Observation of Floquet-Bloch states on the surface of a topological insulator

Light-Induced Topological Phase Transition with Tunable Layer Hall Effect in Axion Antiferromagnets

The intricate interplay between light and matter provides effective tools for manipulating topological phenomena. Here, we theoretically propose and computationally show that circularly polarized light holds the potential to transform the axion insulating phase into a quantum anomalous Hall state in MnBi2Te4 thin films, featuring tunable Chern numbers (ranging up to ±2). In particular, we reveal the spatial rearrangement of the hidden layer-resolved anomalous Hall effect under light-driven Floquet engineering. Notably, upon Bi2Te3 layer intercalation, the anomalous Hall conductance predominantly localizes in the nonmagnetic Bi2Te3 layers that hold zero Berry curvature in the intact state, suggesting a significant magnetic proximity effect. Additionally, we estimate variations in the magneto-optical Kerr effect, giving a contactless method for detecting topological transitions. Our work not only presents a strategy to investigate emergent topological phases but also sheds light on the possible applications of the layer Hall effect in topological antiferromagnetic spintronics.

Light-induced electronic polarization in antiferromagnetic Cr2O3

In a solid, the electronic subsystem can exhibit incipient order with lower point group symmetry than the crystal lattice. Ultrafast external fields that couple exclusively to electronic order parameters have rarely been investigated, however, despite their potential importance in inducing exotic effects. Here we show that when inversion symmetry is broken by the antiferromagnetic order in Cr2O3, transmitting a linearly polarized light pulse through the crystal gives rise to an in-plane rotational symmetry-breaking (from C3 to C1) via optical rectification. Using interferometric time-resolved second harmonic generation, we show that the ultrafast timescale of the symmetry reduction is indicative of a purely electronic response; the underlying spin and crystal structures remain unaffected. The symmetry-broken state exhibits a dipole moment, and its polar axis can be controlled with the incident light. Our results establish a coherent nonlinear optical protocol by which to break electronic symmetries and produce unconventional electronic effects in solids.

Generalized Optical Sum Rules for Light-Dressed Matter

Light-driven matter can exhibit qualitatively distinct electronic and optical properties from those observed at equilibrium. We introduce generalized sum rules for the optical properties of light-driven molecules. Both classical and quantum light are considered. For classical light, the Floquet sum rules show that the sum of all Fourier components, indexed by n = -∞ to ∞, of the time-dependent dipole matrix elements between Floquet modes weighted by the corresponding quasienergy difference in the first Floquet Brillouin zone plus n driving frequency is a constant. Surprisingly, it is impossible to alter the energy exchange rate between matter and a perturbative external probe laser by a strong driving, even though the spectra can differ significantly from the bare ones. These developments provide guidance for the control of effective optical properties of matter by light fields.

Floquet non-equilibrium Green's function and Floquet quantum master equation for electronic transport: The role of electron-electron interactions and spin current with circular light

The non-equilibrium Green's function (NEGF) and quantum master equation (QME) are two main classes of approaches for electronic transport. We discuss various Floquet variances of these formalisms for transport properties of a quantum dot driven via interaction with an external periodic field. We first derived two versions of the Floquet NEGF. We also explore an ansatz of the Floquet NEGF formalism for the interacting systems. In addition, we derived two versions of Floquet QME in the weak interaction regime. With each method, we elaborate on the evaluation of the expectation values of the number and current operators. We examined these methods for transport through a two-level system that is subject to periodic driving. The numerical results of all four methods show good agreement for non-interacting systems in the weak regime. Furthermore, we have observed that circular light can introduce spin current. We expect these Floquet quantum transport methods to be useful in studying molecular junctions exposed to light.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

Floquet Fermi Liquid

We demonstrate the existence of a nonequilibrium "Floquet Fermi liquid" state arising in partially filled Floquet Bloch bands weakly coupled to ideal fermionic baths, which possess a collection of "Floquet Fermi surfaces" enclosed inside each other, resembling matryoshka dolls. We elucidate several properties of these states, including their quantum oscillations under magnetic fields which feature slow beating patterns of their amplitude reflecting the different areas of the Floquet Fermi surfaces, consistent with those observed in microwave induced resistance oscillation experiments. We also investigate their specific heat and thermodynamic density of states and demonstrate how by controlling properties of the drive, such as its frequency, one can tune some of the Floquet Fermi surfaces toward nonequilibrium Van Hove singularities without changing the electron density.

