Attosecond ionization time delays in strong-field physics

Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.

Generating attosecond pulses with controllable polarization from cyclic H_(3)^(2+) molecules by bichromatic circular fields

We investigate the polarization properties of harmonics from the cyclic H_(3)^(2+) molecular ions in tailored bichromatic counter-rotating circularly polarized(BCCP)fields by solving the time-dependent Schrödinger equation.The allowed harmonics and their helicities are associated with the symmetry compatibility of the field-target systems,and large intensity difference between adjacent harmonics with opposite helicities appears in a wide spectral range when the BCCP field is at certain rotation angles.We try to explain the intensity difference by using a recombination model based on the quantum-orbit theory and by analyzing the ionization pathways.Moreover,to synthesize attosecond pulse trains with tunable polarization,the intensity difference is manipulated by introducing a seed XUV field,and by changing the relative amplitude ratio as well as the helicity of BCCP fields.

Electron vortices generation of photoelectron of H_(2)^(+) by counter-rotating circularly polarized attosecond pulses

Molecular-frame photoelectron momentum distributions(MF-PMDs) of an H_(2)^(+) molecule ion in the presence of a pair of counter-rotating circularly polarized attosecond extreme ultraviolet laser pulses is studied by numerically solving the two-dimensional time-dependent Schrodinger equation within the frozen-nuclei approximation. At small time delay, our simulations show that the electron vortex structure is sensitive to the time delay and relative phase between the counterrotating pulses when they are partially overlapped. By adjusting time delay and relative phase, we have the ability to manipulate the MF-PMDs and the appearance of spiral arms. We further show that the internuclear distance can affect the spiral vortices due to its different transition cross sections in the parallel and perpendicular geometries. The lowest-order perturbation theory is employed to interpret these phenomena qualitatively. It is concluded that the internuclear distancedependent transition cross sections and the confinement effect in diatomic molecules are responsible for the variation of vortex structures in the MF-PMDs.

Generation of quasi-chirp-free isolated attosecond pulses from atoms under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields

The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.

Attosecond manipulation of ionization and efficient broadband supercontinuum generation in stretched molecules

We theoretically investigate the high-order harmonic generation from stretched molecules in a linearly polarized intense field. By adopting an infrared pulse combined with an ultraviolet （UV） attosecond pulse, the ionization process can be controlled effectively. In this excitation scheme, the harmonic spectrum beyond Ip ＋ 3.17Up is significantly enhanced by two orders, where Ip and Up = e^2E0^2/（4mew^2） are the ionization and ponderomotive potential, then smooth broadband supercontinuum with the bandwidth of about 120 eV is obtained, which leads to an isolated sub-60- as attosecond pulse with a high signal-noise ratio. Moreover, the bandwidth of the supercontinuum is weakly dependent on the location and pulse duration of the UV pulse.

Attosecond pulse trains driven by IR pulses spectrally broadened via supercontinuum generation in solid thin plates

We utilized a set of fused silica thin plates to broaden the spectrum of 1kHz,30 fs Ti:sapphire amplified laser pulses to an octave.Following the compression by chirped mirror pairs,the generated few-cycle pulses were focused onto an argon filled gas cell.We detected high order harmonics corresponding to a train of 209 as pulses,characterized by the reconstruction of attosecond beating by interference of two-photon transition(RABITT)technique.Compared with the conventional attosecond pulse trains,the broad harmonics in such pulse trains cover more energy range,so it is more efficient in studying some typical cases,such as resonances,with frequency resolved RABITT.As the solid thin plates can support high power supercontinuum generation,it is feasible to tailor the spectrum to have different central wavelength and spectral width,which will make the RABITT source work in different applications.

Generation of isolated attosecond pulses in bowtie-shaped nanostructure with three-color spatially inhomogeneous fields

We theoretically investigate high-order harmonic generation in a two-color multi-cycle inhomogeneous field combined with a 27th harmonic pulse. By considering a bowtie-shaped gold nanostructure, the spatiotemporal profiles of enhanced plasmonic fields are obtained by solving the Maxwell equation using finite-domain time-difference method. Based on quantum-mechanical and classical models, the effect of 27th harmonic pulse, temporal profile of enhanced plasmonic field and inhomogeneity on supercontinuum generation are analyzed and discussed. As a result, broadband supercontinuum can be generated from our approach with optimized gap size of nanostructure. Moreover, these results are not sensitively dependent on the relative phase in the two-color field.

Extension of high-order harmonics and generation of an isolated attosecond pulse in the chirped laser field

This paper theoretically investigates the high-order harmonic generation cutoff extension using intense few-cycle linearly chirped laser pulses. It shows that the cutoff of the harmonic can be extended remarkably by optimising the chirping parameters. The time-frequency characteristics of high-order harmonics with different chirping parameters are analysed by means of wavelet transform of the dipole acceleration. It also gives out the classical three-step model pictures of electron. By superposing a properly selected range of the harmonic spectrum, it obtains an isolated 65as pulse.

