Driven Systems

Frederik Nathan, Mark Spencer Rudner

Recent works have demonstrated that the Floquet–Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energy-like quantity that defines the spectrum of a periodically-driven system. Here we develop a new paradigm for the topological classification of Floquet–Bloch bands, based on the time-dependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologically-protected degeneracies at intermediate times, which control the topology of the Floquet bands of the full driving cycle. This approach provides a natural framework for incorporating the role of symmetries, enabling a unified and complete classification of Floquet–Bloch bands and yielding new insight into the topological features that distinguish driven and non-driven systems.

AUGUST STERN

Hongzheng Zhao, Florian Mintert, Johannes Knolle

We analyze quasiperiodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet time spirals in analogy with spatially incommensurate spiral magnetic states. Generalizing the mechanism to many-body systems, we discover that a form of discrete-time translation symmetry breaking can also occur in quasiperiodically driven systems. We construct a discrete-time quasicrystal stabilized by many-body localization. Crucially, it persists also under perturbations that break the equivalence with periodic systems. As such, it provides evidence of a stable quasiperiodically driven many-body quantum system which does not heat up to the featureless infinite-temperature state.

Ulrich Karrenberg

Joscha Reichert, P. Nalbach, Michael Thorwart

When an open quantum system is driven by an external time-dependent force, the coupling of the driving to the central system is usually included, whereas the impact of the driving field on the bath is neglected. We investigate the effect of a quantum bath of linearly driven harmonic oscillators on the relaxation dynamics of a quantum two-level system which is not directly driven. In particular, we calculate the frequency-dependent response of the system when the bath is subject to Dirac and Gaussian driving pulses. We show that a time-retarded effective force on the system is induced by the driven bath which depends on the full history of the perturbation and the spectral characteristics of the underlying bath. In particular, when a structured Ohmic bath with a pronounced Lorentzian peak is considered, the dynamical response of the system to a driven bath is qualitatively different than that of the undriven bath. Specifically, additional resonances appear which can be directly associated with a Jaynes-Cummings-like effective energy spectrum.