Light-wave-controlled Haldane model in monolayer hexagonal boron nitride

In recent years, the stacking and twisting of atom-thin structures with matching crystal symmetry has provided a unique way to create new superlattice structures in which new properties emerge1,2. In parallel, control over the temporal characteristics of strong light fields has allowed researchers to manipulate coherent electron transport in such atom-thin structures on sublaser-cycle timescales3,4. Here we demonstrate a tailored light-wave-driven analogue to twisted layer stacking. Tailoring the spatial symmetry of the light waveform to that of the lattice of a hexagonal boron nitride monolayer and then twisting this waveform result in optical control of time-reversal symmetry breaking5 and the realization of the topological Haldane model6 in a laser-dressed two-dimensional insulating crystal. Further, the parameters of the effective Haldane-type Hamiltonian can be controlled by rotating the light waveform, thus enabling ultrafast switching between band structure configurations and allowing unprecedented control over the magnitude, location and curvature of the bandgap. This results in an asymmetric population between complementary quantum valleys that leads to a measurable valley Hall current7, which can be detected by optical harmonic polarimetry. The universality and robustness of our scheme paves the way to valley-selective bandgap engineering on the fly and unlocks the possibility of creating few-femtosecond switches with quantum degrees of freedom.

Floquet Engineering of a Diatomic Molecule through a Bichromatic Radiation Field

We report on a theoretical study of a Cs2 molecule illuminated by two lasers and show how this can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming light-induced conical intersections and modifiable avoided crossings. Our findings show how laser field orientation and strength, along with initial phase differences, can control molecular-state transitions, especially on the micromotion scale. We also extensively discuss how the interaction of radiation with matter gives rise to the emergence of potential energy surfaces of hybrids of radiation and molecular states. This research advances a technique for manipulating photoassociation processes in Cs2 molecules, offering potential new avenues in quantum control.

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

A versatile laser-based apparatus for time-resolved ARPES with micro-scale spatial resolution

We present the development of a versatile apparatus for 6.2 eV laser-based time and angle-resolved photoemission spectroscopy with micrometer spatial resolution (time-resolved μ-ARPES). With a combination of tunable spatial resolution down to ∼11 μm, high energy resolution (∼11 meV), near-transform-limited temporal resolution (∼280 fs), and tunable 1.55 eV pump fluence up to 3 mJ/cm2, this time-resolved μ-ARPES system enables the measurement of ultrafast electron dynamics in exfoliated and inhomogeneous materials. We demonstrate the performance of our system by correlating the spectral broadening of the topological surface state of Bi2Se3 with the spatial dimension of the probe pulse, as well as resolving the spatial inhomogeneity contribution to the observed spectral broadening. Finally, after in situ exfoliation, we performed time-resolved μ-ARPES on a ∼30 μm flake of transition metal dichalcogenide WTe2, thus demonstrating the ability to access ultrafast electron dynamics with momentum resolution on micro-exfoliated materials.

High-resolution MHz time- and angle-resolved photoemission spectroscopy based on a tunable vacuum ultraviolet source

The time- and angle-resolved photoemission spectroscopy (trARPES) allows for direct mapping of the electronic band structure and its dynamic response on femtosecond timescales. Here, we present a new ARPES system, powered by a new fiber-based femtosecond light source in the vacuum ultraviolet range, accessing the complete first Brillouin zone for most materials. We present trARPES data on Au(111), polycrystalline Au, Bi2Se3, and TaTe2, demonstrating an energy resolution of 21 meV with a time resolution of <360 fs, at a high repetition rate of 1 MHz. The system is integrated with an extreme ultraviolet high harmonic generation beamline, enabling an excellent tunability of the time-bandwidth resolution.

Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems

While a significant fraction of topological materials has been characterized using symmetry requirements1-4, the past two years have witnessed the rise of novel multi-gap dependent topological states5-9, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium10-15, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an 'anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.

