Optical attosecond pulses and tracking the nonlinear response of bound electrons.

The time it takes a bound electron to respond to the electromagnetic force of light sets a fundamental speed limit on the dynamic control of matter and electromagnetic signal processing. Time-integrated measurements of the nonlinear refractive index of matter indicate that the nonlinear response of bound electrons to optical fields is not instantaneous; however, a complete spectral characterization of the nonlinear susceptibility tensors--which is essential to deduce the temporal response of a medium to arbitrary driving forces using spectral measurements--has not yet been achieved. With the establishment of attosecond chronoscopy, the impulsive response of positive-energy electrons to electromagnetic fields has been explored through ionization of atoms and solids by an extreme-ultraviolet attosecond pulse or by strong near-infrared fields. However, none of the attosecond studies carried out so far have provided direct access to the nonlinear response of bound electrons. Here we demonstrate that intense optical attosecond pulses synthesized in the visible and nearby spectral ranges allow sub-femtosecond control and metrology of bound-electron dynamics. Vacuum ultraviolet spectra emanating from krypton atoms, exposed to intense waveform-controlled optical attosecond pulses, reveal a finite nonlinear response time of bound electrons of up to 115 attoseconds, which is sensitive to and controllable by the super-octave optical field. Our study could enable new spectroscopies of bound electrons in atomic, molecular or lattice potentials of solids, as well as light-based electronics operating on sub-femtosecond timescales and at petahertz rates.

Attosecond nonlinear polarization and light-matter energy transfer in solids.

Electric-field-induced charge separation (polarization) is the most fundamental manifestation of the interaction of light with matter and a phenomenon of great technological relevance. Nonlinear optical polarization produces coherent radiation in spectral ranges inaccessible by lasers and constitutes the key to ultimate-speed signal manipulation. Terahertz techniques have provided experimental access to this important observable up to frequencies of several terahertz. Here we demonstrate that attosecond metrology extends the resolution to petahertz frequencies of visible light. Attosecond polarization spectroscopy allows measurement of the response of the electronic system of silica to strong (more than one volt per ångström) few-cycle optical (about 750 nanometres) fields. Our proof-of-concept study provides time-resolved insight into the attosecond nonlinear polarization and the light-matter energy transfer dynamics behind the optical Kerr effect and multi-photon absorption. Timing the nonlinear polarization relative to the driving laser electric field with sub-30-attosecond accuracy yields direct quantitative access to both the reversible and irreversible energy exchange between visible-infrared light and electrons. Quantitative determination of dissipation within a signal manipulation cycle of only a few femtoseconds duration (by measurement and ab initio calculation) reveals the feasibility of dielectric optical switching at clock rates above 100 terahertz. The observed sub-femtosecond rise of energy transfer from the field to the material (for a peak electric field strength exceeding 2.5 volts per ångström) in turn indicates the viability of petahertz-bandwidth metrology with a solid-state device.

Enhancement of Parametric Effects in Polariton Waveguides Induced by Dipolar Interactions.

Exciton-polaritons are hybrid light-matter excitations arising from the nonperturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However, direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering, is still missing. In this Letter, we demonstrate that dipolar interactions can be used to enhance parametric effects such as self-phase modulation in waveguide polaritons. By quantifying these optical nonlinearities, we provide a reliable experimental measurement of the direct dipolar enhancement of polariton-polariton interactions.

Watt-scale 50-MHz source of single-cycle waveform-stable pulses in the molecular fingerprint region.

We report a coherent mid-infrared (MIR) source with a combination of broad spectral coverage (6-18 µm), high repetition rate (50 MHz), and high average power (0.5 W). The waveform-stable pulses emerge via intrapulse difference-frequency generation (IPDFG) in a GaSe crystal, driven by a 30-W-average-power train of 32-fs pulses spectrally centered at 2 µm, delivered by a fiber-laser system. Electro-optic sampling (EOS) of the waveform-stable MIR waveforms reveals their single-cycle nature, confirming the excellent phase matching both of IPDFG and of EOS with 2-µm pulses in GaSe.

