Lightwave valleytronics in a monolayer of tungsten diselenide.

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 light5-15. Despite being particularly promising information carriers, the internal quantum attributes of spin 16 and valley pseudospin17-21 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.

Lightwave-driven quasiparticle collisions on a subcycle timescale.

Ever since Ernest Rutherford scattered α-particles from gold foils, collision experiments have revealed insights into atoms, nuclei and elementary particles. In solids, many-body correlations lead to characteristic resonances--called quasiparticles--such as excitons, dropletons, polarons and Cooper pairs. The structure and dynamics of quasiparticles are important because they define macroscopic phenomena such as Mott insulating states, spontaneous spin- and charge-order, and high-temperature superconductivity. However, the extremely short lifetimes of these entities make practical implementations of a suitable collider challenging. Here we exploit lightwave-driven charge transport, the foundation of attosecond science, to explore ultrafast quasiparticle collisions directly in the time domain: a femtosecond optical pulse creates excitonic electron-hole pairs in the layered dichalcogenide tungsten diselenide while a strong terahertz field accelerates and collides the electrons with the holes. The underlying dynamics of the wave packets, including collision, pair annihilation, quantum interference and dephasing, are detected as light emission in high-order spectral sidebands of the optical excitation. A full quantum theory explains our observations microscopically. This approach enables collision experiments with various complex quasiparticles and suggests a promising new way of generating sub-femtosecond pulses.

Real-time observation of interfering crystal electrons in high-harmonic generation.

Acceleration and collision of particles has been a key strategy for exploring the texture of matter. Strong light waves can control and recollide electronic wavepackets, generating high-harmonic radiation that encodes the structure and dynamics of atoms and molecules and lays the foundations of attosecond science. The recent discovery of high-harmonic generation in bulk solids combines the idea of ultrafast acceleration with complex condensed matter systems, and provides hope for compact solid-state attosecond sources and electronics at optical frequencies. Yet the underlying quantum motion has not so far been observable in real time. Here we study high-harmonic generation in a bulk solid directly in the time domain, and reveal a new kind of strong-field excitation in the crystal. Unlike established atomic sources, our solid emits high-harmonic radiation as a sequence of subcycle bursts that coincide temporally with the field crests of one polarity of the driving terahertz waveform. We show that these features are characteristic of a non-perturbative quantum interference process that involves electrons from multiple valence bands. These results identify key mechanisms for future solid-state attosecond sources and next-generation light-wave electronics. The new quantum interference process justifies the hope for all-optical band-structure reconstruction and lays the foundation for possible quantum logic operations at optical clock rates.

Quantum droplets of electrons and holes.

Interacting many-body systems are characterized by stable configurations of objects--ranging from elementary particles to cosmological formations--that also act as building blocks for more complicated structures. It is often possible to incorporate interactions in theoretical treatments of crystalline solids by introducing suitable quasiparticles that have an effective mass, spin or charge which in turn affects the material's conductivity, optical response or phase transitions. Additional quasiparticle interactions may also create strongly correlated configurations yielding new macroscopic phenomena, such as the emergence of a Mott insulator, superconductivity or the pseudogap phase of high-temperature superconductors. In semiconductors, a conduction-band electron attracts a valence-band hole (electronic vacancy) to create a bound pair, known as an exciton, which is yet another quasiparticle. Two excitons may also bind together to give molecules, often referred to as biexcitons, and even polyexcitons may exist. In indirect-gap semiconductors such as germanium or silicon, a thermodynamic phase transition may produce electron-hole droplets whose diameter can approach the micrometre range. In direct-gap semiconductors such as gallium arsenide, the exciton lifetime is too short for such a thermodynamic process. Instead, different quasiparticle configurations are stabilized dominantly by many-body interactions, not by thermalization. The resulting non-equilibrium quantum kinetics is so complicated that stable aggregates containing three or more Coulomb-correlated electron-hole pairs remain mostly unexplored. Here we study such complex aggregates and identify a new stable configuration of charged particles that we call a quantum droplet. This configuration exists in a plasma and exhibits quantization owing to its small size. It is charge neutral and contains a small number of particles with a pair-correlation function that is characteristic of a liquid. We present experimental and theoretical evidence for the existence of quantum droplets in an electron-hole plasma created in a gallium arsenide quantum well by ultrashort optical pulses.

