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. Time-periodic fields provide a versatile platform for inducing non-equilibrium topological phenomena in quantum systems. We discuss how such fields can be used for topological band structure engineering, and the conditions for observing robust topological behaviour in a many-body setting.

Band structure engineering and non-equilibrium dynamics in Floquet topological insulators

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties In particular, it has been employed to study topological phenomena in a variety of different platforms In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings Most prominently, there are two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers being equal to zero Here we realize such a system with bosonic atoms in a periodically driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections Standard topological invariants commonly used in static systems are not enough to fully capture the topological properties of Floquet systems In a periodically driven quantum gas, chiral edge modes emerge despite all Chern numbers being equal to zero

Realization of an anomalous Floquet topological system with ultracold atoms

Strong light–matter coupling in quantum cavities provides a pathway to break fundamental materials symmetries, like time-reversal symmetry in chiral cavities. This Comment discusses the potential to realize non-equilibrium states of matter that have so far been only accessible in ultrafast and ultrastrong laser-driven materials.

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Engineering quantum materials with chiral optical cavities

Ultrafast laser pulses can be used to drive materials into nonequilibrium states that have unusual properties and are promising for technological applications. Different classes of phenomena are observed during and after the optical illumination. This Colloquium discusses the recent developments in this field, and the prospects for using these techniques to create materials with novel functionalities in a controlled way.

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Colloquium: Nonthermal pathways to ultrafast control in quantum materials

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there exist two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers are equal to zero. Here, we realize such a system with bosonic atoms in a periodically-driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.

Many non-equilibrium phenomena have been discovered or predicted in optically driven quantum solids1. Examples include light-induced superconductivity2,3 and Floquet-engineered topological phases4–8. These are short-lived effects that should lead to measurable changes in electrical transport, which can be characterized using an ultrafast device architecture based on photoconductive switches9. Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topological band structure4,5, similar to the band structure originally proposed by Haldane10. This includes an approximately 60 meV wide conductance plateau centred at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau the estimated anomalous Hall conductance saturates around 1.8 ± 0.4 e2/h. A transient topological response in graphene is driven by a short pulse of light. When the Fermi energy is in the predicted band gap the Hall conductance is around two conductance quanta. An ultrafast detection technique enables the measurement.

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Light-induced anomalous Hall effect in graphene.

Many striking non-equilibrium phenomena have been discovered or predicted in optically-driven quantum solids, ranging from light-induced superconductivity to Floquet-engineered topological phases. These effects are expected to lead to dramatic changes in electrical transport, but can only be comprehensively characterized or functionalized with a direct interface to electrical devices that operate at ultrafast speeds. Here, we make use of laser-triggered photoconductive switches to measure the ultrafast transport properties of monolayer graphene, driven by a mid-infrared femtosecond pulse of circularly polarized light. The goal of this experiment is to probe the transport signatures of a predicted light-induced topological band structure in graphene, similar to the one originally proposed by Haldane. We report the observation of an anomalous Hall effect in the absence of an applied magnetic field. We also extract quantitative properties of the non-equilibrium state. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect the effective band structure expected from Floquet theory. This includes a ~60 meV wide conductance plateau centered at the Dirac point, where a gap of approximately equal magnitude is expected to open. We also find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around ~1.8$\pm$0.4 e$^2$/h.

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Light-induced anomalous Hall effect in graphene

Excitation of high-Tc cuprates and certain organic superconductors with intense far-infrared optical pulses has been shown to create non-equilibrium states with optical properties that are consistent with transient high-temperature superconductivity These non-equilibrium phases have been generated using femtosecond drives, and have been observed to disappear immediately after excitation, which is evidence of states that lack intrinsic rigidity Here we make use of a new optical device to drive metallic K3C60 with mid-infrared pulses of tunable duration, ranging between one picosecond and one nanosecond The same superconducting-like optical properties observed over short time windows for femtosecond excitation are shown here to become metastable under sustained optical driving, with lifetimes in excess of ten nanoseconds Direct electrical probing, which becomes possible at these timescales, yields a vanishingly small resistance with the same relaxation time as that estimated by terahertz conductivity We provide a theoretical description of the dynamics after excitation, and justify the observed slow relaxation by considering randomization of the order-parameter phase as the rate-limiting process that determines the decay of the light-induced superconductor Evidence for light-induced superconductivity in K3C60 was limited to optical methods due to the short lifetime of the phase Extending the lifetime from picoseconds to nanoseconds now allows measurement of its negligible electrical resistance

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Evidence for metastable photo-induced superconductivity in K3C60

Far and mid infrared optical pulses have been shown to induce non-equilibrium unconventional orders in complex materials, including photo-induced ferroelectricity in quantum paraelectrics, magnetic polarization in antiferromagnets and transient superconducting correlations in the normal state of cuprates and organic conductors. In the case of non-equilibrium superconductivity, femtosecond drives have generally resulted in electronic properties that disappear immediately after excitation, evidencing a state that lacks intrinsic rigidity. Here, we make use of a new optical device to drive metallic K$_3$C$_{60}$ with mid-infrared pulses of tunable duration, ranging between one picosecond and one nanosecond. The same superconducting-like optical properties observed over short time windows for femtosecond excitation are shown here to become metastable under sustained optical driving, with lifetimes in excess of ten nanoseconds. Direct electrical probing becomes possible at these timescales, yielding a vanishingly small resistance. Such a colossal positive photo-conductivity is highly unusual for a metal and, when taken together with the transient optical conductivities, it is rather suggestive of metastable light-induced superconductivity.

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T. Matsuyama

Papers

Light-induced anomalous Hall effect in graphene.

Light-induced anomalous Hall effect in graphene

Evidence for metastable photo-induced superconductivity in K3C60

Evidence for metastable photo-induced superconductivity in K$_3$C$_{60}$