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Strong light fields have created spectacular opportunities to tailor novel functionalities of solids. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases. On subcycle time scales, lightwaves can simultaneously drive intraband currents and interband transitions, which enable high-harmonic generation (HHG) and pave the way towards ultrafast electronics. Yet, the interplay of intra- and interband excitations as well as their relation with Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this pivotal link by pioneering the ultrafast buildup of Floquet-Bloch bands with time- and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator with mid-infrared fields - strong enough for HHG - 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 nonequilibrium calculations explain the simultaneous occurrence of Floquet states with intra- and interband dynamics. Our joint experiment-theory study opens up a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering., Comment: 45 pages, 4 figures, 10 extended data figures

Dressing quantum states of matter with virtual photons can create exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and may drive strong squeezing or entanglement of light and matter modes. The established paradigm of cavity quantum electrodynamics focuses on resonant light-matter interaction to maximize the coupling strength $\Omega_\mathrm{R}/\omega_\mathrm{c}$, defined as the ratio of the vacuum Rabi frequency and the carrier frequency of light. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit to $\Omega_\mathrm{R}/\omega_\mathrm{c}$. Here, we demonstrate a new regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes specifically tailored by our metasurface. This multi-mode coupling creates an ultrabroadband spectrum of over 20 polaritons spanning 6 optical octaves, vacuum ground state populations exceeding 1 virtual excitation quantum for electronic and optical modes, and record coupling strengths equivalent to $\Omega_\mathrm{R}/\omega_\mathrm{c}=3.19$. The extreme interaction drives strongly subcycle exchange of vacuum energy between multiple bosonic modes akin to high-order nonlinearities otherwise reserved to strong-field physics, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations of the common cavity mode. This offers avenues towards tailoring phase transitions by coupling otherwise non-interacting modes, merely by shaping the dielectric environment.

The ultrafast scattering dynamics of intersubband polaritons in dispersive cavities embedding GaAs/AlGaAs quantum wells are studied directly within their band structure using a non-collinear pump-probe geometry with phase-stable mid-infrared pulses. Selective excitation of the lower polariton at a frequency of ~25 THz and at a finite in-plane momentum, $k_{||}$, leads to the emergence of a narrowband maximum in the probe reflectivity at $k_{||}=0$. A quantum mechanical model identifies the underlying microscopic process as stimulated coherent polariton-polariton scattering. These results mark an important milestone towards quantum control and bosonic lasing in custom-tailored polaritonic systems in the mid and far-infrared.

We explore the nonlinear response of tailor-cut light-matter hybrid states in a novel regime, where both the Rabi frequency induced by a coherent driving field and the vacuum Rabi frequency set by a cavity field are comparable to the carrier frequency of light. In this previously unexplored strong-field limit of ultrastrong coupling, subcycle pump-probe and multi-wave mixing nonlinearities between different polariton states violate the normal-mode approximation while ultrastrong coupling remains intact, as confirmed by our mean-field model. We expect such custom-cut nonlinearities of hybridized elementary excitations to facilitate non-classical light sources, quantum phase transitions, or cavity chemistry with virtual photons., Comment: 10 pages, 4 figures, additional supplemental material

Future information technology demands ultimately fast, low-loss quantum control. Intense light fields have facilitated important milestones, such as inducing novel states of matter, accelerating electrons ballistically, or coherently flipping the valley pseudospin. These dynamics leave unique signatures, such as characteristic bandgaps or high-order harmonic radiation. The fastest and least dissipative way of switching the technologically most important quantum attribute - the spin - between two states separated by a potential barrier is to trigger an all-coherent precession. Pioneering experiments and theory with picosecond electric and magnetic fields have suggested this possibility, yet observing the actual dynamics has remained out of reach. Here, we show that terahertz (1 THz = 10$^{12}$ Hz) electromagnetic pulses allow coherent navigation of spins over a potential barrier and we reveal the corresponding temporal and spectral fingerprints. This goal is achieved by coupling spins in antiferromagnetic TmFeO$_{3}$ with the locally enhanced THz electric field of custom-tailored antennas. Within their duration of 1 ps, the intense THz pulses abruptly change the magnetic anisotropy and trigger a large-amplitude ballistic spin motion. A characteristic phase flip, an asymmetric splitting of the magnon resonance, and a long-lived offset of the Faraday signal are hallmarks of coherent spin switching into adjacent potential minima, in agreement with a numerical simulation. The switchable spin states can be selected by an external magnetic bias. The low dissipation and the antenna's sub-wavelength spatial definition could facilitate scalable spin devices operating at THz rates., Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature. The final authenticated version is available online at https://www.nature.com/articles/s41586-019-1174-7. 32 pages, 4 Figures, 9 Extended Data Figures