Light-Induced Ideal Weyl Semimetal in HgTe via Nonlinear Phononics

Interactions between light and matter allow the realization of out-of-equilibrium states in quantum solids. In particular, nonlinear phononics is one of the most efficient approaches to realizing the stationary electronic state in nonequilibrium. Herein, by an extended ab initio molecular dynamics method, we identify that long-lived light-driven quasistationary geometry could stabilize the topological nature in the material family of HgTe compounds. We show that coherent excitation of the infrared-active phonon mode results in a distortion of the atomic geometry with a lifetime of several picoseconds. We show that four Weyl points are located exactly at the Fermi level in this nonequilibrium geometry, making it an ideal long-lived metastable Weyl semimetal. We propose that such a metastable topological phase can be identified by photoelectron spectroscopy of the Fermi arc surface states or ultrafast pump-probe transport measurements of the nonlinear Hall effect.

Aberrant photoelectric effect in the topological insulator/n-GaN heterojunction (Bi2Te3/n-GaN) under unpolarized illumination

A topological insulator has a unique graphene-like Dirac cone conducting surface state, which is excellent for broadband absorption and photodetector applications. Experimental investigations on the Bi2Te3/n-GaN heterojunction exhibited an aberrant photoelectric effect under the influence of unpolarized light. Transport measurements of the Bi2Te3/n-GaN heterojunction revealed a negative photoconductance, with a sudden increase in resistance. This was consistent with the applied range of wavelength and power used for incident light while it was contrary to the usual gap-state transition model, which states that a negative conductance is due to the trapping of charge carriers. The observed aberrant photoelectric effect seen in Bi2Te3/n-GaN heterojunction devices was due to the polycrystalline nature of the Bi2Te3 topological insulator film, where the incident photon-induced bandgap in the Dirac cone surface state resulted in a negative photoelectric effect. This phenomenon opens the possibility for applications in highly sensitive photodetectors and non-volatile memories, along with employing the bandgap-opening concept in retinomorphic devices.

Time-resolved ARPES with probe energy of 6.0/7.2 eV and switchable resolution configuration

We present a detailed exposition of the design for time- and angle-resolved photoemission spectroscopy using a UV probe laser source that combines the nonlinear effects of β-BaB2O4 and KBe2BO3F2 optical crystals. The photon energy of the probe laser can be switched between 6.0 and 7.2 eV, with the flexibility to operate each photon energy setting under two distinct resolution configurations. Under the fully optimized energy resolution configuration, we achieve an energy resolution of 8.5 meV at 6.0 eV and 10 meV at 7.2 eV. Alternatively, switching to the other configuration enhances the temporal resolution, yielding a temporal resolution of 72 fs for 6.0 eV and 185 fs for 7.2 eV. We validated the performance and reliability of our system by applying it to measuring two typical materials: the topological insulator MnBi2Te4 and the excitonic insulator candidate Ta2NiSe5.

Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization

Ultrafast nonlinear optical phenomena in solids have been attracting a great deal of interest as novel methodologies for the femtosecond spectroscopy of electron dynamics and control of the properties of materials. Here, we theoretically investigate strong-field nonlinear optical transitions in a prototypical two-dimensional material, hBN, and show that the k-resolved conduction band charge occupation patterns induced by an elliptically polarized laser can be understood in a multiphoton resonant picture, but, remarkably, only if using the Floquet light-dressed states instead of the undressed matter states. Our work demonstrates that Floquet dressing affects ultrafast charge dynamics and photoexcitation even from a single pump pulse and establishes a direct measurable signature for band dressing in nonlinear optical processes in solids, opening new paths for ultrafast spectroscopy and valley manipulation.

Generation of higher-order topological insulators using periodic driving

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.

Optically induced resonant tunneling of electrons in nanostructures

We developed the theory of elastic electron tunneling through a potential barrier driven by a strong high-frequency electromagnetic field. It is demonstrated that the driven barrier can be considered as a stationary two-barrier potential which contains the quasi-stationary electron states confined between these two barriers. When the energy of an incident electron coincides with the energy of the quasi-stationary state, the driven barrier becomes fully transparent for the electron (the resonant tunneling). The developed theory is applied to describe electron transport through a quantum point contact irradiated by an electromagnetic wave.

