High-harmonic generation from muonic atoms exposed to intense laser fields is considered. Our particular interest lies in effects arising from the finite nuclear mass and size. We numerically perform a fully quantum mechanical treatment of the muon-nucleus dynamics by employing modified soft-core and hard-core potentials. It is shown that the position of the high-energy cutoff of the harmonic spectrum depends on the nuclear mass, while the height of the spectral plateau is sensitive to the nuclear radius. We also demonstrate that $γ$-ray harmonics can be generated from muonic atoms in ultrastrong VUV fields, which have potential to induce photo-nuclear reactions.
High-harmonic generation from hydrogenlike muonic atoms exposed to ultraintense high-frequency laser fields is calculated. Systems of low nuclear charge number Z are considered where a nonrelativistic description applies. By comparing the radiative response for different isotopes we demonstrate characteristic signatures of the finite nuclear mass and size in the harmonic spectra. In particular, for Z>1, an effective muon charge appears in the Schrödinger equation for the relative particle motion, which influences the position of the harmonic cutoff. Cutoff energies in the MeV domain can be ach…
Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of phot…
We present calculations of nuclear structure effects to the Lamb shift in light muonic atoms. We adopt a modern ab-initio approach by combining state-of-the-art nuclear potentials with the hyperspherical harmonics method. Our calculations are instrumental to the determination of nuclear charge radii in the Lamb shift measurements, which will shed light on the proton radius puzzle.
Laser spectroscopy of the Lamb shift (2S-2P energy difference) in light muonic atoms or ions, in which one negative muon $μ^-$ is bound to a nucleus, has been performed. The measurements yield significantly improved values of the root-mean-square charge radii of the nuclei, owing to the large muon mass, which results in a vastly increased muon wave function overlap with the nucleus. The values of the proton and deuteron radii are 10 and 3 times more accurate than the respective CODATA values, but 7 standard deviations smaller. Data on muonic helium-3 and -4 ions is being analyzed and will give…
Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S$\,$-$\,$2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with $Z \geq 3$. In addition, our approaches towards a …
We consider a simplified model of the optical multi-pass cavity that is being currently developed by the FAMU collaboration for the measurement of the hyperfine splitting in the ground state of muonic hydrogen and of the Zemach radius of the proton. The model is focused on the time distribution of the events of laser-stimulated hyperfine transitions in the muonuc atom and may be helpful in the preliminary design of the FAMU experimental set-up and, more generally, in the optimization of multi-pass optical cavities for experiments with pulsed lasers.
Recent progress in laser and x-ray spectroscopy of muonic atoms offers promising long-term possibilities at the intersection of atomic, nuclear and particle physics. In muonic hydrogen, laser spectroscopy measurements will determine the ground-state hyperfine splitting (HFS) and additionally improve the Lamb shift by a factor of 5. Precision spectroscopy with cryogenic microcalorimeters has the potential to significantly improve the charge radii of the light nuclei in the $Z=3-8$ range. Complementary progress in precision should be achieved on the theory of nucleon- and nuclear-structure effec…
High-precision laser spectroscopy of atomic energy levels enables the measurement of nuclear properties. Sensitivity to these properties is particularly enhanced in muonic atoms which are bound systems of a muon and a nucleus. Exemplary is the measurement of the proton charge radius from muonic hydrogen performed by the CREMA collaboration which resulted in an order of magnitude more precise charge radius as extracted from other methods but at a variance of 7 standard deviations. Here, we summarize the role of muonic atoms for the extraction of nuclear charge radii, we present the status of th…
The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($μ$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $μ$p atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature …
Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities) and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen ($μ$H). Updated theory predictions for the Lamb shift and HFS in $μ$H are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in $μ$H and its impact on our understanding of the nucleon spin structure. To narrow down t…
The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields, and more applied areas like Casimir and Casimir--Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of …
We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.
We investigate the process of circularly polarized high harmonic generation in molecules using a bicircular laser field. In this context, we show that molecules offer a very robust framework for the production of circularly polarized harmonics, provided their symmetry is compatible with that of the laser field. Using a discrete time-dependent symmetry analysis, we show how all the features (harmonic order and polarization) of spectra can be explained and predicted. The symmetry analysis is generic and can easily be applied to other target and/or field configurations.
