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.

Tunable non-integer high-harmonic generation in a topological insulator.

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations2-5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16-20. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin-momentum locking17 and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

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.

Temporal and spectral fingerprints of ultrafast all-coherent spin switching.

Future information technology demands ever-faster, low-loss quantum control. Intense light fields have facilitated milestones along this way, including the induction of novel states of matter1-3, ballistic acceleration of electrons4-7 and coherent flipping of the valley pseudospin8. These dynamics leave unique 'fingerprints', 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. Experimental and theoretical studies with picosecond electric and magnetic fields have suggested this possibility9-11, yet observing the actual spin dynamics has remained out of reach. Here we show that terahertz electromagnetic pulses allow coherent steering of spins over a potential barrier, and we report the corresponding temporal and spectral fingerprints. This goal is achieved by coupling spins in antiferromagnetic TmFeO3 (thulium orthoferrite) with the locally enhanced terahertz electric field of custom-tailored antennas. Within their duration of one picosecond, the intense terahertz pulses abruptly change the magnetic anisotropy and trigger a large-amplitude ballistic spin motion. A characteristic phase flip, an asymmetric splitting of the collective spin resonance and a long-lived offset of the Faraday signal are hallmarks of coherent spin switching into adjacent potential minima, in agreement with numerical simulations. The switchable states can be selected by an external magnetic bias. The low dissipation and the antenna's subwavelength spatial definition could facilitate scalable spin devices operating at terahertz rates.

Subcycle observation of lightwave-driven Dirac currents in a topological surface band.

Harnessing the carrier wave of light as an alternating-current bias may enable electronics at optical clock rates1. Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids2-6, charge transport in nanostructures7,8, attosecond-streaking experiments9-16 and atomic-resolution ultrafast microscopy17,18. However, in conventional semiconductors and dielectrics, the finite effective mass and ultrafast scattering of electrons limit their ballistic excursion and velocity. The Dirac-like, quasi-relativistic band structure of topological insulators19-29 may allow these constraints to be lifted and may thus open a new era of lightwave electronics. To understand the associated, complex motion of electrons, comprehensive experimental access to carrier-wave-driven currents is crucial. Here we report angle-resolved photoemission spectroscopy with subcycle time resolution that enables us to observe directly how the carrier wave of a terahertz light pulse accelerates Dirac fermions in the band structure of the topological surface state of Bi2Te3. While terahertz streaking of photoemitted electrons traces the electromagnetic field at the surface, the acceleration of Dirac states leads to a strong redistribution of electrons in momentum space. The inertia-free surface currents are protected by spin-momentum locking and reach peak densities as large as two amps per centimetre, with ballistic mean free paths of several hundreds of nanometres, opening up a realistic parameter space for all-coherent lightwave-driven electronic devices. Furthermore, our subcycle-resolution analysis of the band structure may greatly improve our understanding of electron dynamics and strong-field interaction in solids.

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.

Ultrafast Dissociation of Metastable CO

We triply ionize the van der Waals bound carbon monoxide dimer with intense ultrashort pulses and study the breakup channel (CO)_{2}^{3+}→C^{+}+O^{+}+CO^{+}. The fragments are recorded in a cold target recoil ion momentum spectrometer. We observe a fast CO^{2+} dissociation channel in the dimer, which does not exist for the monomer. We found that a nearby charge breaks the symmetry of a X^{3}Π state of CO^{2+} and induces an avoided crossing that allows a fast dissociation. Calculation on the full dimer complex shows the coupling of different charge states, as predicted from excimer theory, gives rise to electronic state components not present in the monomer, thereby enabling fast dissociation with higher kinetic energy release. These results demonstrate that the electronic structure of molecular cluster complexes can give rise to dynamics that is qualitatively different from that observed in the component monomers.