prospects for resolution.

It is commonly recognized that scientific discoveries result in new technologies. In this talk we will discuss the reverse: behind every conceptual breakthrough lies some technological advance. To illustrate this point, we will review how modern progress in optical technologies is revolutionizing our understanding of quantum matter. We will discuss experiments that showed that we can optically control materials, and even suggest light-induced superconductivity. We’ll delve into a new type of magnetism, discovered in layered materials using sensitive light reflection experiments rather than measurements of magnetization. We’ll cover how we can use optical lattices with tunable geometries to create several paradigmatic models of electron systems and shed light onto their puzzling properties. We will finally discuss why understanding technology is important for theoretical physicists.

In November 2015, Albert Einstein finalized a new theory of gravitation, General Relativity (GR), which describes gravitation as a deformation of the structure of space-time. It took many years of conceptual deepening and observational discoveries to fully grasp several of the most novel predictions of GR (gravitational waves, black holes, cosmological expansion). GR is the current standard model for the gravitational interaction, and plays a crucial role in the description of many physical systems: solar system, neutron stars, binary pulsars, galaxies, black holes, cosmology. For many years, GR was considered as being completely separate from the (quantum) description of the other interactions. However, several theoretical frameworks (string theory, supergravity) point towards a key role of GR in the search for a unified description of physics. GR has passed with flying colors all current experimental tests, but some puzzles remain unanswered.

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient computation. We study the correlation between quantum chaos diagnostics, the circuit expressibility and the optimization of the control parameters.

Superconductivity is a state of matter where electrons can flow without resistance and where magnetic fields are expelled. It was discovered serendipitously more than a hundred years ago. Today, superconductors are essential components of medical imaging devices as well as high energy particles accelerators. Understanding this phenomena was one of the greatest intellectual challenges of the twentieth century. A dramatic advance was provided by the BCS (Bardeen Cooper Schrieffer) theory 45 years after. It posits that superconductivity is the result of macroscopic condensation of electron pairs, which are held together by the vibrations of the lattice. The condensate is a macroscopic quantum objects and its rigidity accounts for its striking macroscopic properties. The BCS theory was so successful that by the early 70’s superconductivity was considered a completely understood subject with the maximum achievable critical temperature having been reached experimentally around 30K. In the late 80’s this field of research took a dramatically turn with the discovery of new ceramic compounds which superconduct at temperatures as high as 160 K. These materials, cannot be described by straightforward extensions of the BCS theory. Scientists are still working on finding new explanations for these materials and we will describe the challenge they pose. The quest for room temperature superconductivity thus continues. A breakthrough in this field would have unimaginable consequences, changing the way we transmit electricity from its generation to its consumption to the way we design computers.

Mathematics has proven to be "unreasonably effective" in understanding nature. The fundamental laws of physics can be captured in beautiful formulae. Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power as well, even though we have little daily experience dealing with elementary particles. The bizarre world of quantum physics not only represents a more fundamental description of nature than what preceded it, it also provides a rich context for modern mathematics. In recent years ideas from quantum field theory, elementary particles physics and string theory have completely transformed mathematics, leading to solutions of deep problems, suggesting new invariants in geometry and topology. Could the logical structure of quantum theory, once fully understood and absorbed, inspire a new realm of mathematics that might be called “quantum mathematics” and will this new language enable us to formulate the fundamental laws of physics?

From copper-oxide superconductors to rare-earth compounds, materials with strong electronic correlations have focused enormous attention over the last two decades. Solid-state chemistry, new elaboration techniques and improved experimental probes are constantly providing us with examples of novel materials with surprising electronic properties, the latest example being the recent discovery of iron-based high-temperature superconductors. In this colloquium, I will emphasize that the classic paradigm of solid-state physics, in which electrons form a gas of wave-like quasiparticles, must be seriously revised for strongly correlated materials. Instead, a description accounting for both atomic-like excitations in real-space and quasiparticle excitations in momentum space is requested. I will review how Dynamical Mean-Field Theory -an approach that has led to significant advances in our understanding of strongly correlated materials- fulfills this goal. New frontiers are also opening up, which bring together condensed-matter physics and quantum optics. `Artificial materials' made of ultra-cold atoms trapped by laser beams can be engineered with a remarkable level of controllability, and allow for the study of strong- correlation physics in previously unexplored regimes.