Memory effects in the long-wave infrared avalanche ionization of gases: a review of recent progress.

There are currently intense efforts being directed towards extending the range and energy of long distance nonlinear pulse propagation in the atmosphere by moving to longer infrared wavelengths, with the purpose of mitigating the effects of turbulence. In addition, picosecond and longer pulse durations are being used to increase the pulse energy. While both of these tacks promise improvements in applications, such as remote sensing and directed energy, they open up fundamental issues regarding the standard model used to calculate the nonlinear optical properties of dilute gases. Amongst these issues is that for longer wavelengths and longer pulse durations, exponential growth of the laser-generated electron density, the so-called avalanche ionization, can limit the propagation range via nonlinear absorption and plasma defocusing. It is therefore important for the continued development of the field to assess the theory and role of avalanche ionization in gases for longer wavelengths. Here, after an overview of the standard model, we present a microscopically motivated approach for the analysis of avalanche ionization in gases that extends beyond the standard model and we contend is key for deepening our understanding of long distance propagation at long infrared wavelengths. Our new approach involves the mean electron kinetic energy, the plasma temperature, and the free electron density as dynamic variables. The rate of avalanche ionization is shown to depend on the full time history of the pulsed excitation, as opposed to the standard model in which the rate is proportional to the instantaneous intensity. Furthermore, the new approach has the added benefit that it is no more computationally intensive than the standard one. The resulting memory effects and some of their measurable physical consequences are demonstrated for the example of long-wavelength infrared avalanche ionization and long distance high-intensity pulse propagation in air. Our hope is that this report in progress will stimulate further discussion that will elucidate the physics and simulation of avalanche ionization at long infrared wavelengths and advance the field.

Non-equilibrium dynamics in the dual-wavelength operation of vertical external-cavity surface-emitting lasers.

Microscopic many-body theory coupled with Maxwell's equation is used to study dual-wavelength operation in vertical external-cavity surface-emitting lasers. The intrinsically dynamic nature of coexisting emission wavelengths in semiconductor lasers is associated with characteristic non-equilibrium carrier dynamics, which causes significant deformations of the quasi-equilibrium gain and carrier inversion. Extended numerical simulations are employed to efficiently investigate the parameter space to identify the regime for dual-wavelength operation. Using a frequency selective intracavity etalon, two families of modes are stabilized with dynamical interchange of the strongest emission peaks. For this operation mode, anti-correlated intensity noise is observed in agreement with the experiment. A method using effective frequency selective filtering is suggested for stabilization of genuine dual-wavelength output.

Control of the nonlinear response of bulk GaAs induced by long-wavelength infrared pulses.

The nonlinear optical response of GaAs is studied using extremely nonresonant 10 µm laser pulses with peak intensities greater than 2 GW/cm 2. We observe over an order of magnitude enhancement in the four-wave mixing efficiency by decreasing the CO 2 laser beat-wave frequency. This enhancement is attributed to currents of photoexcited unbound carriers modulated at the beat frequency, confirmed by measurements of nonlinear absorption at this long wavelength as well as a fully microscopic analysis of the excitation dynamics. Modeling of such nonperturbative semiconductor-laser interactions predicts that further decreasing the beat frequency can increase the nonlinear response and allow for its control over two orders of magnitude.

Self-Channeling of High-Power Long-Wave Infrared Pulses in Atomic Gases.

