Non-equilibrium topological phenomena can be induced in quantum many-body systems using time-periodic fields (for example, by laser or microwave illumination). This Review begins with the key principles underlying Floquet band engineering, wherein such fields are used to change the topological properties of a system’s single-particle spectrum. In contrast to equilibrium systems, non-trivial band structure topology in a driven many-body system does not guarantee that robust topological behaviour will be observed. In particular, periodically driven many-body systems tend to absorb energy from their driving fields and thereby tend to heat up. We survey various strategies for overcoming this challenge of heating and for obtaining new topological phenomena in this non-equilibrium setting. We describe how drive-induced topological edge states can be probed in the regime of mesoscopic transport, and three routes for observing topological phenomena beyond the mesoscopic regime: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of the regimes covered, and their experimental realizations in solid-state, cold atomic, and photonic systems.

可以使用时间周期场（例如，通过激光或微波照射）在量子多体系统中诱发非平衡拓扑现象。本文从浮球带工程的基本原理开始，其中这些场用于改变系统单粒子光谱的拓扑特性。与平衡系统相反，在驱动多体系统中非平凡的能带结构拓扑不能保证将观察到鲁棒的拓扑行为。特别地，周期性驱动的多体系统趋向于从其驱动场吸收能量，从而趋于升温。我们调查了各种策略，以克服这种加热挑战并在这种非平衡环境中获得新的拓扑现象。我们描述了如何在介观运输范围内探测驱动诱发的拓扑边缘状态，以及观察介观范围之外的拓扑现象的三种途径：长寿命瞬态动力学和预热，无序诱发的多体定位和工程耦合到外部浴室。我们讨论了所涵盖的每种状态下可以探索的现象类型，以及它们在固态，冷原子和光子系统中的实验实现。