Attosecond laser station

The attosecond laser station （ALS） at the Synergetic Extreme Condition User Facility （SECUF） is a sophisticated and user-friendly platform for the investigation of the electron dynamics in atoms, molecules, and condensed matter on timescales ranging from tens of femtoseconds to tens of attoseconds. Short and tunable coherent extreme-ultraviolet （XUV） light sources based on high-order harmonic generation in atomic gases are being developed to drive a variety of endstations for inspecting and controlling ultrafast electron dynamics in real time. The combination of such light sources and end-stations offers a route to investigate fundamental physical processes in atoms, molecules, and condensed matter. The ALS consists of four beamlines, each containing a light source designed specifically for application experiments that will be performed in its own end-station. The first beamline will produce broadband XUV light for attosecond photoelectron spectroscopy and attosecond transient absorption spectroscopy. It is also capable of performing attosecond streaking to characterize isolated attosecond pulses and will allow studies on the electron dynamics in atoms, moleculars, and condensed matter. The second XUV beamline will produce narrowband femtoseeond XUV pulses for time-resolved and angle-resolved photoelectron spectroscopy, to study the electronic dynamics on the timescale of fundamental correlations and interactions in solids, especially in superconductors and topological insulators. The third beamline will produce broadband XUV pulses for attosecond coincidence spectroscopy in a cold-target recoil-ion momentum spectrometer, to study the ultrafast dynamics and reactions in atomic and molecular systems. The last beamline produces broadband attosecond XUV pulses designed for time-resolved photoemission electron microscopy, to study the ultrafast dynamics of plasmons in nanostructures and the surfaces of solid materials with high temporal and spatial resolutions simultaneously. The main object of the ALS is to provide domestic and international scientists with unique tools to study fundamental processes in physics, chemistry, biology, and material sciences with ultrafast temporal resolutions on the atomic scale.

Ionization of atoms by chirped attosecond pulses

We investigate the ionization dynamics of atoms by chirped attosecond pulses using the strong field approximation method. The pulse parameters are carefully chosen in the regime where the strong field approximation method is valid. We analyse the effects of the chirp of attosecond pulses on the energy distributions and the corresponding left-right asymmetry of the ionized electrons. For a single chirped attosecond pulse, the ionized electrons can be redistributed and the left-right asymmetry shows oscillations because of the introduction of the chirp. For time-delayed double attosecond pulses at different intensities with the weaker one chirped, exchanging the order of the two pulses shows a relative shift of the energy spectra, which can be explained by the different effective time delays of different frequency components because of the chirp.

Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields

We theoretically study the selection of the quantum path in high-order harmonics（HHG） and isolated attosecond pulse generation from a one-dimensional（1D） model of a H_2~＋ molecule in few-cycle inhomogeneous laser fields.We show that the inhomogeneity of the laser fields play an important role in the HHG process.The cutoff of the harmonics can be extended remarkably,and the harmonic spectrum becomes smooth and has fewer modulations.We investigate the time-frequency profile of the time-dependent dipole,which shows that the short quantum path is enhanced and the long quantum path disappears in spatially inhomogeneous fields.The semi-classical three-step model is also applied to illustrate the physical mechanism of HHG.The influence of driving field carrier-envelop phase（CEP） on HHG is also discussed.By superposing a series of properly selected harmonics,an isolated attosecond pulse（IAP） with duration 53 as can be obtained by a 15-fs,1600-nm laser pulse with the parameter ε = 0.0013（e is the parameter that determines the order of inhomogeneity of the laser field）.

Generation of an isolated sub-30 attosecond pulse in a two-color laser field and a static electric field

We theoretically investigate high-order harmonic generation（HHG） from a helium ion model in a two-color laser field,which is synthesized by a fundamental pulse and its second harmonic pulse.It is shown that a supercontinuum spectrum can be generated in the two-color field.However,the spectral intensity is very low,limiting the application of the generated attosecond（as） pulse.By adding a static electric field to the synthesized two-color field,not only is the ionization yield of electrons contributing to the harmonic emission remarkably increased,but also the quantum paths of the HHG can be significantly modulated.As a result,the extension and enhancement of the supercontinuum spectrum are achieved,producing an intense isolated 26-as pulse with a bandwidth of about 170.5 eV.In particular,we also analyse the influence of the laser parameters on the ultrabroad supercontinuum spectrum and isolated sub-30-as pulse generation.

Helicity of harmonic generation and attosecond polarization with bichromatic circularly polarized laser fields

We theoretically investigate the high-order harmonic generation(HHG) of helium atom driven by bichromatic counterrotating circularly polarized laser fields. By changing the intensity ratio of the two driving laser fields, the spectral chirality of the HHG can be controlled. As the intensity ratio increases, the spectral chirality will change from positive-to negativevalue around a large intensity ratio of the two driving fields when the total laser intensity keeps unchanged. However, the sign of the spectral chirality can be changed from positive to negative around a small intensity ratio of the two driving fields when the total laser intensity changes. At this time, we can effectively control the helicity of the harmonic spectrum and the polarization of the resulting attosecond pulses by adjusting the intensity ratio of the two driving laser fields. As the intensity ratio and the total intensity of the driving laser fields increase, the relative intensity of either the left-circularly or right-circularly polarized harmonic can be enhanced. The attosecond pulses can evolve from being elliptical to near linear correspondingly.

