A driven Kerr oscillator with two-fold degeneracies for qubit protection.

We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, [Formula: see text], the oscillator displays [Formula: see text] exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system.

Giant self-driven exciton-Floquet signatures in time-resolved photoemission spectroscopy of MoS2 from time-dependent GW approach.

Time-resolved, angle-resolved photoemission spectroscopy (TR-ARPES) is a one-particle spectroscopic technique that can probe excitons (two-particle excitations) in momentum space. We present an ab initio, time-domain GW approach to TR-ARPES and apply it to monolayer MoS2. We show that photoexcited excitons may be measured and quantified as satellite bands and lead to the renormalization of the quasiparticle bands. These features are explained in terms of an exciton-Floquet phenomenon induced by an exciton time-dependent bosonic field, which are orders of magnitude stronger than those of laser field-induced Floquet bands in low-dimensional semiconductors. Our findings imply a way to engineer Floquet matter through the coherent oscillation of excitons and open the new door for mechanisms for band structure engineering.

Emergence of tunable periodic density correlations in a Floquet-Bloch system.

In quantum gases, two-body interactions are responsible for a variety of instabilities that depend on the characteristics of both trapping and interactions. These instabilities can lead to the appearance of new structures or patterns. We report on the Floquet engineering of such a parametric instability, on a Bose-Einstein condensate held in a time-modulated optical lattice. The modulation triggers a destabilization of the condensate into a state exhibiting a density modulation with a new spatial periodicity. This new crystal-like order, which shares characteristic correlation properties with a supersolid, directly depends on the modulation parameters: The interplay between the Floquet spectrum and interactions generates narrow and adjustable instability regions, leading to the growth, from quantum or thermal fluctuations, of modes with a density modulation noncommensurate with the lattice spacing. This study demonstrates the production of metastable exotic states of matter through Floquet engineering and paves the way for further studies of dissipation in the resulting phase and of similar phenomena in other geometries.

Novel Quantum States of Exciton-Floquet Composites: Electron-Hole Entanglement and Information.

Coulomb exchange between distinct electron-hole modes, i.e., exciton and Floquet states, in two-dimensional semiconductors is explored. Coherent ultrafast mixing of the exciton and Floquet states under weak optical pumping is investigated through a theoretical description of time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) in an extended Haldane model that includes the electron-hole Coulomb interaction. Two branches of novel quantum states are found in the form of bosonic exciton-Floquet composites, which result from exchange coupling due to the Coulomb interaction. Furthermore, tr-ARPES could be directly employed for the density matrix element of the biparticle subsystem of photoelectron and hole, and electron-hole entanglement and information could be further explored. This finding suggests a unique platform to study the buildup and dephasing of novel exciton-Floquet composites and to resolve the information carried by them, which would enable the pursuit of new reconfigurable devices based on two-dimensional semiconductors.

Floquet Engineering of Excitons in Two-Dimensional Halide Perovskites via Biexciton States.

Layered two-dimensional halide perovskites (2DHPs) exhibit exciting non-equilibrium properties that allow the manipulation of energy levels through coherent light-matter interactions. Under the Floquet picture, novel quantum states manifest through the optical Stark effect (OSE) following intense subresonant photoexcitation. Nevertheless, a detailed understanding of the influence of strong many-body interactions between excitons on the OSE in 2DHPs remains unclear. Herein, we uncover the crucial role of biexcitons in photon-dressed states and demonstrate precise optical control of the excitonic states via the biexcitonic OSE in 2DHPs. With fine step tuning of the driven energy, we fully parametrize the evolution of exciton resonance modulation. The biexcitonic OSE enables Floquet engineering of the exciton resonance with either a blue-shift or a red-shift of the energy levels. Our findings shed new light on the intricate nature of coherent light-matter interactions in 2DHPs and extend the degree of freedom for ultrafast coherent optical control over excitonic states.

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.

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.

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.

Room-Temperature Anomalous Coherent Excitonic Optical Stark Effect in Metal Halide Perovskite Quantum Dots.

