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Final Report Summary - TOPDRIVE (Topology and dynamics in driven quantum systems)

The discovery of quantum mechanics revolutionized our understanding of matter. While macroscopic bodies behave according to Newton’s laws of motion, microscopic objects follow a completely different set of quantum mechanical laws of motion. We now understand that matter may possess some particularly quantum properties, such as coherence and entanglement. Famously, these properties allow Schr¨odinger’s cat to be both alive and dead, or a quantum mechanical bit to take both values 0 and 1 at the same time. These remarkable yet fragile properties have been shown theoretically to offer profound increases in computational power over conventional (classical) circuits.
Recent advances have enabled the quantum mechanical properties of matter to be studied in ever larger systems. This opens the way for exploring many intriguing fundamental questions as well as the possibility of transformative practical advances. In particular, a powerful interplay between theory and experiments will allow us to address: What determines the time and length scales over which quantum mechanical behavior may persist? Do the laws of quantum mechanics impose fundamental limitations on the performance of nanoscale electronic systems? Can the quantum behaviors of microchip-scale systems be enhanced and harnessed for novel applications?

The aim of “TopDrive” is to open new avenues for exploring and addressing the fundamental questions highlighted above, in the context of solid state and cold atomic systems driven out of equilibrium. We seek to identify and elucidate new types of robust quantum mechanical phenomena that may be realized in these systems using newly available tools for driving and control, such as intense time-dependent laser and microwave fields. Drawing on an analogy with equilibrium systems, topological phenomena in driven systems are expected to be particularly robust, making them exciting candidates for investigating the quantum properties of matter.

i. Topological classification for periodically driven quantum systems

Historically, phases of matter have been classified by the “order,” or types of broken symmetries, that they possess. In a crystal, the uniformity of space is broken by the positioning of atoms, which spontaneously take on a periodic arrangement. In a ferromagnet, electronic spins spontaneously pick a particular direction along which to point. The symmetry-based classification organizes our understanding of phases and phase transitions, and helps to identify universality among diverse phenomena which occur in a wide range of both classical and quantum systems.
Recently, another avenue of classification based on the topological features of quantum states has emerged. The topological classification of quantum states is more abstract than the symmetrybased classification, often with no simple classical properties associated with the mathematical quantities used to distinguish different phases. However, some of the most robust and profound quantum mechanical phenomena owe their existence to these topological properties.
Although topologically-nontrivial states are rare to find in nature, their remarkable characteristics provide great motivation for their intensive study. Can analogues or new types of such robust topological phenomena be generated dynamically (“on demand”) in driven systems? This would open many exciting new avenues for exploring and utilizing these remarkable effects. Thus we aim to construct a complete classification scheme for topological behavior in non-interacting periodically driven systems, analogous to the highly useful “periodic table of topological insulators.”

ii. Characterization of non-equilibrium dynamics in driven quantum systems

With TopDrive we aim to elucidate the nature of the steady states achieved in periodically driven systems under general driving and system-bath coupling conditions. We furthermore seek to identify relevant experimental observables, or probes, that can be used to identify new behaviors.

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