Reconstruction of Bloch wavefunctions of holes in a semiconductor.

A central goal of condensed-matter physics is to understand how the diverse electronic and optical properties of crystalline materials emerge from the wavelike motion of electrons through periodically arranged atoms. However, more than 90 years after Bloch derived the functional forms of electronic waves in crystals1 (now known as Bloch wavefunctions), rapid scattering processes have so far prevented their direct experimental reconstruction. In high-order sideband generation2-9, electrons and holes generated in semiconductors by a near-infrared laser are accelerated to a high kinetic energy by a strong terahertz field, and recollide to emit near-infrared sidebands before they are scattered. Here we reconstruct the Bloch wavefunctions of two types of hole in gallium arsenide at wavelengths much longer than the spacing between atoms by experimentally measuring sideband polarizations and introducing an elegant theory that ties those polarizations to quantum interference between different recollision pathways. These Bloch wavefunctions are compactly visualized on the surface of a sphere. High-order sideband generation can, in principle, be observed from any direct-gap semiconductor or insulator. We thus expect that the method introduced here can be used to reconstruct low-energy Bloch wavefunctions in many of these materials, enabling important insights into the origin and engineering of the electronic and optical properties of condensed matter.

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.

Pulsed electron paramagnetic resonance spectroscopy powered by a free-electron laser.

Electron paramagnetic resonance (EPR) spectroscopy interrogates unpaired electron spins in solids and liquids to reveal local structure and dynamics; for example, EPR has elucidated parts of the structure of protein complexes that other techniques in structural biology have not been able to reveal. EPR can also probe the interplay of light and electricity in organic solar cells and light-emitting diodes, and the origin of decoherence in condensed matter, which is of fundamental importance to the development of quantum information processors. Like nuclear magnetic resonance, EPR spectroscopy becomes more powerful at high magnetic fields and frequencies, and with excitation by coherent pulses rather than continuous waves. However, the difficulty of generating sequences of powerful pulses at frequencies above 100 gigahertz has, until now, confined high-power pulsed EPR to magnetic fields of 3.5 teslas and below. Here we demonstrate that one-kilowatt pulses from a free-electron laser can power a pulsed EPR spectrometer at 240 gigahertz (8.5 teslas), providing transformative enhancements over the alternative, a state-of-the-art ∼30-milliwatt solid-state source. Our spectrometer can rotate spin-1/2 electrons through π/2 in only 6 nanoseconds (compared to 300 nanoseconds with the solid-state source). Fourier-transform EPR on nitrogen impurities in diamond demonstrates excitation and detection of EPR lines separated by about 200 megahertz. We measured decoherence times as short as 63 nanoseconds, in a frozen solution of nitroxide free-radicals at temperatures as high as 190 kelvin. Both free-electron lasers and the quasi-optical technology developed for the spectrometer are scalable to frequencies well in excess of one terahertz, opening the way to high-power pulsed EPR spectroscopy up to the highest static magnetic fields currently available.

Detection of nanosecond-scale, high power THz pulses with a field effect transistor.

We demonstrate detection and resolution of high power, 34 ns free electron laser pulses using a rectifying field effect transistor. The detector remains linear up to an input power of 11 ± 0.5 W at a pulse energy of 20 ± 1 µJ at 240 GHz. We compare its performance to a protected Schottky diode, finding a shorter intrinsic time constant. The damage threshold is estimated to be a few 100 W. The detector is, therefore, well-suited for characterizing high power THz pulses. We further demonstrate that the same detector can be used to detect low power continuous-wave THz signals with a post detection limited noise floor of 3.1 µW/√Hz. Such ultrafast, high power detectors are important tools for high power and high energy THz facilities such as free electron lasers.

Experimental observation of electron-hole recollisions.

An intense laser field can remove an electron from an atom or molecule and pull the electron into a large-amplitude oscillation in which it repeatedly collides with the charged core it left behind. Such recollisions result in the emission of very energetic photons by means of high-order-harmonic generation, which has been observed in atomic and molecular gases as well as in a bulk crystal. An exciton is an atom-like excitation of a solid in which an electron that is excited from the valence band is bound by the Coulomb interaction to the hole it left behind. It has been predicted that recollisions between electrons and holes in excitons will result in a new phenomenon: high-order-sideband generation. In this process, excitons are created by a weak near-infrared laser of frequency f(NIR). An intense laser field at a much lower frequency, f(THz), then removes the electron from the exciton and causes it to recollide with the resulting hole. New emission is predicted to occur as sidebands of frequency f(NIR) + 2nf(THz), where n is an integer that can be much greater than one. Here we report the observation of high-order-sideband generation in semiconductor quantum wells. Sidebands are observed up to eighteenth order (+18f(THz), or n = 9). The intensity of the high-order sidebands decays only weakly with increasing sideband order, confirming the non-perturbative nature of the effect. Sidebands are strongest for linearly polarized terahertz radiation and vanish when the terahertz radiation is circularly polarized. Beyond their fundamental scientific significance, our results suggest a new mechanism for the ultrafast modulation of light, which has potential applications in terabit-rate optical communications.