Nonresonant optical driving of confined semiconductors can open up exciting opportunities for experimentally realizing strongly interacting photon-dressed (Floquet) states through the optical Stark effect (OSE) for coherent modulation of the exciton state. Here we report the first room-temperature observation of the Floquet biexciton-mediated anomalous coherent excitonic OSE in CsPbBr3 quantum dots (QDs). Remarkably, the strong exciton-biexciton interaction leads to a coherent red shift and splitting of the exciton resonance as a function of the drive photon frequency, similar to Autler-Townes splitting in atomic and molecular systems. The large biexciton binding energy of ∼71 meV and exciton-biexciton transition dipole moment of ∼25 D facilitate the hallmark observations, even at large detuning energies of >300 meV. This is accompanied by an unusual crossover from linear to nonlinear fluence dependence of the OSE as a function of the drive photon frequency. Our findings reveal crucial information on the unexplored many-body coherent interacting regime, making perovskite QDs suitable for room temperature quantum devices.

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.

Quantum Control by Few-Cycles Pulses: The Two-Level Problem.

We investigate the problem of population transfer in a two-states system driven by an external electromagnetic field featuring a few cycles, until the extreme limit of two or one cycle. Taking the physical constraint of zero-area total field into account, we determine strategies leading to ultrahigh-fidelity population transfer despite the failure of the rotating wave approximation. We specifically implement adiabatic passage based on adiabatic Floquet theory for a number of cycles as low as 2.5 cycles, finding and making the dynamics follow an adiabatic trajectory connecting the initial and targeted states. Nonadiabatic strategies with shaped or chirped pulses, extending the π-pulse regime to two- or single-cycle pulses, are also derived.

Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems.

Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic and aperiodic systems. In the phase-space of FTNM coefficients, SVs are shown to equate with unit norm FTNMs at critical times. In the long-time limit, when SVs approach OLVs, the Oseledec theorem and the relationships between OLVs and CLVs are used to connect CLVs to FTNMs in this phase-space. The covariant properties of both the CLVs, and the FTNMs, together with their phase-space independence, and the norm independence of global Lyapunov exponents and FTNM growth rates, are used to establish their asymptotic convergence. Conditions on the dynamical systems for the validity of these results, particularly ergodicity, boundedness and non-singular FTNM characteristic matrix and propagator, are documented. The findings are deduced for systems with nondegenerate OLVs, and, as well, with degenerate Lyapunov spectrum as is the rule in the presence of waves such as Rossby waves. Efficient numerical methods for the calculation of leading CLVs are proposed. Norm independent finite-time versions of the Kolmogorov-Sinai entropy production and Kaplan-Yorke dimension are presented.

An overview of elastic waveguides with dynamic sub-structures.

The dynamic response of elastic waveguides is important for a wide range of applications that involve dispersive waves as well as wave localization. In particular, a case of special interest relates to waveguides subjected to moving loads. In the case where the elongated structure includes a sequence of built-in resonators, the range of resonance regimes may be extended accordingly. The present paper gives an overview of several mathematical formulations that connect Floquet theory to the dynamic response of multi-scale waveguides, which include inertial sub-structures subjected to external forces. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Dispersal-induced growth in a time-periodic environment.

Dispersal-induced growth (DIG) occurs when several populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect, and the corresponding conditions on the parameters involved.

Interaction frames in solid-state NMR: A case study for chemical-shift-selective irradiation schemes.

Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual (Zeeman) rotating frame, or the radio-frequency-field (rf) Hamiltonian to describe the efficiency of decoupling or recoupling sequences. Going into an interaction frame can also make parts of a time-dependent Hamiltonian time independent like the rf-field Hamiltonian in the usual (Zeeman) rotating frame. Eliminating the dominant term often allows a better understanding of the details of the spin dynamics. Going into an interaction frame can also reduces the energy-level splitting in the Hamiltonian leading to a faster convergence of perturbation expansions, average Hamiltonian, or Floquet theory. Often, there is no obvious choice of the interaction frame to use but some can be more convenient than others. Using the example of frequency-selective dipolar recoupling, we discuss the differences, advantages, and disadvantages of different choices of interaction frames. They always include the complete radio-frequency Hamiltonian but can also contain the chemical shifts of the spins and may or may not contain the effective fields over one cycle of the pulse sequence.

Giant Third-Harmonic Optical Generation from Topological Insulator Heterostructures.

The downscaling of nonlinear optical devices is significantly hindered by the inherently weak nonlinearity in regular materials. Here, we report a giant third-harmonic generation discovered in epitaxial thin films of V-VI chalcogenide topological insulators. Using a tailored substrate and capping layer, a single reflection from a 13 nm film can produce a nonlinear conversion efficiency of nearly 0.01%, a performance that rivals micron-scale waveguides made from conventional materials or metasurfaces with far more complex structures. Such strong nonlinear optical emission, absent from the topologically trivial member in the same compound family, is found to be generated by the same bulk band characteristics that are responsible for producing the band inversion and the nontrivial topological ordering. This finding reveals the possibility of obtaining superior optical nonlinearity by examining the large pool of newly discovered topological materials with similar band characteristics.