Superconducting nonlinear transport in optically driven high-temperature K3C60

Optically driven quantum materials exhibit a variety of non-equilibrium functional phenomena, which to date have been primarily studied with ultrafast optical, X-Ray and photo-emission spectroscopy. However, little has been done to characterize their transient electrical responses, which are directly associated with the functionality of these materials. Especially interesting are linear and nonlinear current-voltage characteristics at frequencies below 1 THz, which are not easily measured at picosecond temporal resolution. Here, we report on ultrafast transport measurements in photo-excited K3C60. Thin films of this compound were connected to photo-conductive switches with co-planar waveguides. We observe characteristic nonlinear current-voltage responses, which in these films point to photo-induced granular superconductivity. Although these dynamics are not necessarily identical to those reported for the powder samples studied so far, they provide valuable new information on the nature of the light-induced superconducting-like state above equilibrium Tc. Furthermore, integration of non-equilibrium superconductivity into optoelectronic platforms may lead to integration in high-speed devices based on this effect.

Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current

Nonlinear responses of superconductors to intense terahertz radiation has been an active research frontier. Using terahertz pump-terahertz probe spectroscopy, we investigate the c-axis nonlinear optical response of a high-temperature superconducting cuprate. After excitation by a single-cycle terahertz pump pulse, the reflectivity of the probe pulse oscillates as the pump-probe delay is varied. Interestingly, the oscillatory central frequency scales linearly with the probe frequency, a fact widely overlooked in pump-probe experiments. By theoretically solving the nonlinear optical reflection problem on the interface, we show that our observation is well explained by the Josephson-type third-order nonlinear electrodynamics, together with the emission coefficient from inside the material into free space. The latter results in a strong enhancement of the emitted signal whose physical frequency is around the Josephson plasma edge. Our result offers a benchmark for and new insights into strong-field terahertz spectroscopy of related quantum materials.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states

Light-matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting-semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current-phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current-phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet-Andreev states, our study rules out this scenario. The distortion of the current-phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light-matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices.

Quasi-Floquet Prethermalization in a Disordered Dipolar Spin Ensemble in Diamond

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.

Non-Hermitian Floquet Topological Matter-A Review

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

Porphyrin Supramolecule as Surface Carrier Modulator Imparts Hole Transporter with Enhanced Mobility for Perovskite Photovoltaics

Modulating the surface charge transport behavior of hole transport materials (HTMs) would be as an potential approach to improve their hole mobility, while yet realized for fabricating efficient photovoltaic devices. Here, an oxygen bridged dimer-based monoamine FeIII porphyrin supramolecule is prepared and doped in HTM film. Theoretical analyses reveal that the polaron distributed on dimer can be coupled with the parallel arranged polarons on adjacent dimers. This polaron coupling at the interface of supramolecule and HTM can resonates with hole flux to increase hole transport efficiency. Mobility tests reveal that the hole mobility of doped HTM film is improved by 8-fold. Doped perovskite device exhibits an increased efficiency from 19.8 % to 23.2 %, and greatly improved stability. This work provides a new strategy to improve the mobility of HTMs by surface carrier modulation, therefore fabricating efficient photovoltaic devices.

Floquet Engineering of Black Phosphorus upon Below-Gap Pumping

Time-periodic light field can dress the electronic states and lead to light-induced emergent properties in quantum materials. While below-gap pumping is regarded favorable for Floquet engineering, so far direct experimental evidence of momentum-resolved band renormalization still remains missing. Here, we report experimental evidence of light-induced band renormalization in black phosphorus by pumping at photon energy of 160 meV, which is far below the band gap, and the distinction between below-gap pumping and near-resonance pumping is revealed. Our Letter demonstrates light-induced band engineering upon below-gap pumping, and provides insights for extending Floquet engineering to more quantum materials.

