Eleftherios Goulielmakis

Single-cycle nonlinear optics

Nonlinear optics plays a central role in the advancement of optical science and laser-based technologies. We report on the confinement of the nonlinear interaction of light with matter to a single wave cycle and demonstrate its utility for time-resolved and strong-field science. The electric field of 3.3-femtosecond, 0.72-micron laser pulses with a controlled and measured waveform ionizes atoms near the crests of the central wave cycle, with ionization being virtually switched off outside this interval. Isolated sub-100-attosecond pulses of extreme ultraviolet light (photon energy ∼ 80 electron volts), containing ∼0.5 nanojoule of energy, emerge from the interaction with a conversion efficiency of ∼10–6. These tools enable the study of the precision control of electron motion with light fields and electron-electron interactions with a resolution approaching the atomic unit of time (∼24 attoseconds).

Atomic transient recorder

In Bohrs model of the hydrogen atom, the electron takes about 150 attoseconds (1 as = 10-18 s) to orbit around the proton, defining the characteristic timescale for dynamics in the electronic shell of atoms. Recording atomic transients in real time requires excitation and probing on this scale. The recent observation of single sub-femtosecond (1 fs = 10-15 s) extreme ultraviolet (XUV) light pulses has stimulated the extension of techniques of femtochemistry into the attosecond regime. Here we demonstrate the generation and measurement of single 250-attosecond XUV pulses. We use these pulses to excite atoms, which in turn emit electrons. An intense, waveform-controlled, few cycle laser pulse obtains ‘tomographic images’ of the time-momentum distribution of the ejected electrons. Tomographic images of primary (photo)electrons yield accurate information of the duration and frequency sweep of the excitation pulse, whereas the same measurements on secondary (Auger) electrons will provide insight into the relaxation dynamics of the electronic shell following excitation. With the current ∼750-nm laser probe and ∼100-eV excitation, our transient recorder is capable of resolving atomic electron dynamics within the Bohr orbit time.

Real-time observation of valence electron motion

The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1 fs = 10−15 s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump–probe measurement of the density matrix of valence electrons in atomic krypton ions. We generate the ions with a controlled few-cycle laser field and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse, which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes.

Delay in Photoemission

Defining Time-Zero When a high-energy photon hits an atom and is absorbed, the result can be the excitation and emission of an electron. This photoemission, or photoelectric effect, is generally assumed to occur instantaneously, and represents the definition of “time-zero” in clocking such ultrafast events. Schultze et al. (p. 1658, see the cover; see the Perspective by van der Hart) use ultrafast spectroscopy, with light pulses on the time scale of several tens of attoseconds, to test this assumption directly. They excite neon atoms with 100 eV photons and find that there is a small (20-attosecond) time delay between the emission of electrons from the 2s and 2p orbitals of the atoms. These results should have implications in modeling electron dynamics occurring on ultrafast time scales. Ultrafast metrology reveals a 20-attosecond delay between photoemission from different electronic orbitals in neon atoms. 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.

Synthesized Light Transients

Light spanning the near infrared to the ultraviolet has been confined in pulses shorter than a single optical cycle. Manipulation of electron dynamics calls for electromagnetic forces that can be confined to and controlled over sub-femtosecond time intervals. Tailored transients of light fields can provide these forces. We report on the generation of subcycle field transients spanning the infrared, visible, and ultraviolet frequency regimes with a 1.5-octave three-channel optical field synthesizer and their attosecond sampling. To demonstrate applicability, we field-ionized krypton atoms within a single wave crest and launched a valence-shell electron wavepacket with a well-defined initial phase. Half-cycle field excitation and attosecond probing revealed fine details of atomic-scale electron motion, such as the instantaneous rate of tunneling, the initial charge distribution of a valence-shell wavepacket, the attosecond dynamic shift (instantaneous ac Stark shift) of its energy levels, and its few-femtosecond coherent oscillations.

Attosecond Double-Slit Experiment

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.

Phase-controlled amplification of few-cycle laser pulses

Several methods of carrier-envelope-phase stabilization of amplified ultrashort laser pulses are presented. Full temporal characterization of the resultant intense few-cycle light waveforms, reproducible with every laser shot, was achieved by combining conventional pulse characterization techniques with observing the signature of soft-X- ray emission. Many demanding experiments in strong-field laser physics and coherent control of light-matter interactions would greatly benefit from the use of haser amplifiers that deliver ultrashort optical pulses with a stabilized carrier-envelope phase (CEP). Whereas CEP-stabilized oscillators (I) are now routinely used by several research groups, subsequent pulse amplification to sub-mJ and mJ energy levels remains a difficult technical issue. In this talk, two different approaches to CEP-controlled pulse amplification will be treated and compared with each other: i) optical parametric amplifiers (OPA) with a passive CEP-locking mechanism and ii) conventional amplifiers based on a laser gain medium and equipped with an active CEP stabilization loop. Additionally, practical diagnostics methods for tracking the pulse-to-pulse slippage of CEP in kHz-repetition-rate amplifiers will be reviewed. CEP stabilization in an OPA can be attained in an all-optical way, i.e. without an active feedback loop. The link between the phases of all three pulses taking part in a parametric interaction can be described by a simplified phase equation w, =-lr/2 +y,, -y,, where w stands for a pulse-to-pulse fluctuation of CEP, and I, S, and P denote idler, signal, and pump, respectively. Therefore, CEP self-stabilization of the idler is achieved in an OPA seeded with a white light that is derived from the pump pulse. Alternatively, if a frequency-broadened version of the fundamental pulse is employed as a seed and the second harmonic is used as a pump, such an OPA transfers the CEP fluctuation of the fundamental pulse to both the idler and the signal waves (phase-repeating OPA). Experimental observation of CEP stabilization in 1-pJ pulses and a comparison of both OPA types will be presented. Whereas parametric CEF control in an OPA is straightforward, its significant drawback is the inevitable frequency shift of the CEP-stabilized pulse with respect to the input laser pulse. This complicates further pulse amplification. To maintain the same frequency, a chain of laser amplifiers can be seeded with pulses from an actively CEP-stabilized MHz-repetition-rate oscillator, provided the phase coherence is not destroyed in the amplification process. It will be shown that with such a seed CEP control in a kHz I-mJ multipass amplifier becomes feasible after adding a servo loop that corrt:cts for the slow CEP drift of the amplified pulses. Furthermore, the generation of intense phase-reproducible pulses opens the way to calibrate the actual value of the CEP, which is required to obtain the full information on the shape of the electric field. Among several candidate methods to determine the value of CEP, soft-X-ray emission in a noble gas was chosen for the intuitive dependence between the spectral shape of the highest-energy radiation and the magnitude of the peak optical oscillation of a few-cycle pulse (2). Figure 1 shows the experimental results of the first-time CEP calibration. XI1 Yll 11lil 111) 1211 130 IJII lill -15 .IO -5 I1 5 Io 15 Photon enerqy (eV) Time (Is)

Extreme ultraviolet high-harmonic spectroscopy of solids

Extreme ultraviolet (EUV) high-harmonic radiation emerging from laser-driven atoms, molecules or plasmas underlies powerful attosecond spectroscopy techniques and provides insight into fundamental structural and dynamic properties of matter. The advancement of these spectroscopy techniques to study strong-field electron dynamics in condensed matter calls for the generation and manipulation of EUV radiation in bulk solids, but this capability has remained beyond the reach of optical sciences. Recent experiments and theoretical predictions paved the way to strong-field physics in solids by demonstrating the generation and optical control of deep ultraviolet radiation in bulk semiconductors, driven by femtosecond mid-infrared fields or the coherent up-conversion of terahertz fields to multi-octave spectra in the mid-infrared and optical frequencies. Here we demonstrate that thin films of SiO2 exposed to intense, few-cycle to sub-cycle pulses give rise to wideband coherent EUV radiation extending in energy to about 40 electronvolts. Our study indicates the association of the emitted EUV radiation with intraband currents of multi-petahertz frequency, induced in the lowest conduction band of SiO2. To demonstrate the applicability of high-harmonic spectroscopy to solids, we exploit the EUV spectra to gain access to fine details of the energy dispersion profile of the conduction band that are as yet inaccessible by photoemission spectroscopy in wide-bandgap dielectrics. In addition, we use the EUV spectra to trace the attosecond control of the intraband electron motion induced by synthesized optical transients. Our work advances lightwave electronics in condensed matter into the realm of multi-petahertz frequencies and their attosecond control, and marks the advent of solid-state EUV photonics.

Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua

We demonstrate sub-millijoule-energy, sub-4?fs-duration near-infrared laser pulses with a controlled waveform comprised of approximately 1.5 optical cycles within the full-width at half-maximum (FWHM) of their temporal intensity profile. We further demonstrate the utility of these pulses for producing high-order harmonic continua of unprecedented bandwidth at photon energies around 100?eV. Ultra-broadband coherent continua extending from 90?eV to more than 130?eV with smooth spectral intensity distributions that exhibit dramatic, never-before-observed sensitivity to the carrier-envelope offset (CEO) phase of the driver laser pulse were generated. These results suggest the feasibility of sub-100-attosecond XUV pulse generation for attosecond spectroscopy in the 100?eV range, and of a simple yet highly sensitive on-line CEO phase detector with sub-50-ms response time.

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.