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We study the nonlinear optomechanically induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order sidebands, including the transmission rate and the group delay; (ii) for active-passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength and group delay of not only the probe light but also its higher-order sidebands.

Strong light fields have created opportunities to tailor novel functionalities of solids 1 – 5 . Floquet–Bloch states can form under periodic driving of electrons and enable exotic quantum phases 6 – 15 . On subcycle timescales, lightwaves can simultaneously drive intraband currents 16 – 29 and interband transitions 18 , 19 , 30 , 31 , which enable high-harmonic generation 16 , 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 insulator 32 , 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. The build-up and dephasing of Floquet-–Bloch bands is visualized in both subcycle band-structure videography and quantum theory, revealing the interplay of strong-field intraband and interband excitations in a non-equilibrium Floquet picture.

Huygens’ metasurfaces demonstrate almost arbitrary control over the shape of a scattered beam; however, its spatial profile is typically fixed at the fabrication time. The dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens’ condition across the tuning range. In this work, we experimentally demonstrate that a time-varying metadevice which performs frequency conversion can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens’ metadevice is made of both electric and magnetic meta-atoms with independently controlled modulation, and the phase of this modulation is imprinted on the scattered parametric waves, controlling their shapes and directions. We develop a theory which shows how the scattering directionality, phase, and conversion efficiency of sidebands can be manipulated almost arbitrarily. We demonstrate novel effects including all-angle beam steering and frequency-multiplexed functionalities at microwave frequencies around 4 GHz, using varactor diodes as tunable elements. We believe that the concept can be extended to other frequency bands, enabling metasurfaces with an arbitrary phase pattern that can be dynamically tuned over the complete2πrange.

Integrated photonics facilitates extensive control over fundamental light–matter interactions in manifold quantum systems including atoms 1 , trapped ions 2 , 3 , quantum dots 4 and defect centres 5 . Ultrafast electron microscopy has recently made free-electron beams the subject of laser-based quantum manipulation and characterization 6 – 11 , enabling the observation of free-electron quantum walks 12 – 14 , attosecond electron pulses 10 , 15 – 17 and holographic electromagnetic imaging 18 . Chip-based photonics 19 , 20 promises unique applications in nanoscale quantum control and sensing but remains to be realized in electron microscopy. Here we merge integrated photonics with electron microscopy, demonstrating coherent phase modulation of a continuous electron beam using a silicon nitride microresonator. The high-finesse ( Q 0  ≈ 10 6 ) cavity enhancement and a waveguide designed for phase matching lead to efficient electron–light scattering at extremely low, continuous-wave optical powers. Specifically, we fully deplete the initial electron state at a cavity-coupled power of only 5.35 microwatts and generate >500 electron energy sidebands for several milliwatts. Moreover, we probe unidirectional intracavity fields with microelectronvolt resolution in electron-energy-gain spectroscopy 21 . The fibre-coupled photonic structures feature single-optical-mode electron–light interaction with full control over the input and output light. This approach establishes a versatile and highly efficient framework for enhanced electron beam control in the context of laser phase plates 22 , beam modulators and continuous-wave attosecond pulse trains 23 , resonantly enhanced spectroscopy 24 – 26 and dielectric laser acceleration 19 , 20 , 27 . Our work introduces a universal platform for exploring free-electron quantum optics 28 – 31 , with potential future developments in strong coupling, local quantum probing and electron–photon entanglement. A silicon nitride microresonator is used for coherent phase modulation of a transmission electron microscope beam, with future applications in combining high-resolution microscopy with spectroscopy, holography and metrology.

As conventional electronics approaches its limits 1 , nanoscience has urgently sought methods of fast control of electrons at the fundamental quantum level 2 . Lightwave electronics 3 —the foundation of attosecond science 4 —uses the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light 5 – 15 . Despite being particularly promising information carriers, the internal quantum attributes of spin 16 and valley pseudospin 17 – 21 have not been switchable on the subcycle scale. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical readout. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high-odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates. A strong lightwave in a monolayer of tungsten diselenide drives changes in the valley pseudospin, making valley pseudospin an information carrier that is switchable faster than a single light cycle.