Photocurrent Induced by a Bicircular Light Drive in Centrosymmetric Systems

A bicircular light (BCL) consists of left and right circularly polarized lights with different frequencies, and draws a roselike pattern with a rotational symmetry determined by the ratio of the two frequencies. Here we show that an application of a BCL to centrosymmetric systems allows a photocurrent generation through introduction of an effective polarity to the system. We derive formulas for the BCL-induced photocurrent from a standard perturbation theory, which is then applied to a simple 1D model and 3D Dirac and Weyl semimetals. A nonperturbative effect with strong light intensity is also discussed with the Floquet technique.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Complete characterization of a Yb-based OPA at a high repetition rate using frequency resolved optical switching

We demonstrate experimentally that frequency resolved optical switching (FROSt) can be used to characterize ultra-broadband pulses at high repetition rates up to 500 kHz. Specifically, we present the complete temporal characterization of an optical parametric amplifier (OPA), from the supercontinuum (SC) to the second stage of amplification. Simultaneous characterization of co-propagating signal and idler pulses enables retrieval of their group delay, as well as their temporal phase and intensity. Our study focuses on an extensive frequency range spanning the infrared region (1.2 to 2.4 µm) and confirms the strength and convenience of FROSt as a single tool for characterizing a wide range of pulses at high repetition rates.

Effects of Floquet Engineering on the Coherent Exciton Dynamics in Monolayer WS2

Coherent optical manipulation of electronic bandstructures via Floquet Engineering is a promising means to control quantum systems on an ultrafast time scale. However, the ultrafast switching on/off of the driving field comes with questions regarding the limits of the Floquet formalism (which is defined for an infinite periodic drive) through the switching process and to what extent the transient changes can be driven adiabatically. Experimentally addressing these questions has been difficult, in large part due to the absence of an established technique to measure coherent dynamics through the duration of the pulse. Here, using multidimensional coherent spectroscopy we explicitly excite, control, and probe a coherent superposition of excitons in the K and K' valleys in monolayer WS₂. With a circularly polarized, red-detuned pump pulse, the degeneracy of the K and K' excitons can be lifted, and the phase of the coherence rotated. We directly measure phase rotations greater than π during the 100 fs driving pulse and show that this can be described by a combination of the AC-Stark shift of excitons in one valley and the Bloch-Siegert shift of excitons in the opposite valley. Despite showing a smooth evolution of the phase that directly follows the intensity envelope of the nonresonant pump pulse, the process is not perfectly adiabatic. By measuring the magnitude of the macroscopic coherence as it evolves before, during, and after the nonresonant pump pulse we show that there is additional decoherence caused by power broadening in the presence of the nonresonant pump. This nonadiabaticity arises as a result of interactions with the otherwise adiabatic Floquet states and may be a problem for many applications, such as manipulating qubits in quantum information processing; however, these measurements also suggest ways such effects can be minimized or eliminated.

Ultrafast Switching from the Charge Density Wave Phase to a Metastable Metallic State in 1T-TiSe_{2}

The ultrafast electronic structures of the charge density wave material 1T-TiSe_{2} were investigated by high-resolution time- and angle-resolved photoemission spectroscopy. We found that the quasiparticle populations drove ultrafast electronic phase transitions in 1T-TiSe_{2} within 100 fs after photoexcitation, and a metastable metallic state, which was significantly different from the equilibrium normal phase, was evidenced far below the charge density wave transition temperature. Detailed time- and pump-fluence-dependent experiments revealed that the photoinduced metastable metallic state was a result of the halted motion of the atoms through the coherent electron-phonon coupling process, and the lifetime of this state was prolonged to picoseconds with the highest pump fluence used in this study. Ultrafast electronic dynamics were well captured by the time-dependent Ginzburg-Landau model. Our work demonstrates a mechanism for realizing novel electronic states by photoinducing coherent motion of atoms in the lattice.