We simulate and elucidate the self-channeling of high-power 10 µm infrared pulses in atomic gases. The major new result is that the peak intensity can remain remarkably stable over many Rayleigh ranges. This arises from the balance between the self-focusing, diffraction, and defocusing caused by the excitation induced dephasing due to many-body Coulomb effects that enhance the low-intensity plasma densities. This new paradigm removes the Rayleigh range limit for sources in the 8-12 µm atmospheric transmission window and enables transport of individual multi-TW pulses over multiple kilometer ranges.

Atomic structure of 'W'-type quantum well heterostructures investigated by aberration-corrected STEM.

The atomic structure of (GaIn)As/Ga(AsSb)/(GaIn)As-'W'-type quantum well heterostructures ('W'-QWHs) is investigated by scanning transmission electron microscopy (STEM). These structures were grown by metal organic vapour phase epitaxy and are built for type-II laser systems in the infrared wavelength regime. For two samples grown at 525°C and 550°C, intensity profiles are extracted from the STEM images for each sublattice separately. These intensity profiles are compared to the one obtained from an image simulation of an ideal 'W'-QWH that is modelled in close agreement with the experiment. From the intensity profiles, the width of the different quantum wells (QWs) can be determined. Additionally, characteristics connected to the growth of the structures, such as segregation coefficients and material homogeneity, are calculated. Finally, composition profiles are derived from the STEM intensity profiles to a first approximation. For these composition profiles, the expected photoluminescence (PL) is computed based using the semiconductor luminescence equations. The PL spectra are then compared to experimental measurements for both samples.

Coherent terahertz control of vertical transport in semiconductor heterostructures.

Coherent-control protocols are introduced to selectively transport electrons, excitons, or pure two-particle correlations through semiconductor interfaces. The scheme is tested in a double-quantum-well structure where a sequence of terahertz pulses is applied to induce the vertical excitation transfer between the wells. Using a microscopic theory, it is shown that efficient and highly selective transfer can be realized even in the presence of the unavoidable scattering and dephasing processes.

Nonequilibrium and thermal effects in mode-locked VECSELs.

Ultrafast femtosecond timescale dynamics in Vertical External Cavity Surface Emitting Lasers (VECSELs) have recently been employed to achieve record average power and duration mode-locked pulses by employing different types of saturable absorbers and Kerr Lens elements. Microscopic many-body dynamics are expected to dominate when attempting to push pulse durations below 100 fs. We present a preliminary microscopic simulation of ultrafast mode-locking in order to expose the role of hot carrier distributions in establishing ultrafast mode-locking.

Quantum-memory effects in the emission of quantum-dot microcavities.

The experimentally measured input-output characteristics of optically pumped semiconductor microcavities exhibits unexpected oscillations modifying the fundamentally linear slope in the excitation power regime below lasing. A systematic microscopic analysis reproduces these oscillations, identifying them as a genuine quantum-memory effect, i.e., a photon-density correlation accumulated during the excitation. With the use of projected quantum measurements, it is shown that the input-output oscillations can be controlled and enhanced by an order of magnitude when the quantum fluctuations of the pump are adjusted.

Observation of forbidden exciton transitions mediated by Coulomb interactions in photoexcited semiconductor quantum wells.

We use terahertz pulses to induce resonant transitions between the eigenstates of optically generated exciton populations in a high-quality semiconductor quantum well sample. Monitoring the excitonic photoluminescence, we observe transient quenching of the 1s exciton emission, which we attribute to the terahertz-induced 1s-to-2p excitation. Simultaneously, a pronounced enhancement of the 2s exciton emission is observed, despite the 1s-to-2s transition being dipole forbidden. A microscopic many-body theory explains the experimental observations as a Coulomb-scattering mixing of the 2s and 2p states, yielding an effective terahertz transition between the 1s and 2s populations.

Nonequilibrium evolution of strong-field anisotropic ionized electrons towards a delayed plasma-state.