The ability to control the structure of a crystalline solid on ultrafast timescales bears enormous potential for information storage and manipulation or generating new functional states of matter [1]. In many materials where the ultrafast control of crystalline structures has been explored, optical excitation pushes materials towards their less ordered high temperature phase [2{9] as electronically driven ordered phases melt and possible concomitant structural modifications relax. Nonetheless, for a few select materials it has been shown that photoexcitation can slightly enhance the amplitude of an electronic ordering phenomenon (i.e. its electronic order parameter) [9{13]. Here we show via femtosecond hard X-ray diffraction that photodoping of the perovskite EuTiO3 transiently increases the order parameter associated with a purely structural [14] phase transition represented by the antiferrodistortive rotation of the oxygen octahedra. This can be understood from an ultrafast charge-transfer induced reduction of the Goldschmidt tolerance factor [15], which is a fundamental control parameter for the properties of perovskites, Comment: 11 pages, 3 figures

We present a microcavity structure with a shifted photonic stop-band to enable efficient non-resonant injection of a polariton condensate with spectrally broad femtosecond pulses. The concept is demonstrated theoretically and confirmed experimentally for a planar GaAs/AlGaAs multilayer heterostructure pumped with ultrashort near-infrared pulses while photoluminescence is collected to monitor the optically injected polariton density. As the excitation wavelength is scanned, a regime of polariton condensation can be reached in our structure at a consistently lower fluence threshold than in a state-of-the-art conventional microcavity. Our microcavity design improves the polariton injection efficiency by a factor of 4, as compared to a conventional microcavity design, when broad excitation pulses are centered at a wavelength of 740 nm. Most remarkably, this improvement factor reaches 270 when the excitation wavelength is centered at 750 nm.

Condensation of bosons causes spectacular phenomena such as superfluidity or superconductivity. Understanding the nature of the condensed particles is crucial for active control of such quantum phases. Fascinating possibilities emerge from condensates of light-matter coupled excitations, such as exciton polaritons, photons hybridized with hydrogen-like bound electron-hole pairs. So far, only the photon component has been resolved, while even the mere existence of excitons in the condensed regime has been challenged. Here we trace the matter component of polariton condensates by monitoring intra-excitonic terahertz transitions. We study how a reservoir of optically dark excitons forms and feeds the degenerate state. Unlike atomic gases, the atom-like transition in excitons is dramatically renormalized upon macroscopic ground state population. Our results establish fundamental differences between polariton condensation and photon lasing and open possibilities for coherent control of condensates.

Atomically thin two-dimensional crystals have revolutionized materials science. In particular, monolayer transition metal dichalcogenides promise novel optoelectronic applications, due to their direct energy gaps in the optical range. Their electronic and optical properties, however, are complicated by exotic room-temperature excitons, whose fundamental structure and dynamics has been under intense investigation. While interband spectroscopy probes energies of excitons with vanishing centre-of-mass momenta, the majority of excitons has remained elusive, raising questions about their unusual internal structure, symmetry, many-body effects, and dynamics. Here we report the first direct experimental access to all relevant excitons in single-layer WSe2. Phase-locked mid-infrared pulses reveal the internal orbital 1s-2p resonance, which is highly sensitive to the shape of the excitonic envelope functions and provides accurate transition energies, oscillator strengths, densities and linewidths. Remarkably, the observed decay dynamics indicates a record fast radiative annihilation of small-momentum excitons within 150 fs, whereas Auger recombination prevails for optically dark states. The results provide a comprehensive view of excitons and introduce a new degree of freedom for quantum control, optoelectronics and valleytronics of dichalcogenide monolayers.

The simultaneous ordering of different degrees of freedom in complex materials undergoing spontaneous symmetry-breaking transitions often involves intricate couplings that have remained elusive in phenomena as wide ranging as stripe formation, unconventional superconductivity or colossal magnetoresistance. Ultrafast optical, x-ray and electron pulses can elucidate the microscopic interplay between these orders by probing the electronic and lattice dynamics separately, but a simultaneous direct observation of multiple orders on the femtosecond scale has been challenging. Here we show that ultrabroadband terahertz pulses can simultaneously trace the ultrafast evolution of coexisting lattice and electronic orders. For the example of a charge-density-wave (CDW) in 1T-TiSe2, we demonstrate that two components of the CDW order parameter - excitonic correlations and a periodic lattice distortion (PLD) - respond very differently to 12-fs optical excitation. Even when the excitonic order of the CDW is quenched, the PLD can persist in a coherently excited state. This observation proves that excitonic correlations are not the sole driving force of the CDW transition in 1T-TiSe2, and exemplifies the sort of profound insight that disentangling strongly coupled components of order parameters in the time domain may provide for the understanding of a broad class of phase transitions.