Fractionalized Prethermalization in a Driven Quantum Spin Liquid

Quantum spin liquids subject to a periodic drive can display fascinating nonequilibrium heating behavior because of their emergent fractionalized quasiparticles. Here, we investigate a driven Kitaev honeycomb model and examine the dynamics of emergent Majorana matter and Z_{2} flux excitations. We uncover a distinct two-step heating profile-dubbed fractionalized prethermalization-and a quasistationary state with vastly different temperatures for the matter and the flux sectors. We argue that this peculiar prethermalization behavior is a consequence of fractionalization. Furthermore, we discuss an experimentally feasible protocol for preparing a zero-flux initial state of the Kiteav honeycomb model with a low energy density, which can be used to observe fractionalized prethermalization in quantum information processing platforms.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Floquet Engineering of Nonequilibrium Valley-Polarized Quantum Anomalous Hall Effect with Tunable Chern Number

Here, we propose that Floquet engineering offers a strategy to realize the nonequilibrium quantum anomalous Hall effect (QAHE) with tunable Chern number. Using first-principles calculations and Floquet theorem, we unveil that QAHE related to valley polarization (VP-QAHE) is formed from the hybridization of Floquet sidebands in the two-dimensional family MSi₂Z₄ (M = Mo, W, V; Z = N, P, As) by irradiating circularly polarized light (CPL). Through the tuning of frequency, intensity, and handedness of CPL, the Chern number of VP-QAHE is highly tunable and up to C = ±4, which attributes to light-induced trigonal warping and multiple-band inversion at different valleys. The chiral edge states and quantized plateau of Hall conductance are visible inside the global band gap, thereby facilitating the experimental measurement. Our work not only establishes Floquet engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials but also provides an avenue to explore emergent topological phases under light irradiation.

Control of Yu-Shiba-Rusinov States through a Bosonic Mode

We investigate the impact of a bosonic degree of freedom on Yu-Shiba-Rusinov states emerging from a magnetic impurity in a conventional superconductor. Starting from the Anderson impurity model, we predict that an additional p-wave conduction band channel opens up if a bosonic mode is coupled to the tunneling between impurity and host, which implies an additional pair of odd-parity Yu-Shiba-Rusinov states. The bosonic mode can be a vibrational mode or the electromagnetic field in a cavity. The exchange couplings in the two channels depend sensitively on the state of the bosonic mode (ground state, few quanta, or classically driven Floquet state), which opens possibilities for phononics or photonics control of such systems, with a rich variety of ground and excited states.

Witnessing Nonequilibrium Entanglement Dynamics in a Strongly Correlated Fermionic Chain

Many-body entanglement in condensed matter systems can be diagnosed from equilibrium response functions through the use of entanglement witnesses and operator-specific quantum bounds. Here, we investigate the applicability of this approach for detecting entangled states in quantum systems driven out of equilibrium. We use a multipartite entanglement witness, the quantum Fisher information, to study the dynamics of a paradigmatic fermion chain undergoing a time-dependent change of the Coulomb interaction. Our results show that the quantum Fisher information is able to witness distinct signatures of multipartite entanglement both near and far from equilibrium that are robust against decoherence. We discuss implications of these findings for probing entanglement in light-driven quantum materials with time-resolved optical and x-ray scattering methods.

Pseudospin-selective Floquet band engineering in black phosphorus

Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials^1-3, cold atoms⁴ and photonic systems⁵ through hybridization with photon-dressed Floquet states⁶ in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials^7-11, for example, modifications of the topological properties of Dirac materials^12,13 and modulation of the optical response^14-16. Despite extensive research interests over the past decade^3,8,17-20, there is no experimental evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report experimental signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is observed near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favouring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.

Diabatic and adiabatic transitions between Floquet states imprinted in coherent exciton emission in monolayer WSe2

Floquet engineering is a promising way of controlling quantum system with photon-dressed states on an ultrafast time scale. So far, the energy structure of Floquet states in solids has been intensively investigated. However, the dynamical aspects of the photon-dressed states under ultrashort pulse have not been explored yet. Their dynamics become highly sensitive to the driving field transients, and thus, understanding them is crucial for ultrafast manipulation of a quantum state. Here, we observed the coherent exciton emission in monolayer WSe₂ at room temperature at the appropriate photon energy and the field strength of the driving light pulse using high-harmonic spectroscopy. Together with numerical calculations, our measurements revealed that the coherent exciton emission spectrum reflects the diabatic and adiabatic dynamics of Floquet states of excitons. Our results provide a previosuly unexplored approach to Floquet engineering and lead to control of quantum materials through pulse shaping of the driving field.

