We report a novel quasi-phase matching technique for high-order harmonic generation in low-density gases. Numerical simulations show that in few-optical cycle pulsed Bessel beams it is possible to control the pulse envelope and phase velocities which in turn allows to control the carrier-envelope phase during propagation. The resulting oscillations in the peak intensity allow to phase-match the high-order harmonic generation process with a nearly two decade enhancement in the XUV power spectrum.
We present a method to distinguish the high harmonics generated in individual half-cycle of the driving laser pulse by mixing a weak ultraviolet pulse, enabling one to observe the cutoff of each half-cycle harmonic. We show that the detail information of the driving laser pulse, including the laser intensity, pulse duration and carrier-envelope phase, can be {\it in situ} retrieved from the harmonic spectrogram. In addition, our results show that this method also distinguishes the half-cycle high harmonics for a pulse longer than 10 fs, suggesting a potential to extend the CEP measurement to t…
Advancing table-top attosecond sources in brightness and pulse duration is of immense interest and importance for an expanding sphere of applications. Recent theoretical studies [New J. Phys., 22 093030 (2020)] have found that high-order frequency mixing (HFM) in a two-color laser field can be much more efficient than high-order harmonic generation (HHG). Here we study the attosecond properties of the coherent XUV generated via HFM analytically and numerically, focusing on the practically important case when one of the fields has much lower frequency and much lower intensity than the other one…
We theoretically study the carrier-envelope phase dependent inversion generated in a two-level system by excitation with a few-cycle pulse. Based on the invariance of the inversion under time reversal of the exciting field, parameters are introduced to characterize the phase sensitivity of the induced inversion. Linear and nonlinear phase effects are numerically studied for rectangular and sinc-shaped pulses. Furthermore, analytical results are obtained in the limits of weak fields as well as strong dephasing, and by nearly degenerate perturbation theory for sinusoidal excitation. The results …
We report on tunnel ionization of Xe by 2-cycle, intense, infrared laser pulses and its dependence on carrier-envelope-phase (CEP). At low values of optical field ($E$), the ionization yield is maximum for cos-like pulses with the dependence becoming stronger for higher charge states. At higher $E$-values, the CEP dependence either washes out or flips. A simple phenomenological model is developed that predicts and confirms the observed results. CEP effects are seen to persist for 8-cycle pulses. Unexpectedly, electron rescattering plays an unimportant role in the observed CEP dependence. Our r…
Carrier envelope phase (CEP) stabilized pulses of intense 800 nm light of 5 fs duration are used to probe the dissociation dynamics of dications of isotopically-substituted water, HOD. HOD$^{2+}$ dissociates into either H$^+$ + OD$^+$ or D$^+$ + OH$^+$. The branching ratio for these two channels is CEP-dependent; the OD$^+$/OH$^+$ ratio (relative to that measured with CEP-unstabilized pulses) varies from 150% to over 300% at different CEP values, opening prospects of isotope-dependent control over molecular bond breakage. The kinetic energy released as HOD$^{2+}$ Coulomb explodes is also CEP-d…
We investigate numerically with Hylleraas coordinates the frequency dependence of the carrier-envelope phase (CEP) effect on bound-bound transitions of helium induced by an ultrashort laser pulse of few cycles. We find that the CEP effect is very sensitive to the carrier frequency of the laser pulse, occurring regularly even at far-off resonance frequencies. By analyzing a two-level model, we find that the CEP effect can be attributed to the quantum interference between neighboring multi-photon transition pathways, which is made possible by the broadened spectrum of the ultrashort laser pulse.…
We present accurate measurements of carrier-envelope phase effects on ionisation of the noble gases with few-cycle laser pulses. The experimental apparatus is calibrated by using atomic hydrogen data to remove any systematic offsets and thereby obtain accurate CEP data on other generally used noble gases such as Ar, Kr and Xe. Experimental results for H are well supported by exact TDSE theoretical simulations however significant differences are observed in case of noble gases.
