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Author(s): C. P. Schmid [sup.1] , L. Weigl [sup.1] , P. Grössing [sup.2] , V. Junk [sup.2] , C. Gorini [sup.2] [sup.7] , S. Schlauderer [sup.1] , S. Ito [sup.3] [...], When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material.sup.1-11. Sub-optical-cycle dynamics--such as dynamical Bloch oscillations.sup.2-5, quasiparticle collisions.sup.6,12, valley pseudospin switching.sup.13 and heating of Dirac gases.sup.10--leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter.sup.14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation.sup.16-20. 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 locking.sup.17 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. High-harmonic generation from the Dirac-like surface state of a topological insulator is separated from bulk contributions and continuously tuned by the carrier-envelope phase of the driving lightwave.

We demonstrate an active carrier-envelope phase (CEP) stabilization scheme for optical waveforms generated by difference-frequency mixing of two spectrally detuned and phase-correlated pulses. By performing ellipsometry with spectrally overlapping parts of two co-propagating near-infrared generation pulse trains, we stabilize their relative timing to 18 as. Consequently, we can lock the CEP of the generated mid-infrared (MIR) pulses with a remaining phase jitter below 30 mrad. To validate this technique, we employ these MIR pulses for high-harmonic generation in a bulk semiconductor. Our compact, low-cost, and inherently drift-free concept could bring long-term CEP stability to the broad class of passively phase-locked OPA and OPCPA systems operating in a wide range of spectral windows, pulse energies, and repetition rates.

A single quantum emitter can possess a very strong intrinsic nonlinearity, but its overall promise for nonlinear effects is hampered by the challenge of efficient coupling to incident photons. Common nonlinear optical materials, on the other hand, are easy to couple to but are bulky, imposing a severe limitation on the miniaturization of photonic systems. In this Letter, we show that a single organic molecule acts as an extremely efficient nonlinear optical element in the strong coupling regime of cavity quantum electrodynamics. We report on single-photon sensitivity in nonlinear signal generation and all-optical switching. Our work promotes the use of molecules for applications such as integrated photonic circuits operating at very low powers.