Long regarded as a model system for studying insulator-to-metal phase transitions, the correlated electron material vanadium dioxide (VO$_2$) is now finding novel uses in device applications. Two of its most appealing aspects are its accessible transition temperature ($\sim$341 K) and its rich phase diagram. Strain can be used to selectively stabilize different VO$_2$ insulating phases by tuning the competition between electron and lattice degrees of freedom. It can even break the mesoscopic spatial symmetry of the transition, leading to a quasi-periodic ordering of insulating and metallic nanodomains. Nanostructuring of strained VO$_2$ could potentially yield unique components for future devices. However, the most spectacular property of VO$_2$ - its ultrafast transition - has not yet been studied on the length scale of its phase heterogeneity. Here, we use ultrafast near-field microscopy in the mid-infrared to study individual, strained VO$_2$ nanobeams on the 10 nm scale. We reveal a previously unseen correlation between the local steady-state switching susceptibility and the local ultrafast response to below-threshold photoexcitation. These results suggest that it may be possible to tailor the local photo-response of VO$_2$ using strain and thereby realize new types of ultrafast nano-optical devices.

Phase-locked ultrashort pulses in the rich terahertz (THz) spectral range have provided key insights into phenomena as diverse as quantum confinement, first-order phase transitions, high-temperature superconductivity, and carrier transport in nanomaterials. Ultrabroadband electro-optic sampling of few-cycle field transients can even reveal novel dynamics that occur faster than a single oscillation cycle of light. However, conventional THz spectroscopy is intrinsically restricted to ensemble measurements by the diffraction limit. As a result, it measures dielectric functions averaged over the size, structure, orientation and density of nanoparticles, nanocrystals or nanodomains. Here, we extend ultrabroadband time-resolved THz spectroscopy (20 - 50 THz) to the sub-nanoparticle scale (10 nm) by combining sub-cycle, field-resolved detection (10 fs) with scattering-type near-field scanning optical microscopy (s-NSOM). We trace the time-dependent dielectric function at the surface of a single photoexcited InAs nanowire in all three spatial dimensions and reveal the ultrafast ($<$50 fs) formation of a local carrier depletion layer.

Terahertz near fields of gold metamaterials resonant at a frequency of $0.88\,\rm THz$ allow us to enter an extreme limit of non-perturbative ultrafast THz electronics: Fields reaching a ponderomotive energy in the keV range are exploited to drive nondestructive, quasi-static interband tunneling and impact ionization in undoped bulk GaAs, injecting electron-hole plasmas with densities in excess of $10^{19}\,\rm cm^{-3}$. This process causes bright luminescence at energies up to $0.5\,\rm eV$ above the band gap and induces a complete switch-off of the metamaterial resonance accompanied by self-amplitude modulation of transmitted few-cycle THz transients. Our results pave the way towards highly nonlinear THz optics and optoelectronic nanocircuitry with sub-picosecond switching times., Comment: Published in Physical Review Letters

Accelerating and colliding particles has been a key strategy to explore the texture of matter. Strong lightwaves can control and recollide electronic wavepackets, generating high-harmonic (HH) radiation which encodes the structure and dynamics of atoms and molecules and lays the foundations of attosecond science. The recent discovery of HH generation in bulk solids combines the idea of ultrafast acceleration with complex condensed matter systems and sparks hope for compact solid-state attosecond sources and electronics at optical frequencies. Yet the underlying quantum motion has not been observable in real time. Here, we study HH generation in a bulk solid directly in the time-domain, revealing a new quality of strong-field excitations in the crystal. Unlike established atomic sources, our solid emits HH radiation as a sequence of subcycle bursts which coincide temporally with the field crests of one polarity of the driving terahertz waveform. We show that these features hallmark a novel non-perturbative quantum interference involving electrons from multiple valence bands. The results identify key mechanisms for future solid-state attosecond sources and next-generation lightwave electronics. The new quantum interference justifies the hope for all-optical bandstructure reconstruction and lays the foundation for possible quantum logic operations at optical clock rates.

We present a rapid-scan, time-domain terahertz spectrometer employing femtosecond Er:fiber technology and an acousto-optic delay with attosecond precision, enabling scanning of terahertz transients over a 12.4 ps time window at a waveform refresh rate of 36 kHz, and a signal-to-noise ratio of $1.7 \times 10^5/\sqrt{\rm Hz}$. Our approach enables real-time monitoring of dynamic THz processes at unprecedented speeds, which we demonstrate through rapid 2D thickness mapping of a spinning teflon disc at a precision of $10\,\rm nm/\sqrt{\rm Hz}$. The compact, all-optical design ensures alignment-free operation even in harsh environments., Comment: Published in Applied Physics Letters

Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and intraband dynamics. Our results pave the way towards all-coherent THz-rate electronics.