We present the first theoretical investigation of carrier-wave Rabi flopping in real atoms by employing numerical simulations of high-order harmonic generation (HHG) in alkali species. Given the short HHG cutoff, related to the low saturation intensity, we concentrate on the features of the third harmonic of sodium (Na) and potassium (K) atoms. For pulse areas of 2$π$ and Na atoms, a characteristic unique peak appears, which, after analyzing the ground state population, we correlate with the conventional Rabi flopping. On the other hand, for larger pulse areas, carrier-wave Rabi flopping occur…
With the emergence of high-repetition-rate few-cycle laser pulse amplifiers, aimed at investigating ultrafast dynamics in atomic, molecular and solid state science, the need for ever faster carrier-envelope phase (CEP) detection and control has arisen. Here we demonstrate a high speed, continuous, every-single-shot measurement and fast feedback scheme based on a stereo above-threshold ionization time-of-flight spectrometer capable of detecting the CEP and pulse duration at a repetition rate of up to 400 kHz. This scheme is applied to a 100 kHz optical parametric chirped pulse amplification (OP…
We have investigated the ionization of the H atom by intense few-cycle laser pulses, in particular the intra-pulse interference effects, and their dependence on the carrier-envelope phase (CEP) of the laser pulse. In the final momentum distribution of the continuum electrons the imprint of two types of intra-pulse interference effects can be observed, namely the temporal and spatial interference. During the spatial interference electronic wave packets emitted at the same time, but following different paths interfere leading to an interference pattern measurable in the electron spectra. This ca…
We consider a quantum state interacting with a short intense linearly polarized laser pulse. Using the two-dimensional time representation and Floquet picture we establish a straightforward connection between the laser carrier-envelope phase (CEP) and the wave function. This connection is revealed as a unitary transformation in the space of Floquet components. It allows any CEP effect to be interpreted as an interference between the components and to put limits on using the CEP in coherent control. A 2-level system is used to illustrate the theory. On this example we demonstrate strong intensi…
The dissociation of an H$_2^+$ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4$\times10^{14} $W/cm$^2$ with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H$^+$ fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net-zero photon and 1-photon interference predominantly contributes at H$^+$+H kinetic energy releases of 0.2 -- 0.45 eV, and …
In few-cycle pulses, the exact value of the carrier-envelope phase difference (CEPD) has a pronounced influence on the ionization dynamics of atoms and molecules. We show that for atoms in circularly polarized light, a change in the CEPD is mapped uniquely to an overall rotation of the system, and results for arbitrary CEPD are obtained by rotation of the results from a single calculation with fixed CEPD. For molecules this is true only for linear molecules aligned parallel with the propagation direction of the field. The effects of CEPD are classified as geometric or non-geometric. The observ…
We perform theoretical investigations of laser-induced nonsequential double ionization with few cycle pulses, with particular emphasis on the dependence of the electron-momentum distributions on the carrier-envelope phase. We focus on the recollision-excitation with subsequent tunneling ionization (RESI) pathway, in which a released electron, upon return to its parent ion, gives part of its kinetic energy to promote a second electron to an excited state. At a subsequent time, the second electron is freed through tunneling ionization. We show that the RESI electron-momentum distributions vary d…
The creation of electron-positron pairs by the strong-field Breit-Wheeler process in intense short laser pulses is investigated in the framework of laser-dressed quantum electrodynamics. Regarding laser field parameters in the multiphoton regime, special attention is brought to the energy spectrum of the created particles, which can be reproduced and explained by means of an intuitive model. The model is based on the probabilities of multiphoton events driven by the spectral components of the laser pulse. It allows, in particular, to identify interferences between different pair production cha…
A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulae, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realisti…
We present an experimental and theoretical study of carrier-envelope phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigated the influence of CEP on the control of phase dependent multi-photon transitions between the Zeeman sub-levels of the ground state of $^{87}$Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities…
Carrier envelope phase (CEP) stabilized 5 fs and 22 fs pulses of intense 800 nm light are used to probe the strong-field ionization dynamics of multielectron entities, xenon and carbon disulfide. We compare ion yields obtained with and without CEP-stabilization: with 8-cycle (22 fs) pulses, Xe$^{6+}$ yields are suppressed (relative to Xe$^+$ yields) by between 30% and 50%, depending on phase, reflecting the phase dependence of non-sequential ionization and its contribution to the formation of higher charge states. On the other hand, ion yields for Xe$^{q+}$ ($q$=2-4) with CEP-stablized pulses …
