Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - TopDyn (Probing topology and dynamics in driven quantum many-body systems)

Teaser

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...

Summary

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.

Remarkably, new types of particles may emerge in condensed matter systems, with properties that are both intellectually intriguing and potentially useful, e.g., holding promise for powerful new applications in classical and quantum information processing. In recent years, so-called “topological materials” have become the subject of intense interest due to the impressive robustness of the peculiar phenomena that they host. For example, defects in two-dimensional topological superconductors are predicted to exhibit non-Abelian braiding statistics, which can serve as the basis for an error-protected quantum computing architecture. Topological insulators provide another remarkable example: in the interior these materials are inert like ordinary insulators, but on the surface they host robust conducting states that cannot be destroyed by a wide range of perturbations.

The properties of topological materials stoke the imagination and expose a wide frontier ahead which is ripe for exploration. However, such materials are rather rare to find in nature. Even when examples are found, sample quality may still present significant hurdles to realizing their full potential. Therefore, in order to fully explore the breadth of phenomena supported by many-body systems, it is imperative that we seek out alternative routes to realizing such behaviors.

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, we will supply fresh conceptual ideas, identifying interesting new phenomena to explore.

Work performed

\"In the first half of the project period, we have achieved several of the ambitious goals set out in the proposal. 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 is to elucidate the role of electron-electron interactions in schemes where driving is 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. One drawback of graphene, which has so far prevented it from replacing traditional semiconductors in digital electronic systems, is that while graphene can be a very good conductor (giving a good \"\"ON\"\" state), its lack of a band gap prevents it from being turned \"\"OFF.\"\" 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 recently 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.

In the work just described, the rotating electric field of a circularly polarized laser is used to dynamically modify a material\'s electronic structure. One of the key hypotheses in the project proposal was that electron-electron interactions in driven systems could lead to intriguing new regimes of nonlinear quantum dynamics. 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 recent work with collaborator Justin Song at NTU in Singapore, 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 hi\"

Final results

Looking ahead, we will continue to press forward in all areas of the project. Our results from the first period are encouraging, and we will build further upon them. These results include a few unexpected discoveries, such as the new paradigm for non-equilibrium phase transitions discussed above, which have opened exciting new avenues for exploration.

Currently we are in the process of developing new numerical techniques that will benefit our work in all three of the work packages described above. In addition, we are in contact with experimental groups with whom we are discussing the possibilities for realizing the phenomena that we have proposed. We look forward to helping to enable experiments and to further refining our ideas in the second period of the project.