Generating Many Majorana Corner Modes and Multiple Phase Transitions in Floquet Second-Order Topological Superconductors

A d-dimensional, nth-order topological insulator or superconductor has localized eigenmodes at its (d−n)-dimensional boundaries (n≤d). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain a wide variety of Floquet second-order topological superconducting (SOTSC) phases with many Majorana corner modes at both zero and π quasienergies. Two distinct Floquet SOTSC phases are found to be separated by three possible kinds of transformations, i.e., a topological phase transition due to the closing/reopening of a bulk spectral gap, a topological phase transition due to the closing/reopening of an edge spectral gap, or an entirely different phase in which the bulk spectrum is gapless. Thanks to the strong interplay between driving and intrinsic energy scales of the system, all the found phases and transitions are highly controllable via tuning a single hopping parameter of the system. Our discovery not only enriches the possible forms of Floquet SOTSC phases, but also offers an efficient scheme to generate many coexisting Majorana zero and π corner modes, which may find applications in Floquet quantum computation.

Photo-induced phase-transitions in complex solids

Photo-induced phase-transitions (PIPTs) driven by highly cooperative interactions are of fundamental interest as they offer a way to tune and control material properties on ultrafast timescales. Due to strong correlations and interactions, complex quantum materials host several fascinating PIPTs such as light-induced charge density waves and ferroelectricity and have become a desirable setting for studying these PIPTs. A central issue in this field is the proper understanding of the underlying mechanisms driving the PIPTs. As these PIPTs are highly nonlinear processes and often involve multiple time and length scales, different theoretical approaches are often needed to understand the underlying mechanisms. In this review, we present a brief overview of PIPTs realized in complex materials, followed by a discussion of the available theoretical methods with selected examples of recent progress in understanding of the nonequilibrium pathways of PIPTs.

Controlling Floquet states on ultrashort time scales

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.

Influence of Tartrate Ligand Coordination over Luminescence Properties of Chiral Lanthanide-Based Metal-Organic Frameworks

The present work reports on a detailed discussion about the synthesis, characterization, and luminescence properties of three pairs of enantiopure 3D metal-organic frameworks (MOFs) with general formula {[Ln₂(L/D-tart)₃(H₂O)₂]·3H₂O}_n (3D_Ln-L/D, where Ln = Sm(III), Eu(III) or Gd(III), and L/D-tart = L- or D-tartrate), and ten pairs of enantiopure 2D coordination polymers (CPs) with general formula [Ln(L/D-Htart)₂(OH)(H₂O)₂]_n (2D_Ln-L/D, where Ln = Y(III), Sm(III), Eu(III), Gd(III), Tb(III), Dy(III), Ho(III), Er(III), Tm(III) or Yb(III), and L/D-Htart = hydrogen L- or D-tartrate) based on single-crystal X-ray structures. Enantiopure nature of the samples has been further corroborated by Root Mean Square Deviation (RMSD) as well as by circular dichroism (CD) spectra. Solid-state emission spectra of Eu(III), Tb(III), and Dy(III)-based compounds confirm the occurrence of ligand-to-metal charge transfers in view of the characteristic emissions for these lanthanide ions, and emission decay curves were also recorded to estimate the emission lifetimes for the reported compounds. A complete theoretical study was accomplished to better understand the energy transfers occurring in the Eu-based counterparts, which allows for explaining the different performances of 3D-MOFs and 2D-layered compounds. As inferred from the colorimetric diagrams, emission characteristics of Eu-based 2D CPs depend on the temperature, so their luminescent thermometry has been determined on the basis of a ratiometric analysis between the ligand-centered and Eu-centered emission. Finally, a detailed study of the polarized luminescence intensity emitted by the samples is also accomplished to support the occurrence of chiro-optical activity.

Stimulated Rayleigh Scattering Enhanced by a Longitudinal Plasma Mode in a Periodically Driven Dirac Semimetal Cd_{3}As_{2}

Using broadband (12-45 THz) multi-terahertz spectroscopy, we show that stimulated Rayleigh scattering dominates the transient optical conductivity of cadmium arsenide, a Dirac semimetal, under an optical driving field at 30 THz. The characteristic dispersive line shape with net optical gain is accounted for by optical transitions between light-induced Floquet subbands, strikingly enhanced by the longitudinal plasma mode. Stimulated Rayleigh scattering with an unprecedentedly large refractive index change may pave the way for slow light generation in conductive solids at room temperature.

