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Probing topology and dynamics in driven quantum many-body systems

Periodic Reporting for period 4 - TopDyn (Probing topology and dynamics in driven quantum many-body systems)

Reporting period: 2020-08-01 to 2021-07-31

Just one hundred years ago Niels Bohr published his seminal work on the structure of atoms, paving the way for the birth of quantum mechanics and to our understanding of the periodic table of elements. A century later, the discovery of the Higgs boson provided the final link in the Standard Model of particle physics, completing the catalog of atomic and subatomic particles that populate our universe. With this observation we now, it seems, have a nearly complete view of the microscopic constituents of our universe and of the basic quantum mechanical laws that govern their behavior.

If the twentieth century was about discovering the basic laws of quantum mechanics, then the twenty first century will be about pushing quantum systems to new frontiers, and learning how to control them. One of the central themes of this project is to find new routes to controlling quantum many-body systems. In the process I aim to provide a deeper and broader theoretical understanding of quantum dynamics in driven many-body systems, and to expose new routes for experimental investigation. A particular emphasis will be directed towards the exciting area of topological phenomena, which by their nature are expected to be particularly robust and therefore to have a good chance of persisting in the intrinsically out-of-equilibrium regime of strong driving.

The advent of lasers and powerful microwave sources has given experimentalists impressive levels of control over quantum few-body systems. These capabilities inspire us to investigate the possibilities for using time-dependent fields to drive many-body systems into topological states that, e.g. realize phenomena that so far have proved challenging to find in ordinary materials.

The theoretical description and realization of topological phenomena in driven many-body systems is a multifaceted problem that serves as a vehicle for elucidating many general aspects of driven quantum dynamics that are relevant on an even broader scale. In going beyond the traditional paradigms of equilibrium physics, through this project we developed fresh conceptual ideas, discovered new mechanisms and paradigms for non-equilibrium quantum dynamical phases and phase transitions, elucidated experimental signatures of these phenomena and provided guidance to experiments towards their realization, and developed new analytical and numerical tools to enable these and future studies of non-equilibrium quantum many-body dynamics.
Overall, the project was a great success. Here I will include an overview of some of our most significant/impactful results.

First, in collaboration with partners at the Technion Institute of Technology and the Weizmann Institute of Science, we discovered a new regime of universal dynamics in periodically-driven many-body systems. One of the biggest challenges that arises when strong laser or microwave driving fields are used to control quantum systems is that these control fields tend to heat up the system and destroy all of its fragile quantum mechanical characteristics or behaviors. In our work, we flipped this conventional wisdom on its head, and showed that, under appropriate conditions, the heating that naturally accompanies driving can actually be used as a resource, which pushes the system into a novel regime where new robustly quantized quantum transport phenomena can be observed. This work is published in Physical Review X.

Another one of the major goals of this project was to elucidate the role of electron-electron interactions in schemes where optical fields are used to modify a system's electronic properties. As a prototypical example, graphene has received wide attention for its wide range of outstanding electrical, mechanical, thermal, and optical properties. Previously, in a simplified setting where the (naturally strong) interaction between electrons in the material is ignored, it was shown that circularly polarized laser light could be used to dynamically induce a band gap in graphene, opening the potential for greater functionality. In a paper published in Physical Review Letters, we presented the first study of the effects of electron-electron interactions on light-induced gap opening in graphene and graphene-like systems. We identified promising parameter regimes where optically-induced dynamical gap opening can be observed experimentally, and provided a detailed characterization of the competing processes and timescales that must be considered to successfully implement this approach in experiments. To facilitate this study, we developed a new theoretical approach which formed the basis for an extensive set of numerical simulations, and will enable the community to undertake future studies of dynamics in driven electronic systems.

Interacting many-body systems support collective modes of excitation, which may have properties utterly unlike those of the microscopic constituent particles. When such collective modes are excited, the system may host strong oscillating internal fields, associated with the restoring force that sustains the collective oscillation. This property is used extensively in the field of nanoplasmonics, where collective charge density oscillations are routinely used to compress and enhance electric fields by many orders of magnitude over the values that can be applied externally. In a work with collaborator Justin Song at NTU in Singapore which was published in Nature Physics, we showed that such internal fields can indeed modify the electronic structure of a metallic system, thus altering its response characteristics to external driving fields. This feedback gives rise to nonlinear collective mode dynamics, which we showed can lead to novel types of non-equilibrium phase transitions and spontaneous symmetry breaking. In this work we made detailed estimates and showed that the phenomena that we describe should be observable using present day high quality graphene devices and laser sources.

While the topology of non-interacting driven systems is now reasonably well understood, a crucial outstanding question remains: under what conditions does a driven many-body system occupy its dynamically-induced "Floquet states" in such a way that robust band topology is reflected in observables? To address this question we undertook several wide-ranging studies of the steady states of driven semiconductors, identifying key parameter regimes, observables, and novel phases/phenomena that may emerge.
Over the course of the project we pushed the state of the art of the field forward in a number of ways summarized as follows. We:

1) identified several new types of non-equilibrium phases that can be realized in quantum many-body systems through the application of time-dependent (e.g. optical) driving fields.

2) discovered and elucidated novel physical mechanisms through which the combination of periodic driving electron-electron interactions can give rise to spontaneous symmetry breaking and other nonlinear quantum dynamical phenomena.

3) developed a new analytical approach for the theoretical study of (driven or non-driven) open systems, with much broader applicability than previously existing methods.

4) developed new efficient numerical tools for studying systems of interest across all themes of this project.

5) developed new understanding of spin dynamics in quantum Hall and superconducting systems, enabling new possibilities for non-equilibrium control.
Image depicting the novel "Berryogenesis" mechanism of non-equilibrium spontaneous symmetry breaking
Robust quantized observables proposed for identifying the Anomalous Floquet Anderson Insulator
Overview of the distinct types of nonequilibrium phases/phase transitions considered in this project