Two of the most amazing ideas in physics are the holographic principle and quantum error correction. The holographic principle asserts that all the information contained in a region of space is encoded on the boundary of the region, albeit in a highly scrambled form. Quantum error correction is the foundation of our hope that large-scale quantum computer can be operated to solve hard problems. I will argue that these two ideas are closely related, and will describe quantum codes which realize the holographic principle. These codes provide simplified models of quantum spacetime, opening new directions in the study of quantum gravity, though many questions remain.

Where do we come from? Science is making progress on this age-old question of humankind. The Universe was once much smaller than the size of an atom. Small things mattered in the small Universe, where quantum physics dominated the scene. To understand the way the Universe is today, we have to solve remaining major puzzles. The Higgs boson that was discovered recently is holding our body together from evaporating in a nanosecond. But we still do not know what exactly it is. The mysterious dark matter is holding the galaxy together, and we would not have been born without it. But nobody has seen it directly. And what is the very beginning of the Universe?

In recent decades, physicists and astronomers have discovered two beautiful Standard Models, one for the quantum world of extremely short distances, and one for the universe as a whole. Both models have had spectacular success, but there are also strong arguments for new physics beyond these models. In this lecture, we will review these models, their successes and their shortfalls. We will describe how experiments in the near future could point to new physics suggesting a profound conceptual revolution, which could change our view of the world.

The quantum laws governing atoms and other tiny objects seem to defy common sense, and information encoded in quantum systems has weird properties that baffle our feeble human minds. John Preskill will explain why he loves quantum entanglement, the elusive feature making quantum information fundamentally different from information in the macroscopic world. By exploiting quantum entanglement, quantum computers should be able to solve otherwise intractable problems, with far-reaching applications to cryptology, materials, and fundamental physical science. Preskill is less weird than a quantum computer, and easier to understand.

Advances in light sources and time resolved spectroscopy have made it possible to excite specific atomic vibrations in solids and to observe the resulting changes in electronic properties. I argue that in narrow-band systems the dominant symmetry-allowed coupling between electron density and dipole active modes implies an electron density-dependent squeezing of the phonon state which provides an attractive contribution to the electron-electron interaction, independent of the sign of the bare electron-phonon coupling and with a magnitude proportional to the degree of laser-induced phonon excitation. Reasonable excitation amplitudes lead to non-negligible attractive interactions that may cause significant transient changes in electronic properties including superconductivity. The mechanism is generically applicable to a wide range of systems, offering a promising route to manipulating and controlling electronic phase behavior in novel materials.

According to the Landau description of Fermi liquids, low- energy excitations in metals are constructed out of quasiparticles – long-lived excitations which have the same quantum numbers as those of an electron in vacuum. In metals with strong correlations however, quasiparticles become fragile: they are destroyed above a characteristic energy or temperature scale, the quasiparticle coherence scale. This energy scale can be remarkably low, even in materials which are not close to a Mott metal-insulator transition, for example as a result of the Hund's rule coupling. I will provide evidence that this is relevant for many materials, especially oxides of the 4d transition metals. In other materials, such as cuprates, quasiparticles are destroyed selectively in specific regions of momentum-space. The understanding of charge and thermal transport in such ``bad metals'' is a key issue, with both fundamental and practical implications.

A piece of paper or candy wrapper crackles when it is crumpled. A magnet crackles when you change its magnetization slowly. The earth crackles as the continents slowly drift apart, forming earthquakes. Crackling noise happens when a material, when put under a slowly increasing strain, slips through a series of short, sharp events with an enormous range of sizes. There are many thousands of tiny earthquakes each year, but only a few huge ones. The sizes and shapes of earthquakes show regular patterns that they share with magnets and many other systems. This suggests that there must be a shared scientific explanation. We shall hear about crackling noise and that it is a symptom of a surprising truth: the system behaves the same on small, medium, and large scales.

The amazing and mysterious laws of the quantum world will be outlined: superposition, entanglement and no cloning. Their impact on science and technology will be discussed, including quantum teleportation, secure quantum communication, quantum money, powerful quantum algorithms and quantum machine learning.

Random matrix models are ubiquitous in physics and have been studied from many perspectives. One important application is producing exactly solvable toy models of quantum gravity and string theory. These models relate to deep mathematical structures of the moduli space of Riemann surfaces. Recent work has extended these models to open strings and surfaces with boundaries. This generalization is less straightforward that one imagines and involves the introduction of additional degrees of freedom. These models have become relevant in recent studies of the gravitational dual of the SYK model, two-dimensional black holes, and gravity with constant curvature. Based on work done in collaboration with Edward Witten.