A diffraction-compensating 0-25 ns free space terahertz delay line for coherent quantum control.

Free space delay lines provide pulses of variable time spacing for optical experiments such as pump-probe spectroscopy and coherent quantum control, including spin and photon echo techniques. However, in the terahertz region of the spectrum, beam divergence due to diffraction limits the useful length of traditional free space delay lines. We present a novel double-folded variable delay line for light in the frequency range 0.24-1.2 THz, which incorporates a symmetric arrangement of lenses whose spacing can be adjusted to compensate for diffraction at each delay. Scalable for use in other wavelength regimes, the design relays an input Gaussian beam waist to the output with up to 25 ns ( approximately 8 m) total delay and is enclosed in a desiccated volume of <0.5 m3. The delay line can deliver two or three pulses with relative amplitudes controlled via variable spacing silicon etalon beam splitters. Profiles of a 0.24 THz beam show good agreement with calculations at long delays, with insertion loss per delay stage of approximately 3 dB.

Growth, structural, and optical properties of self-assembled (In,Ga)as quantum posts on GaAs.

Self-assembled quantum dots embedded in semiconductor heterostructures have proved to be a rich system for exploring the physics of three dimensionally confined charges and excitons. We present here a novel structure, which allows adjusting the level of confinement between 3D and 2D for electrons and holes, respectively. The quantum post consists of a quantum dot connected to a short quantum wire. The molecular beam epitaxy deposition of these self-assembled structures is discussed, and their structural and chemical compositions are presented. Their optical properties measured by photoluminescence are compared to an eight-band strain-dependent k.p model incorporating detailed structure and alloy composition. The calculations show electron delocalization in the quantum wire part of the quantum post and hole localization in the strain-induced regions at the ends of the quantum post. The quantum post offers the possibility of controlling the dipole moment in the structure and opens up new means for tuning the intra-subband transitions by controlling its dimensions.

Quantum coherence in an optical modulator.

Semiconductor quantum well electroabsorption modulators are widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1 terahertz (THz). Here, the NIR absorption of undoped quantum wells was modulated by strong electric fields with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency- and power-dependent NIR absorption line. Nonperturbative theory and experiment indicate that the THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quantum coherence may yield new applications for quantum well modulators in optical communications.

Dissipation of intersubband plasmons in wide quantum wells.

This Letter reports detailed measurements of the dissipation times tau(d) of approximately 10 meV intersubband (ISB) plasmons, and of the (single-particle) transport lifetimes tau(mu), in a remotely doped 40 nm GaAs quantum well. Introduced here as the time for ISB plasmons to dissipate into other modes of the electron gas, tau(d) is deduced from the homogeneous ISB absorption linewidth, measured as a function of sheet concentration and perpendicular dc electric field. Modeling in this and the next Letter [C. A. Ullrich and G. Vignale, Phys. Rev. Lett. 87, 037402 (2001)] indicates that scattering from rough interfaces dominates tau(d), while scattering from ionized impurities dominates tau(mu).

Coherent manipulation of semiconductor quantum bits with terahertz radiation.

Quantum bits (qubits) are the fundamental building blocks of quantum information processors, such as quantum computers. A qubit comprises a pair of well characterized quantum states that can in principle be manipulated quickly compared to the time it takes them to decohere by coupling to their environment. Much remains to be understood about the manipulation and decoherence of semiconductor qubits. Here we show that hydrogen-atom-like motional states of electrons bound to donor impurities in currently available semiconductors can serve as model qubits. We use intense pulses of terahertz radiation to induce coherent, damped Rabi oscillations in the population of two low-lying states of donor impurities in GaAs. Our observations demonstrate that a quantum-confined extrinsic electron in a semiconductor can be coherently manipulated like an atomic electron, even while sharing space with approximately 10(5) atoms in its semiconductor host. We anticipate that this model system will be useful for measuring intrinsic decoherence processes, and for testing both simple and complex manipulations of semiconductor qubits.