Survival of Floquet-Bloch States in the Presence of Scattering.

Floquet theory has spawned many exciting possibilities for electronic structure control with light, with enormous potential for future applications. The experimental demonstration in solids, however, remains largely unrealized. In particular, the influence of scattering on the formation of Floquet-Bloch states remains poorly understood. Here we combine time- and angle-resolved photoemission spectroscopy with time-dependent density functional theory and a two-level model with relaxation to investigate the survival of Floquet-Bloch states in the presence of scattering. We find that Floquet-Bloch states will be destroyed if scattering-activated by electronic excitations-prevents the Bloch electrons from following the driving field coherently. The two-level model also shows that Floquet-Bloch states reappear at high field intensities where energy exchange with the driving field dominates over energy dissipation to the bath. Our results clearly indicate the importance of long scattering times combined with strong driving fields for the successful realization of various Floquet phenomena.

Environmental limits of Rift Valley fever revealed using ecoepidemiological mechanistic models.

Vector-borne diseases (VBDs) of humans and domestic animals are a significant component of the global burden of disease and a key driver of poverty. The transmission cycles of VBDs are often strongly mediated by the ecological requirements of the vectors, resulting in complex transmission dynamics, including intermittent epidemics and an unclear link between environmental conditions and disease persistence. An important broader concern is the extent to which theoretical models are reliable at forecasting VBDs; infection dynamics can be complex, and the resulting systems are highly unstable. Here, we examine these problems in detail using a case study of Rift Valley fever (RVF), a high-burden disease endemic to Africa. We develop an ecoepidemiological, compartmental, mathematical model coupled to the dynamics of ambient temperature and water availability and apply it to a realistic setting using empirical environmental data from Kenya. Importantly, we identify the range of seasonally varying ambient temperatures and water-body availability that leads to either the extinction of mosquito populations and/or RVF (nonpersistent regimens) or the establishment of long-term mosquito populations and consequently, the endemicity of the RVF infection (persistent regimens). Instabilities arise when the range of the environmental variables overlaps with the threshold of persistence. The model captures the intermittent nature of RVF occurrence, which is explained as low-level circulation under the threshold of detection, with intermittent emergence sometimes after long periods. Using the approach developed here opens up the ability to improve predictions of the emergence and behaviors of epidemics of many other important VBDs.

Dynamic Behavior Analysis and Stability Control of Tethered Satellite Formation Deployment.

In recent years, Tethered Space Systems (TSSs) have received significant attention in aerospace research as a result of their significant advantages: dexterousness, long life cycles and fuel-less engines. However, configurational conversion processes of tethered satellite formation systems in a complex space environment are essentially unstable. Due to their structural peculiarities and the special environment in outer space, TSS vibrations are easily produced. These types of vibrations are extremely harmful to spacecraft. Hence, the nonlinear dynamic behavior of systems based on a simplified rigid-rod tether model is analyzed in this paper. Two stability control laws for tether release rate and tether tension are proposed in order to control tether length variation. In addition, periodic stability of time-varying control systems after deployment is analyzed by using Floquet theory, and small parameter domains of systems in asymptotically stable states are obtained. Numerical simulations show that proposed tether tension controls can suppress in-plane and out-of-plane librations of rigid tethered satellites, while spacecraft and tether stability control goals can be achieved. Most importantly, this paper provides tether release rate and tether tension control laws for suppressing wide-ranging TSS vibrations that are valuable for improving TSS attitude control accuracy and performance, specifically for TSSs that are operating in low-eccentricity orbits.

Mechanical Stabilization of Nanoscale Conductors by Plasmon Oscillations.

External driving of the Fermion reservoirs interacting with a nanoscale charge-conductor is shown to enhance its mechanical stability during resonant tunneling. This counterintuitive cooling effect is predicted despite the net energy flow into the device. Field-induced plasmon oscillations stir the energy distribution of charge carriers near the reservoir's chemical potentials into a nonequilibrium state with favored transport of low-energy electrons. Consequently, excess heating of mechanical degrees of freedom in the conductor is suppressed. We demonstrate and analyze this effect for a generic model of mechanical instability in nanoelectronic devices, covering a broad range of parameters. Plasmon-induced stabilization is suggested as a feasible strategy to confront a major problem of current-induced heating and breakdown of nanoscale systems operating far from equilibrium.