Rigorous quantum calculations of the femtosecond ionization of hydrogen atoms in air lead to highly anisotropic electron and ion angular (momentum) distributions. A quantum Monte-Carlo analysis of the subsequent many-body dynamics reveals two distinct relaxation steps, first to a nearly isotropic hot nonequilibrium and then to a quasi-equilibrium configuration. The collective isotropic plasma state is reached on a picosecond timescale well after the ultrashort ionizing pulse has passed.

Terahertz excitation of a coherent λ-type three-level system of exciton-polariton modes in a quantum-well microcavity.

Interactions of few-cycle terahertz pulses with the induced optical polarization in a quantum-well microcavity reveal that the lower and higher exciton-polariton modes together with the optically forbidden 2p-exciton state form a unique Λ-type three-level system. Pronounced nonlinearities are observed via time-resolved strong-terahertz and weak-optical excitation spectroscopy and explained with a fully microscopic theory. The results show that the terahertz pulses strongly couple the exciton-polariton states to the 2p-exciton state while no resonant transition between the two polariton levels is observed.

Effective mass anisotropy of hot electrons in nonparabolic conduction bands of n-doped InGaAs films using ultrafast terahertz pump-probe techniques.

The anisotropic effective mass of energetic electrons in an isotropic, nonparabolic conduction band is revealed using ultrafast THz-pump-THz-probe techniques in a n-doped InGaAs semiconductor thin film. A microscopic theory is applied to identify the origin of the observed anisotropy and to show that the self-consistent light-matter coupling contributes significantly to the THz response.

Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells.

Detailed electronic many-body configurations are extracted from quantitatively measured time-resolved nonlinear absorption spectra of resonantly excited GaAs quantum wells. The microscopic theory assigns the observed spectral changes to a unique mixture of electron-hole plasma, exciton, and polarization effects. Strong transient gain is observed only under cocircular pump-probe conditions and is attributed to the transfer of pump-induced coherences to the probe.

Microscopic Coulomb interaction in transition-metal dichalcogenides.

The quasi-two dimensional Coulomb interaction potential in transition metal dichalcogenides is determined using the Kohn-Sham wave functions obtained fromab initiocalculations. An effective form factor is derived that accounts for the finite extension of the wave functions in the direction perpendicular to the material layer. The resulting Coulomb matrix elements are used in microscopic calculations based on the Dirac Bloch equations yielding an efficient method to calculate the band gap and the opto-electronic material properties in different environments and under various excitation conditions.

Super-resolution lightwave tomography of electronic bands in quantum materials.

Searching for quantum functionalities requires access to the electronic structure, constituting the foundation of exquisite spin-valley-electronic, topological, and many-body effects. All-optical band-structure reconstruction could directly connect electronic structure with the coveted quantum phenomena if strong lightwaves transported localized electrons within preselected bands. Here, we demonstrate that harmonic sideband (HSB) generation in monolayer tungsten diselenide creates distinct electronic interference combs in momentum space. Locating these momentum combs in spectroscopy enables super-resolution tomography of key band-structure details in situ. We experimentally tuned the optical-driver frequency by a full octave and show that the predicted super-resolution manifests in a critical intensity and frequency dependence of HSBs. Our concept offers a practical, all-optical, fully three-dimensional tomography of electronic structure even in microscopically small quantum materials, band by band.

One dimensional resonant Fibonacci quasicrystals: noncanonical linear and canonical nonlinear effects.

A detailed experimental and theoretical study of the linear and nonlinear optical properties of different Fibonacci-spaced multiple-quantum-well structures is presented. Systematic numerical studies are performed for different average spacing and geometrical arrangement of the quantum wells. Measurements of the linear and nonlinear (carrier density dependent) reflectivity are shown to be in good agreement with the computational results. As the pump pulse energy increases, the excitation-induced dephasing broadens the exciton resonances resulting in a disappearance of sharp features and reduction in peak reflectivity.