Matthias Hohenleutner

Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations

Terahertz waveforms with peak fields of 72 MV cm−1 and a central frequency of 30 THz drive interband polarization in bulk GaSe off-resonantly and accelerate excited electron–hole pairs, inducing dynamical Bloch oscillations. This results in the emission of phase-stable, high-harmonic transients over the whole frequency range of 0.1–675 THz.

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.

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.

Symmetry-controlled temporal structure of high-harmonic carrier fields from a bulk crystal

High-harmonic (HH) generation in crystalline solids1–6 marks an exciting development, with potential applications in high-efficiency attosecond sources7, all-optical bandstructure reconstruction8,9, and quasiparticle collisions10,11. Although the spectral1–4 and temporal shape5 of the HH intensity has been described microscopically1–6,12, the properties of the underlying HH carrier wave have remained elusive. Here we analyse the train of HH waveforms generated in a crystalline solid by consecutive half cycles of the same driving pulse. Extending the concept of frequency combs13–15 to optical clock rates, we show how the polarization and carrier-envelope phase (CEP) of HH pulses can be controlled by crystal symmetry. For some crystal directions, we can separate two orthogonally polarized HH combs mutually offset by the driving frequency to form a comb of even and odd harmonic orders. The corresponding CEP of successive pulses is constant or offset by π, depending on the polarization. In the context of a quantum description of solids, we identify novel capabilities for polarization- and phase-shaping of HH waveforms that cannot be accessed with gaseous sources.

Coherent cyclotron motion beyond Kohn’s theorem

Kohn’s theorem states that the electron cyclotron resonance is unaffected by many-body interactions in a static magnetic field. Yet, intense terahertz pulses do introduce Coulomb effects between electrons—holding promise for quantum control of electrons.

High-harmonic generation in solids

A microscopic theory is presented to describe high-harmonic generation in solids with the semiconductor-Bloch equations. The approach includes the relevant interband polarizations and intraband currents. The appearance of even harmonic orders is shown to require at least three electronic bands and a mutual interband coupling between them. In experimental and theoretical time-resolved studies, this also manifests as a unipolar emission signature of the high-harmonic radiation.

Efficient nonlinear control of spins by ultrashort THz-fields

Ultrashort pulses of intense THz radiation have been shown to represent a powerful and versatile tool for spin control [1–6].

Quantum-interference controlled high harmonics in semiconductors

Theory — experiment comparison reveals how an electronic quantum interference introduces several macroscopic signatures to the high-harmonic emission in semiconductors, making it possible to shape temporal, spectral, and polarization-direction features of sources on a subcycle level.

Extending nonlinear coherent quantum control with intense terahertz pulses

Dynamics in solid-state systems are governed by many-body interactions that are inherently tied to the high density of electrons and ions. For most elementary excitations, however, Coulomb (i.e., elastic) scattering leads to dephasing within a few to a fewhundreds of femtoseconds. Coherent quantum control (the precise manipulation of the phases of quantum states) is therefore usually considered to be a daunting challenge in many-body systems. In 1961, however, Walter Kohn found that the cyclotron resonance (CR) of Landau electrons (i.e., the harmonic motion of electrons in a magnetic field) is immune to electron–electron Coulomb interactions. Kohn’s theorem thus shows that the CR is one of the most robust manifestations of the quantum harmonic oscillator, and excludes the possibility of any nonlinear light– matter interactions.1 Although the CR has given rise to a number of sophisticated quantum phenomena, such as ultrastrong light–matter coupling,2 superradiance,3 coherent control,4 and superfluorescence,5 the complete absence of nonlinearities suggests that many intriguing possibilities (e.g., quantum logic operations) are excluded. In this work,6 we show how strong terahertz (THz) pulses can be used to create non-perturbative THz excitations of a magnetically biased, 2D electron gas (2DEG). The pulses induce strong, coherent nonlinearities and facilitate coherent quantum control of multiple Landau levels, leading to population inversion. In our approach, the 2DEG is contained within two 30nm-wide gallium arsenide quantum wells (each n-doped at 1.6 1011cm 2) Figure 1. (a) The transmitted terahertz (THz) field is used to monitor the coherent inter-Landau level polarization. Results are shown for different amplitudes of the driving field (between 0.7 and 8.7kVcm 1), as a function of the electro-optic sampling (EOS) delay time (t). (b) The decay constant ( c) that is extracted from the data in (a), as a function of the initial field (E0). The Landau-level population, for fields of 4.3 and 8.7kVcm 1 (blue and red bars, respectively), is shown in the inset. f: Population density. h̄!LO: Longitudinal optical phonon energy.

Nonperturbative THz nonlinearities for many-body quantum control in semiconductors

Quantum computing and ultrafast quantum electronics constitute pivotal technologies of the 21st century and revolutionize the way we process information. Successful implementations require controlling superpositions of states and coherence in matter, and exploit nonlinear effects for elementary logic operations. In the THz frequency range between optics and electronics, solid state systems offer a rich spectrum of collective excitations such as excitons, phonons, magnons, or Landau electrons. Here, single-cycle THz transients of 8.7 kV/cm amplitude centered at 1 THz strongly excite inter-Landau-level transitions of magnetically biased GaAs quantum wells, facilitating coherent Landau ladder climbing by more than six rungs, population inversion, and coherent polarization control. Strong, highly nonlinear pump-probe and four- and six-wave mixing signals, entirely unexpected for this paragon of the harmonic oscillator, are revealed through two-time THz spectroscopy. In this scenario of nonperturbative polarization dynamics, our microscopic theory shows how the protective limits of Kohn’s theorem are ultimately surpassed by dynamically enhanced Coulomb interactions, opening the door to exploiting many-body dynamics for nonlinear quantum control.