A variety of factors such as time-varying transfer paths, planet shifts, etc., can induce additional modulation sidebands in the spectrum of planetary gearboxes. Most of previous work only considers the effect of a single factor on the sidebands, while these factors may occur at the same time and the corresponding results are not studied. Moreover, although all of these factors can result in additional sidebands, it is unclear that which the most important factor is, and brings difficulty to the fault diagnosis of planetary gearboxes. Aiming at this issue, a universal equation of phenomenological models of planetary gearboxes is developed in this paper to predict the importance of a certain factor in arising modulation sidebands. This model extends the previous phenomenological models which only contain a single factor of sideband formation and can describe the spectral structures of planetary gearboxes with multiple factors considered simultaneously. Effects of multiple factors including time-varying transfer paths, planet shifts and load sharing ratios on the modulation sidebands are analyzed. Furthermore, arbitrary one, two and multiple factors are introduced in the established phenomenological model to make a comparison between these factors. It is found that when the unequal load sharing among planet gears is not severe, a planet shift can result in abundant frequency components more prominently. Finally, the formation mechanisms of modulation sidebands are derived and some experimental validations are carried out to prove the effectiveness of proposed model.

Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications ranging from spectroscopy to quantum information processing. Unfortunately, existing tunable parametric sources are marred by deficiencies that obstruct their widespread adoption. Here, we show that ultrahigh-Q crystalline microresonators made of magnesium fluoride can overcome these limitations, enabling compact and power-efficient devices capable of generating clean and widely tunable sidebands. We consider several different resonators with carefully engineered dispersion profiles, achieving hundreds of nanometres of sideband tunability in each device. In addition to direct observations of discrete tunability over an optical octave from 1,083 nm to 2,670 nm, we record signatures of mid-infrared sidebands at almost 4,000 nm. The simplicity of the demonstrated devices—compounded by their remarkable tunability—paves the way for low-cost, widely tunable sources of electromagnetic radiation.

The optical vector analyzer is a device used to measure the magnitude, phase responses, and other parameters of optical devices. There have been increasingly higher demands placed on optical vector analyzers during the development of optical technologies, which are satisfied by the creation of new devices and their operating principles. For further development in this area, it is necessary to generalize the experience gained during the development of optical vector analyzers. Thus, in this report, we provide an overview of all the basic types of approaches used for the realization of optical vector analyzers, including the advanced ones with the best performances. The principles of their working, as well as their associated advantages, disadvantages, and existing solutions to the identified problems, are examined in detail. The presented approaches could be of value and interest to those working in the field of laser dynamics and optical devices, as we propose one use of the optical vector analyzer as being the characterization of Fano resonance structures.

The coupling between superconductors and oscillation cycles of light pulses, i.e., lightwave engineering, is an emerging control concept for superconducting quantum electronics. Although progress has been made towards terahertz-driven superconductivity and supercurrents, the interactions able to drive non-equilibrium pairing are still poorly understood, partially due to the lack of measurements of high-order correlation functions. In particular, the sensing of exotic collective modes that would uniquely characterize light-driven superconducting coherence, in a way analogous to the Meissner effect, is very challenging but much needed. Here we report the discovery of parametrically driven superconductivity by light-induced order-parameter collective oscillations in iron-based superconductors. The time-periodic relative phase dynamics between the coupled electron and hole bands drives the transition to a distinct parametric superconducting state out-of-equalibrium. This light-induced emergent coherence is characterized by a unique phase–amplitude collective mode with Floquet-like sidebands at twice the Higgs frequency. We measure non-perturbative, high-order correlations of this parametrically driven superconductivity by separating the terahertz-frequency multidimensional coherent spectra into pump–probe, Higgs mode and bi-Higgs frequency sideband peaks. We find that the higher-order bi-Higgs sidebands dominate above the critical field, which indicates the breakdown of susceptibility perturbative expansion in this parametric quantum matter.Multidimensional coherent spectroscopy measurements in iron-based superconductors demonstrate how the coupling between a superconductor and strong light pulses can drive the transition into a non-equilibrium superconducting state with distinct collective modes.

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the 'generalized alignment index' method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the Neimark-Sacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos.