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Attosecond four-wave mixing spectroscopy is a relatively new technique for studying ultrafast dynamics of highly excited states with exquisite temporal precision and spectral resolution. The attosecond four-wave mixing technique, as described in this paper, uses non-collinear beam geometries of one attosecond pulse together with two optical pulses to obtain background-free, spatially isolated emission signals in the extreme ultraviolet range that directly resolve coherent dynamics in the time domain. This method is advantageous by avoiding the strong spectral modulations that often complicate the interpretation of collinear attosecond transient absorption studies while also enabling greater control over the spatial and temporal characteristics of each light-matter interaction used to probe the ultrafast processes. This paper describes a broad range of attosecond four-wave mixing experiments performed in gas phase atoms and molecules, and a recent extension into solids.

Attosecond science requires a substantial rethinking of how to make measurements on very short timescales; how to acquire the necessary equipment, technology, and personnel; and how to build a set of laboratories for such experiments. This entails a rejuvenation of the author in many respects, in the laboratory itself, with regard to students and postdocs, and in generating funding for research. It also brings up questions of what it means to do attosecond science, and the discovery of the power of X-ray spectroscopy itself, which complements the short timescales addressed. The lessons learned, expressed in the meanderings of this autobiographical article, may be of benefit to others who try to reinvent themselves. [ABSTRACT FROM AUTHOR]

ABSTRACTAttosecond photoelectron spectroscopy has opened up for studying light–matter interaction on ultrafast time scales. It is often performed with interferometric experimental setups that require outstanding stability. We demonstrate and characterize in detail an actively stabilized, versatile, high spectral resolution attosecond beamline based on a Mach-Zehnder interferometer. The active stabilization keeps the interferometer ultra-stable for several hours with an RMS stability of 13 as and a total pump-probe delay scanning range of [Formula: see text] fs. A tunable femtosecond laser source to drive high-order harmonic generation allows for precisely addressing atomic and molecular resonances. Furthermore, the interferometer includes a spectral shaper in 4f-geometry in the probe arm as well as a tunable bandpass filter in the pump arm, which offer additional high flexibility in terms of tunability as well as narrowband or polychromatic probe pulses. We demonstrate the capabilities of the beamline via experiments using several variants of the RABBIT (reconstruction of attosecond beating by two photon transitions) technique. In this setup, the temporal-spectral resolution of photoelectron spectroscopy can reach a new level of accuracy and precision.

Noncollinear wave-mixing spectroscopies with attosecond extreme ultraviolet (XUV) pulses provide unprecedented insight into electronic dynamics. In infrared and visible regimes, heterodyne detection techniques utilize a reference field to amplify wave-mixing signals while simultaneously allowing for phase-sensitive measurements. Here, we implement a self-heterodyned detection scheme in noncollinear wave-mixing measurements with a short attosecond XUV pulse train and two few-cycle near infrared (NIR) pulses. The initial spatiotemporally overlapped XUV and NIR pulses generate a coherence of both odd (1snp) and even (1sns and 1snd) parity states within gaseous helium. A variably delayed noncollinear NIR pulse generates angularly-dependent four-wave mixing signals that report on the evolution of this coherence. The diffuse angular structure of the XUV harmonics underlying these emission signals is used as a reference field for heterodyne detection, leading to cycle oscillations in the transient wave-mixing spectra. With this detection scheme, wave-mixing signals emitting from at least eight distinct light-induced, or dressed, states can be observed, in contrast to only one light induced state identified in a similar homodyne wave-mixing measurement. In conjunction with the self-heterodyned detection scheme, the noncollinear geometry permits the conclusive identification and angular separation of distinct wave-mixing pathways, reducing the complexity of transient spectra. These results demonstrate that the application of heterodyne detection schemes can provide signal amplification and phase-sensitivity, while maintaining the versatility and selectivity of noncollinear attosecond XUV wave-mixing spectroscopies. These techniques will be important tools in the study of ultrafast dynamics within complex chemical systems in the XUV regime.

High-order harmonic generation of atoms irradiated by an ultrashort laser pulse was calculated by numerically solving the time-dependent Schrödinger equation and the Bohmian trajectory scheme. The harmonic spectra with the two schemes are quantitatively consistent. Using the wavelet behavior of the Bohmian trajectory, the spatio-temporal features of harmonic emission from different energy regions are analyzed. It is found that the spatio-temporal distribution of the harmonic well revealed the physical mechanism of harmonic generation. This method will contribute to the understanding of harmonic emission mechanisms in complex systems, which include many atoms. [ABSTRACT FROM AUTHOR]

Determination and interpretation of Wigner-like photoionisation delays is one of the most active fields of attosecond science. Previous results have suggested that large photoionisation delays are associated with structured continua, but a quantitative relation between photoionisation cross sections and time delays has been missing. Here, we derive a Kramers–Kronig-like relation between these quantities and demonstrate its validity for (anti)resonances. This new concept defines a topological analysis, which rationalises the sign of photoionisation delays and thereby sheds new light on a long-standing controversy regarding the sign of the photoionisation delay near the Ar 3 s Cooper minimum. Our work bridges traditional photoionisation spectroscopy with attosecond chronoscopy and offers new methods for analysing and interpreting photoionisation delays.

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

Gas phase experiments combined with ultrafast technologies can provide information on the intrinsic properties of molecular systems at picosecond, femtosecond, or even attosecond timescales. However, these experiments are often limited to relatively simple model systems. In this context, electrospray ionization sources (ESI) have offered new perspectives as they allow to produce large or fragile molecular ions in the gas phase, mimicking molecules in their natural environment. While time-resolved UV-visible ultrafast experiments on molecular ions have been successfully developed over the past decades, efforts are still required to perform experiments using ultrashort extreme ultraviolet (XUV) pulses with the goal of reaching attosecond resolution. In this article, we present recent results obtained using the combination of ultrafast technologies and ESI sources. We show that ultrafast dynamics experiments can be performed on molecular ions without ion trapping devices and can reveal UV-induced charge transfer in small peptides with controlled micro-environment. Non-adiabatic relaxation dynamics in large (bio)molecular ions is also presented. Such experiments are compatible with high harmonic generation XUV sources as shown here in the case of a metal complex. These ultrafast dynamics studies on large molecular ions offer new perspectives in attosecond science.

We study resonant two-photon ionization of helium atoms via the 1s3p, 1s4p and 1s5p1P1 states using the 15th harmonic of a titanium-sapphire laser for the excitation and a weak fraction of the laser field for the ionization. The phase of the photoelectron wavepackets is measured by an attosecond interferometric technique, using the 17th harmonic. We perform experiments with angular resolution using a velocity map imaging spectrometer and with high energy resolution using a magnetic bottle electron spectrometer. Our results are compared to calculations using the two-photon random phase approximation with exchange to account for electron correlation effects. We give an interpretation for the multiple π-rad phase jumps observed, both at and away from resonance, as well as their dependence on the emission angle.

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray freeelectron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a submicrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program. [ABSTRACT FROM AUTHOR]

High-order harmonic generation of atoms irradiated by an ultrashort laser pulse was calculated by numerically solving the time-dependent Schrödinger equation and the Bohmian trajectory scheme. The harmonic spectra with the two schemes are quantitatively consistent. Using the wavelet behavior of the Bohmian trajectory, the spatio-temporal features of harmonic emission from different energy regions are analyzed. It is found that the spatio-temporal distribution of the harmonic well revealed the physical mechanism of harmonic generation. This method will contribute to the understanding of harmonic emission mechanisms in complex systems, which include many atoms.

With the intensive research on ultrafast dynamics in physics and chemistry, the single‐shot measurement of ultrashort time change has become increasingly important. The most advanced oscilloscope with the time‐lens technique possesses subpicosecond resolution, while the interferometer can single‐shot probe time event within one optical cycle. However, the single‐shot measurement of time difference beyond optical cycle but less than time‐lens’ resolution is still inaccessible. Herein, a technique, the dispersive temporal interferometer (DTI), to break through the gap between interferometer and time lens on single‐shot time measurement, is reported. The concept is an analogy to the spatial interference: a pulse passes two paths to assemble into a pulse pair, and temporal interference arises after large dispersion, which can single‐shot record the imposed time change. Experimentally, it is measured that its resolution is sub‐20 as (0.004 optical cycle) over a range of larger than 2 ps (400 optical cycle), with a range‐to‐resolution ratio of 105 and sampling rate of 42.8 MHz. Moreover, a DTI‐based gyroscope with sensitivity of 348 as/(deg s−1) is fabricated to demonstrate its applications in optical sensors. This technique can precisely single‐shot monitor ultrashort time change in attosecond resolution and has a prosperous application prospect in capturing ultrafast process.

Interferometry, a key technique in modern precision measurements, has been used for length measurement in engineering metrology and astronomy. An analogous time-domain interferometric technique would represent a significant complement to spatial domain applications and require the manipulation of interference on extreme time and energy scales. Here, we report an all-optical interferometer using laser-driven high order harmonics as attosecond temporal slits. By controlling the phase of the temporal slits with an external field, a time domain interferometer that preserves both attosecond temporal resolution and hundreds of meV energy resolution is implemented. We apply this exceptional temporal resolution to reconstruct the waveform of an arbitrarily polarized optical pulse, and utilize the provided energy resolution to interrogate the abnormal character of the transition dipole near the Cooper minimum in argon. This novel attosecond interferometry paves the way for high precision measurements in the time-energy domain using all-optical approaches. [ABSTRACT FROM AUTHOR]

We propose a new photon-coincidence measurement based on the time- and wavevector-resolved detection of photons generated by the scattering of multiple x-ray pulses with variable delays. The technique directly measures multipoint correlation functions of the charge density through superpositions of valence excitations which are created impulsively by the scattering process. © 2014 IOP Publishing Ltd.

We present an interferometric HHG-2ω0 scheme and compare it to the usual XUV-IR RABBIT method that is widely used in attosecond science. Both methods are able to reconstruct the properties of an attosecond pulse train and can be used to measure attosecond ionization time delays in atoms and molecules. While they have several similarities, they also have conceptual differences. Here, we present some particularities of the HHG-2ω0 method and its advantages and drawbacks, which would help to define situations where it can provide information inaccessible by other technics. [ABSTRACT FROM AUTHOR]

Intriguing properties of photoemission from free, unsupported particles and droplets were predicted nearly 50 years ago, though experiments were a technical challenge. The last few decades have seen a surge of research in the field, due to advances in aerosol technology (generation, characterization, and transfer into vacuum), the development of photoelectron imaging spectrometers, and advances in vacuum ultraviolet and ultrafast light sources. Particles and droplets offer several advantages for photoemission studies. For example, photoemission spectra are dependent on the particle's size, shape, and composition, providing a wealth of information that allows for the retrieval of genuine electronic properties of condensed phase. In this review, with a focus on submicrometer-sized, dielectric particles and droplets, we explain the utility of photoemission from such systems, summarize several applications from the literature, and present some thoughts on future research directions. [ABSTRACT FROM AUTHOR]

Practical aspects of the robust method we proposed for producing few-cycle attosecond pulses with arbitrary waveform in the extreme ultraviolet spectral range are studied numerically. It is based on the undulator radiation of relativistic ultrathin electron layers produced by laser-driven energy modulation. By using realistic specifications, we show that isolated waveform-controlled extreme ultraviolet attosecond pulses at 5 nm with 10 nJ energy and 20 as pulse duration, at 20 nm with 90 nJ energy and 80 as pulse duration, and at 60 nm with 200 nJ energy and 240 as duration can be generated, respectively.PACS numbers: 41.60.Cr, 41.50.+h, 41.75.Ht

The ability to produce ultrashort, high-brightness X-ray pulses is revolutionizing the field of ultrafast X-ray spectroscopy. Free-electron laser (FEL) facilities are driving this revolution, but unique aspects of the FEL process make the required characterization and use of the pulses challenging. In this paper, we describe a number of developments in the generation of ultrashort X-ray FEL pulses, and the concomitant progress in the experimental capabilities necessary for their characterization and use at the Linac Coherent Light Source. This includes the development of sub-femtosecond hard and soft X-ray pulses, along with ultrafast characterization techniques for these pulses. We also describe improved techniques for optical cross-correlation as needed to address the persistent challenge of external optical laser synchronization with these ultrashort X-ray pulses. [ABSTRACT FROM AUTHOR]

The dynamics of the photoelectric effect in solid-state systems can be investigated via attosecond-time-resolved photoelectron spectroscopy. This article provides a comparison of delay information accessible by the two most important techniques, attosecond streaking spectroscopy and reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) at solid surfaces, respectively. The analysis is based on simulated time-resolved photoemission spectra obtained by solving the time-dependent Schrödinger equation in a single-active-electron approximation. We show a continuous transition from the few-cycle RABBITT regime to the streaking regime as two special cases of laser-assisted photoemission. The absolute delay times obtained by both methods agree with each other, within the uncertainty limits for kinetic energies >10 eV. Moreover, for kinetic energies >10 eV, both streaking delay time and RABBITT delay time coincide with the classical time of flight for an electron propagating from the emitter atom to the bulk-vacuum interface, with only small deviations of less than 4 as due to quantum mechanical interference effects. [ABSTRACT FROM AUTHOR]

Current conception of attosecond pulse is based on Fourier optics and refers to an electromagnetic pulse with a broad, homogeneous weight Fourier spectrum. Its preparation/generation is along an indirect route in which the output of commercial available μ m-level wavelength laser is "processed" by elaborately designed optics medium allowing high-order harmonics effect to change its Fourier spectrum to be of a flat high-frequency tail. Such an indirect, quantum scheme is limited by its efficiency in high-order harmonics generation. For higher efficiency, other routes for the same goal, i.e., light pulse with an attosecond-level duration, deserve to be tried. The method proposed is a direct, classic scheme. It is to directly control the time duration of classic electrons doing acceleration/deceleration in a feasible, elaborately-designed driving DC fields configuration. The duration can be adjusted by initial electrons velocity, geometric dimension of driving field configuration. The maximum strength of a generated pulse is controlled by the number of electrons. The frequency of a generated pulse is controlled by initial electrons position in the configuration. The shortest duration of single pulse can be down to sub-attosecond-level according to currently available minimum geometric dimension of driving field and suitable gesture of electrons entering into the driving field configuration. This work displays a feasible, direct, classic route of achieving EM pulse with an attosecond-level duration. In particular, the pulse is mono-color, rather than a superposition of Fourier components with nearly-equal weight. [ABSTRACT FROM AUTHOR]

The emerging research field of attosecond science allows for the temporal investigation of one of the fastest dynamics in nature: electron dynamics in matter. These dynamics are responsible for chemical and biological processes, and the ability to understand and control them opens a new door of fundamental science, with the possibility to influence all lives if medical issues can thereby be addressed. Multilayer optics are key elements in attosecond experiments; they are used to tailor attosecond pulses with well-defined characteristics to facilitate detailed and accurate insight into processes, e.g., photoemission, Auger decay, or (core-) excitons. Based on the investigations and research efforts from the past several years, multilayer mirrors today are routinely used optical elements in attosecond beamlines. As a consequence, the generation of ultrashort pulses, combined with their dispersion control, has proceeded from the femtosecond range in the visible/infrared spectra to the attosecond range, covering the extreme ultraviolet and soft X-ray photon range up to the water window. This article reviews our work on multilayer optics over the past several years, as well as the impact from other research groups, to reflect on the scientific background of their nowadays routine use in attosecond physics. [ABSTRACT FROM AUTHOR]

We discuss the efficient generation of intense "water window" (0.28–0.54 keV) isolated attosecond pulses (IAPs) using a mid-infrared (MIR) waveform synthesizer. Our numerical simulations clearly indicate that not only a longer-wavelength driving laser but also a weak control pulse in the waveform synthesizer helps extend the continuum cutoff region and reduce the temporal chirp of IAPs in high-order harmonic generation (HHG). This insight indicates that a single-cycle laser field is not an optimum waveform for generating the shortest IAP from the veiwpoints of reducing the attochirp and increasing the efficiency of HHG. By combining a waveform synthesizer technology and a 100 mJ MIR femtosecond pulse based on a dual-chirped optical parametric amplification (DC-OPA) method, a gigawatt-scale IAP (55 as with 10 nJ order) in the water window region can be generated even without attochirp compensation. The MIR waveform synthesizer is highly beneficial for generating a shorter IAP duration in the soft X-ray region because there are no suitable transparent dispersive materials that can be used for compressing the attochirp. [ABSTRACT FROM AUTHOR]

Laser driven high harmonic generation from relativistically oscillating plasma surfaces is a promising route to isolated attosecond pulses with high peak brightness. Here we investigate a double optical gating scheme to restrict the emission to only a single, intense, attosecond pulse even with a multi-cycle driving laser. This scheme, which uses a second harmonic field, combined with a pair of counter-rotating circularly polarized laser pulses, leads to more efficient attosecond pulse generation with improved temporal isolation when compared to a single colour polarization gating scheme.

We investigate the electron quantum path interference (QPI) effects during high harmonic generation in atomic gas medium driven by ultrashort chirped laser pulses. To achieve that, we identify and vary the different experimentally relevant control parameters of such a driving laser pulse influencing the high harmonic spectra. Specifically, the impact of the pulse duration (from the few-cycle to the multi-cycle domain), peak intensity and instantaneous frequency is studied in a self-consistent manner. Simulations involving macroscopic propagation effects are also considered. The study aims to reveal the microscopic background behind a variety of interference patterns capturing important information both about the fundamental laser field and the generation process itself. The results provide guidance towards experiments with chirp control as a tool to unravel, explain and utilize the rich and complex interplay between QPIs including the tuning of the periodicity of the intensity dependent oscillation of the harmonic signal, and the curvature of spectrally resolved Maker fringes.