# Floquet physics

## Floquet physics

Equilibrium macroscopic phenomena are described by thermodynamics, relying only on a small number of state variables such as temperature and pressure. As a consequence, many technological applications as well as going about everyday life do not require any knowledge about the underlying quantum mechanics. This changes, however, when a system is driven continuously by external means such as in a time-periodic fashion. These so-called Floquet systems have recently become a major focus of work. To a large extent this has been motivated by experimental advances in systems such as cold atoms and trapped ions, where it is nowadays possible to realize coherent Floquet dynamics of quantum many-body systems.

Significant progress has been made over the last years in the general understanding of such quantum Floquet systems. Specifically, they relax to a steady state which is generically time-periodic due to the drive. For these periodic steady states, we have identified generalized statistical ensembles, extending the notion of equilibrium to driven quantum systems. Moreover, we have proposed genuine nonequilibrium quantum phases without an equilibrium counterpart, such as the recently experimentally realized $\pi$-spin glass, also known as the discrete time crystal.

Along these lines we further explore the rich physics of quantum Floquet systems with an emphasis on providing a guide for experiments to realize the interesting phenomena occurring in this context. For more details on current and recent research highlights see the collection below.

Laser-Driven Multiferroics and Ultrafast Spin Current Generation
Masahiro Sato, Shintaro Takayoshi, Takashi Oka

We propose an ultrafast way to generate spin chirality and spin current in a class of multiferroic magnets using a terahertz circularly polarized laser. Using the Floquet formalism for periodically driven systems, we show that it is possible to dynamically control the Dzyaloshinskii-Moriya interaction in materials with magnetoelectric coupling. This is supported by numerical calculations, by which additional resonant phenomena are found. Specifically, when a static magnetic field is applied in addition to the circularly polarized laser, a large resonant enhancement of spin chirality is observed resembling the electron spin resonance. Spin current is generated when the laser is spatially modulated by chiral plasmonic structures and could be detected using optospintronic devices.

Phys. Rev. Lett. 117, 147202 (2016)

Prethermalization without Temperature
D. J. Luitz, R. Moessner, S. L. Sondhi, V. Khemani

While a clean, driven system generically absorbs energy until it reaches “infinite temperature,” it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many- body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.

Phys. Rev. X 10, 021046 (2020)

Equilibration and order in quantum Floquet matter
R. Moessner, S. L. Sondhi

Equilibrium thermodynamics is characterized by two fundamental ideas: thermalization-that systems approach a late time thermal state; and phase structure-that thermal states exhibit singular changes as various parameters characterizing the system are changed. We summarize recent progress that has established generalizations of these ideas to periodically driven, or Floquet, closed quantum systems. This has resulted in the discovery of entirely new phases which exist only out of equilibrium, such as the π-spin glass/Floquet time crystal.

Nature Physics 13, 424 (2017)

Quantifying and Controlling Prethermal Nonergodicity in Interacting Floquet Matter
K. Singh, C. J. Fujiwara, Z. A. Geiger, E. Q. Simmons, M. Lipatov, A. Cao, P. Dotti, S. V. Rajagopal, R. Senaratne, T. Shimasaki, M. Heyl, A. Eckardt, D. M. Weld

The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This dependence motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation. Using a double-quench protocol, we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions. We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space. Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization. The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.

Phys. Rev. X 9, 041021 (2019)