We present a joint experimental-theoretical study on the effect of the carrier-envelope phase (CEP) of a few-cycle pulse on the atomic excitation process. We focus on the excitation rates of argon as a function of CEP in the intensity range from 50-300 TW/cm$^2$, which covers the transition between the multiphoton and tunneling regimes. Through numerical simulations based on solving the time-dependent Schrödinger equation (TDSE), we show that the resulting bound-state population is highly sensitive to both the intensity and the CEP. Because the intensity varies over the interaction region, the…
Formation of electron vortices and momentum spirals in photodetachment of the H$^-$ anion driven by isolated ultrashort laser pulses of circular polarization or by pairs of such pulses (of either corotating or counterrotating polarizations) are analyzed under the scope of the strong-field approximation. It is demonstrated that the carrier-envelope phase (CEP) and helicity of each individual pulse can be used to actively manipulate and control the vortical pattern in the probability amplitude of photodetachment. Specifically, the two-dimensional mappings of probability amplitude can be rotated …
We characterize the temporal profile of the high-order harmonic emission from ablation plasma plumes using cross-correlations with the infrared (IR) laser beam provided by 2-photon harmonic+IR ionization of rare gas atoms. We study both non-resonant plasmas (lead, gold and chrome) and resonant plasmas (indium and tin), i.e. plasmas presenting in the singly-charged ions a strong radiative transition coinciding with an harmonic order. The cross-correlation traces are found very similar for all harmonic orders and all plasma targets. The recovered harmonic pulse durations are very similar to the …
We studied dependence of dissociative ionization in H2 on carrier-envelope phase (CEP) of few-cycle (6fs) near-infrared (NIR) laser pulses. For low-energy channels, we present the first experimental observation of CEP dependence for total dissociation yield and the highest dwgree of asymmetry reported to date (40%). The observed modulations in both asymmetry and total yield could be understood in terms of interference between different n-photon dissociation pathways - n and (n+1) photon channels for asymmetry, n and (n+2) photon channels for yield - as suggested by the general theory of CEP ef…
We show how to optimize the process of high-harmonic generation (HHG) by gating the interaction using the field gradient of a driving pulse with a linear ramp waveform. Since maximized field gradients are efficiently generated by self-steepening processes, we first present a generalized theory of optical carrier-wave self-steepened (CSS) pulses. This goes beyond existing treatments, which only consider third-order nonlinearity, and has the advantage of describing pulses whose wave forms have a range of symmetry properties. Although a fertile field for theoretical work, CSS pulses are difficult…
Harmonics of femtosecond and continuous-wave radiation for precision spectroscopy: generation efficiency and spectral line shape
P.N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯科学院列别杰夫物理研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Russian Quantum Center（俄罗斯量子中心）
When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first order beyond-dipole correction to the H…
We describe phase-dependent wavelength scaling of high-order harmonic generation efficiency driven by ultra-short laser fields in the mid-infrared. We employ both numerical solution of the time-dependent Schrödinger equation and the Strong Field Approximation to analyze the fine-scale oscillations in the harmonic yield in the context of channel-closing effects. We show, by varying the carrier-envelope phase, that the amplitude of these oscillations depend strongly on the number of returning electron trajectories. Furthermore, the peak positions of the oscillations vary significantly as a funct…
Brunel harmonics appear in the optical response of an atom in process of laser-induced ionization, when the electron leaves the atom and is accelerated in the strong optical field. In contrast to recollision-based harmonics, the Brunel mechanism does not require the electron returning to the core. Here we show that in the presence of a strong ionizing terahertz (THz) field, even a weak driving field at the optical frequencies allow for generating Brunel harmonics effectively. The strong ionizing THz pump suppresses recollisions, making Brunel dominant in a wide spectral range. High-order Brune…
We investigate the carrier-envelope phase and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above-threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750\,nm is varied in a range between $0.7 \times 10^{14}$ and $\unit[5.5 \times 10^{14}]{W/cm^2}$. Our measurements reveal a prominent maximum in the carrier-envelope phase-dependent asymmetry at photoelectron energies of 2\,$U_\mathrm{P}$ ($U_\mathrm{P}$ being the ponderomotive potential), that is persistent over the entire intensity ra…
