In the past decade, quantum simulators have increased in their power and scope, offering exquisite dynamical control of tens or even hundreds of individual qubits. Central to this development is the external driving toolbox. Be it resonant or off-resonant, continuous or pulsed, driving protocols have come a long way since the early days of NMR to provide detailed control of both effective Hamiltonian and state. In this talk, I will argue for the addition of a new class of driving protocol to the quantum mechanics’ toolbox: quasiperiodic driving.
First, I will show that quasiperiodically driven systems realize robust non-classical energy pumps, with topological invariants characterizing the dynamical response. Remarkably, the pumped energy quasi-periodically re-coheres. I will describe current experimental efforts in superconducting circuits to exploit this re-coherence to prepare highly excited non-classical cavity states. Next, I will show that quasiperiodic driving can lead to chaotic response, even in a single qubit. Chaos requires a minimum number of incommensurate driving tones; I will argue that the number is three, and discuss prospects of designer baths in such systems. More generally, multi-tone driving can be understood in terms of "synthetic dimensions", which enables a broad range of condensed matter phenomena to be translated into robust dynamical responses of lower dimensional systems.