Isolated attosecond pulses from laser-driven synchrotron radiation.

A quantitative theory of attosecond pulse generation in relativistically driven overdense plasma slabs is presented based on an explicit analysis of synchrotron-type electron trajectories. The subcycle, field-controlled release, and subsequent nanometer-scale acceleration of relativistic electron bunches under the combined action of the laser and ionic potentials give rise to coherent radiation with a high-frequency cutoff, intensity, and radiation pattern explained in terms of the basic laws of synchrotron radiation. The emerging radiation is confined to time intervals much shorter than the half-cycle of the driver field. This intuitive approach will be instrumental in analyzing and optimizing few-cycle-laser-driven relativistic sources of intense isolated extreme ultraviolet and x-ray pulses.

The speed limit of optoelectronics.

Light-field driven charge motion links semiconductor technology to electric fields with attosecond temporal control. Motivated by ultimate-speed electron-based signal processing, strong-field excitation has been identified viable for the ultrafast manipulation of a solid's electronic properties but found to evoke perplexing post-excitation dynamics. Here, we report on single-photon-populating the conduction band of a wide-gap dielectric within approximately one femtosecond. We control the subsequent Bloch wavepacket motion with the electric field of visible light. The resulting current allows sampling optical fields and tracking charge motion driven by optical signals. Our approach utilizes a large fraction of the conduction-band bandwidth to maximize operating speed. We identify population transfer to adjacent bands and the associated group velocity inversion as the mechanism ultimately limiting how fast electric currents can be controlled in solids. Our results imply a fundamental limit for classical signal processing and suggest the feasibility of solid-state optoelectronics up to 1 PHz frequency.

Attosecond streaking enables the measurement of quantum phase.

Attosecond streaking, as a measurement technique, was originally conceived as a means to characterize attosecond light pulses, which is a good approximation if the relevant transition matrix elements are approximately constant within the bandwidth of the light pulse. Our analysis of attosecond streaking measurements on systems with a complex response to the photoionizing pulse reveals the relation between the momentum-space wave function of the outgoing electron and the result of conventional retrieval algorithms. This finding enables the measurement of the quantum phase associated with bound-continuum transitions.

Soft x-ray excitonics.

The dynamic response of excitons in solids is central to modern condensed-phase physics, material sciences, and photonic technologies. However, study and control have hitherto been limited to photon energies lower than the fundamental band gap. Here we report application of attosecond soft x-ray and attosecond optical pulses to study the dynamics of core-excitons at the L2,3 edge of Si in silicon dioxide (SiO2). This attosecond x-ray absorption near-edge spectroscopy (AXANES) technique enables direct probing of the excitons' quasiparticle character, tracking of their subfemtosecond relaxation, the measurement of excitonic polarizability, and observation of dark core-excitonic states. Direct measurement and control of core-excitons in solids lay the foundation of x-ray excitonics.

Delay in photoemission.

Photoemission from atoms is assumed to occur instantly in response to incident radiation and provides the basis for setting the zero of time in clocking atomic-scale electron motion. We used attosecond metrology to reveal a delay of 21 +/- 5 attoseconds in the emission of electrons liberated from the 2p orbitals of neon atoms with respect to those released from the 2s orbital by the same 100-electron volt light pulse. Small differences in the timing of photoemission from different quantum states provide a probe for modeling many-electron dynamics. Theoretical models refined with the help of attosecond timing metrology may provide insight into electron correlations and allow the setting of the zero of time in atomic-scale chronoscopy with a precision of a few attoseconds.

Coherent terahertz echo of tunnel ionization in gases.

We study tunnel ionized electron wave packet dynamics during the initial transition from a gas to a plasma by detecting the terahertz radiation emitted in the process. Experimental and theoretical results show that much of the observed radiation is due to coherent buildup of bremsstrahlung released during the first electron-atom collision. Coherent control of the tunnel ionization process combined with ab initio modeling provides a real-time view of the initial stages of the formation of a laser-induced plasma and allows us to fully understand this important source of terahertz radiation.