Isolated sub-30-attosecond pulse generation using a multicycle two-color chirped laser and a static electric field

We present a theoretical investigation of high-order harmonic generation in a chirped two-color laser field, which is synthesized by a 10-fs/800-nm fundamental chirped pulse and a 10-fs/1760-nm subharmonic pulse. It is shown that a supercontinuum can be produced using the multicycle two-color chirped field. However, the supercontinuum reveals a strong modulation structure, which is not good for the generation of an isolated attosecond pulse. By adding a static electric field to the multicycle two-color chirped field, not only the harmonic cutoff is extended remarkably, but also the quantum paths of the high-order harmonic generation （HHG） are modified significantly. As a result, both the extension of the supercontinuum and the selection of a single quantum path are achieved, producing an isolated 23-as pulse with a bandwidth of about 170.6 eV. Furthermore, the influences of the laser intensities on the supercontinuum and isolated attosecond pulse generation are investigated.

Carrier Envelope Phase Description for an Isolated Attosecond Pulse by Momentum Vortices

As a crucial parameter for a few-cycle laser pulse, the carrier envelope phase(CEP) substantially determines the laser waveform. We propose a method to directly describe the CEP of an isolated attosecond pulse(IAP) by the vortex-shaped momentum pattern, which is generated from the tunneling ionization of a hydrogen atom by a pair of time-delayed, oppositely and circularly polarized IAP-IR pulses. Superior to the angular streaking method that characterizes the CEP in terms of only one streak, our method describes the CEP of an IAP by the features of multiple streaks in the vortex pattern. The proposed method may open the possibility of capturing sub-cycle extreme ultraviolet dynamics.

Harmonic and attosecond pulse enhancement in the presence of noise

In this paper, we theoretically investigate the effect of noise on the photoionization, the generation of the high-order harmonic and the attosecond pulse irradiated from a model He＋ ion. It shows that by properly adding noise fields, such as Gaussian white noise, random light or colored noise, both the ionization probabilities （IPs） and the harmonic yields can be enhanced by several orders of magnitude. Further, by tuning the noise intensity, a stochastic resonance-like curve is observed, showing the existence of an optimal noise in the ionization enhancement process. Finally, by superposing a properly selected harmonic, an intense attosecond pulse with a duration of 67 as is directly generated.

Attosecond spectroscopy for filming the ultrafast movies of atoms,molecules and solids

Three decades ago,a highly nonlinear nonpertubative phenomenon,now well-known as the high harmonic generation(HHG),was discovered when intense laser irradiates gaseous atoms.As the HHG produces broadband coherent radiation,it becomes the most promising source to obtain attosecond pulses.The door to the attosecond science was opened ever since.In this review,we will revisit the incredible adventure to the attoworld.Firstly,the progress of attosecond pulse generation is outlined.Then,we introduce the efforts on imaging the structures or filming the ultrafast dynamics of nuclei and electrons with unprecedented attosecond temporal and Angstrom spatial resolutions,utilizing the obtained attosecond pulses as well as the high harmonic spectrum itself.

Multi-Electron Effects in Attosecond Transient Absorption of CO Molecules

Using the fully propagated time-dependent Hartree–Fock method, we identify that both the dynamic core polarization and multiorbital contributions are important in the attosecond transient absorption of CO molecules.The dynamics of core electrons effectively modifies the behaviors of electrons in the highest occupied molecular orbital, resulting in the modulation of intensity and position of the absorption peaks. Depending on the alignment angles, different inner orbitals are identified to contribute, and even dominate the total absorption spectra. As a result, multi-electron fingerprints are encoded in the absorption spectra, which shed light on future applications of attosecond transient absorption in complex systems.

Effects of pressure and gas-jet thickness on the generation of attosecond pulse

We investigate how the intensity and duration of an attosecond pulse generated from high-order harmonic generation are affected by the pressure and thickness of the gas jet by taking into account the macroscopic propagation of both fun- damental and harmonic fields. Our simulations show that, limited by the propagation effects, especially the absorption of harmonics, the intensity of an attosecond pulse cannot be improved by just independently increasing the gas pressure or the medium length. On the other hand, due to good phase-matching conditions, the duration of a generated attosecond pulse can be improved by changing the gas pressure.

Attosecond pulse generation from two-electron harmonic emission spectrum

In this paper, we theoretically investigate the high-order harmonic generation and attosecond pulse generation when a two-electron He atom is exposed to the intense laser pulse. It shows that due to the two-electron double recombination mechanism, an extended plateau beyond the classical single-electron harmonic has been obtained on the two-electron harmonic spectrum. Further by using this two-electron harmonic extension scheme combined with the two-color field, two supercontinuum bandwidths with 200 e V have been obtained. As a result, a series of sub-60 as extreme ultraviolet（XUV）pulses have been directly generated.