Revealing non-Hermitian band structure of photonic Floquet media

Periodically driven systems are ubiquitously found in both classical and quantum regimes. In the field of photonics, these Floquet systems have begun to provide insight into how time periodicity can extend the concept of spatially periodic photonic crystals and metamaterials to the time domain. However, despite the necessity arising from the presence of nonreciprocal coupling between states in a photonic Floquet medium, a unified non-Hermitian band structure description remains elusive. We experimentally reveal the unique Bloch-Floquet and non-Bloch band structures of a photonic Floquet medium emulated in the microwave regime with a one-dimensional array of time-periodically driven resonators. These non-Hermitian band structures are shown to be two measurable distinct subsets of complex eigenfrequency surfaces of the photonic Floquet medium defined in complex momentum space.

Excitonic Bloch-Siegert shift in CsPbI3 perovskite quantum dots

Coherent interaction between matter and light field induces both optical Stark effect and Bloch-Siegert shift. Observing the latter has been historically challenging, because it is weak and is often accompanied by a much stronger Stark shift. Herein, by controlling the light helicity, we can largely restrict these two effects to different spin-transitions in CsPbI₃ perovskite quantum dots, achieving room-temperature Bloch-Siegert shift as strong as 4 meV with near-infrared pulses. The ratio between the Bloch-Siegert and optical Stark shifts is however systematically higher than the prediction by the non-interacting, quasi-particle model. With a model that explicitly accounts for excitonic effects, we quantitatively reproduce the experimental observations. This model depicts a unified physical picture of the optical Stark effect, biexcitonic optical Stark effect and Bloch-Siegert shift in low-dimensional materials displaying strong many-body interactions, forming the basis for the implementation of these effects to information processing, optical modulation and Floquet engineering.

Two-photon IR pumped UV-Vis transient absorption spectroscopy of Dirac fermions in the topological insulator Bi2Se3

It is often taken for granted that in pump-probe experiments on the topological insulator (TI) Bi₂Se₃using IR pumping with a commercial Ti:sapphire laser [∼800 nm (1.55 eV photon energy)], the electrons are excited in the one-photon absorption regime, even when pumped with absorbed fluences in the mJ cm^-2range. Here, using UV-Vis transient absorption (TA) spectroscopy, we show that even at low-power Infrared (IR) pumping with absorbed fluences in theμJ cm^-2range, the TA spectra of the TI Bi₂Se₃extend across a part of the UV and the entire visible region. This observation suggests unambiguously that the two-photon pumping regime accompanies the usual one-photon pumping regime even at low laser powers applied. We attribute the high efficiency of two-photon pumping to the giant nonlinearity of Dirac fermions in the Dirac surface states (SS). On the contrary, one-photon pumping is associated with the excitation of bound valence electrons in the bulk into the conduction band. Two mechanisms of absorption bleaching were also revealed since they manifest themselves in different spectral regions of probing and cause the appearance of three different relaxation dynamics. These two mechanisms were attributed to the filling of the phase-space in the Dirac SS and bulk states, followed by the corresponding Pauli blocking.

Multispectral time-resolved energy-momentum microscopy using high-harmonic extreme ultraviolet radiation

A 790-nm-driven high-harmonic generation source with a repetition rate of 6 kHz is combined with a toroidal-grating monochromator and a high-detection-efficiency photoelectron time-of-flight momentum microscope to enable time- and momentum-resolved photoemission spectroscopy over a spectral range of 23.6-45.5 eV with sub-100 fs time resolution. Three-dimensional (3D) Fermi surface mapping is demonstrated on graphene-covered Ir(111) with energy and momentum resolutions of ≲100 meV and ≲0.1 Å^-1, respectively. The tabletop experiment sets the stage for measuring the k_z-dependent ultrafast dynamics of 3D electronic structure, including band structure, Fermi surface, and carrier dynamics in 3D materials as well as 3D orbital dynamics in molecular layers.