We theoretically investigate correlated electron dynamics in high-harmonic generation (HHG), using all-electron \emph{ab initio} simulations for three-dimensional real alkali-metal atoms. The resulting harmonic spectra exhibit a plateau extended beyond the usual cutoff and a prominent resonance peak above the plateau. These remarkable features arise from the cation response dramatically enhanced by laser-induced electron recollision, which is a key process of attosecond science. This demonstrates that high-harmonic spectroscopy provides new possibilities to explore dynamical electron correlati…
We present studies of high-order harmonic generation (HHG) at laser intensities well above saturation. We use driving laser pulses which present a particular electron dynamics in the turn-on stage. Our results predict an increasing on the harmonic yield, after an initial dropping, when the laser intensity is increased. This fact contradicts the general belief of a progressive degradation of the harmonic emission at ultrahigh intensities. We have identified a particular set of trajectories which emerges in the turn-on stage of these singular laser pulses, responsible of the unexpected growth on…
We present theoretical results on the high-harmonic generation (HHG) in bulk diamond induced by intense laser pulse of wavelength 800 nm and duration 15 fs. For laser intensity in the range $1 \le I \le 50 $ TW/cm$^2$ above bandgap harmonics are generated after the pulse peak. We find that the intensity of individual harmonics increases non-linearly with the peak laser intensity, following a non-perturbative trend. For moderate intensity the HHG spectrum exhibits a primary plateau with noisy odd order harmonic structure and a cutoff. For increased laser intensity a secondary plateau emerges wi…
When a laser pulse impinges on a molecule which is invariant under certain symmetry operations selection rules for harmonic generation (HG) arise. In other words: symmetry controls which channels are open for the deposition and emission of laser energy---with the possible application of filtering or amplification. We review the derivation of HG selection rules and study numerically the interaction of laser pulses with an effectively one-dimensional ring-shaped model molecule. The harmonic yields obtained from that model and their dependence on laser frequency and intensity are discussed. In a …
We investigate the polarization properties of high harmonics generated with the bichromatic counterrotating circularly polarized (BCCP) laser fields by numerically solving time-dependent Schrödinger equation (TDSE). It is found that, the helicity of the elliptically polarized harmonic emission is reversed at particular harmonic orders. Based on the time-frequency analysis and the classical three-step model, the correspondence between the positions of helicity reversions and the classical trajectories of continuum electrons is established. It is shown that, the electrons ionized at one lobe of …
New approach to study the spontaneous emission of the atomic system in the presence of the high-intensity laser field is used to study the process of harmonic generation. The analysis is based on the consideration of quantum system interaction with quantized field modes beeing in vacuum state, while the intense laser field is considered classically beyond the perturbation theory. The numerical analysis of the emission from the single one-electron one dimensional atom irradiated by the femtosecond laser pulse of Ti-Sa laser is discussed. It is demonstrated that not only odd but also even harmon…
By analyzing ``exact'' theoretical results from solving the time-dependent Schrödinger equation of atoms in few-cycle laser pulses, we established the general conclusion that differential elastic scattering and photo-recombination cross sections of the target ion with {\em free} electrons can be extracted accurately from laser-generated high-energy electron momentum spectra and high-order harmonic spectra, respectively. Since both electron scattering and photoionization (the inverse of photo-recombination) are the conventional means for interrogating the structure of atoms and molecules, this …
We generate high-order harmonics at high pulse repetition rates using a turnkey laser. High-order harmonics at 400 kHz are observed when argon is used as target gas. In neon we achieve generation of photons with energies exceeding 90 eV ($\sim$13 nm) at 20 kHz. We measure a photon flux of 4.4$\cdot10^{10}$ photons per second per harmonic in argon at 100 kHz. Many experiments employing high-order harmonics would benefit from higher repetition rates, and the user-friendly operation opens up for applications of coherent extreme ultra-violet pulses in new research areas.
We study the influence of the pulse duration on high harmonic generation (HHG) with exploring a wide laser-parameter region theoretically. Previous studies have showed that for high laser intensities near to the saturation ionization intensity, the HHG inversion efficiency is higher for shorter pulses since the ground-state depletion is weaker in the latter. Surprisingly, our simulations show this high efficiency also appears even for a moderate laser intensity at which the ionization is not strong. A classical effect relating to shorter travel distances of the rescattering electron in shorter…
We study high-order harmonic generation (HHG) from aligned molecules in strong elliptically polarized laser fields numerically and analytically. Our simulations show that the spectra and polarization of HHG depend strongly on the molecular alignment and the laser ellipticity. In particular, for small laser ellipticity, large ellipticity of harmonics with high intensity is observed for parallel alignment, with forming a striking ellipticity hump around the threshold. We show that the interplay of the molecular structure and two-dimensional electron motion plays an important role here. This phen…
Based upon our previous works (Eur.Phys.J.D 6, 319(1999); Chin.Phys.Lett. 18, 236(2001)), we develop a classical approach to calculate the high-order harmonic generation of the laser driven atoms and molecules. The Coulomb singularities in the system have been removed by a regularization procedure. Action-angle variables have been used to generate the initial microcanonical distribution which satisfies the inversion symmetry of the system. The numerical simulation show, within a proper laser intensity, a harmonic plateau with only odd harmonics appears. At higher intensities, the spectra becom…
The selection rules of high harmonic generation (HHG) are investigated using three-dimensional time-dependent density functional theory (TDDFT). From the harmonic spectra obtained with various real molecules and different forms of laser fields, several factors that contribute to selection rules are revealed. Extending the targets to stereoscopic molecules, it is shown that the allowed harmonics are dependent on the symmetries of the projections of molecules. For laser fields, the symmetries contributing to the selection rules are discussed according to Lissajous figures and their dynamical dir…
The tunneling ionization of exotic atoms such as muonic hydrogen, muonium and positronium in a strong laser field of circular polarization is investigated taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center of mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for comm…
The generation of harmonics by atoms interacting with two circularly polarized and frequency related laser fields is addressed through ab initio numerical simulations. A detailed charaterization of a few specific harmonics is given. In particular, the two different cases where the total energy absorbed through photons is far-off or close to the energy gap between different atomic states are investigated. It is found that the conversion efficiency in the harmonic generation is strongly dependent on the inner atomic structure and in certain specific cases it can be significantly enhanced within …
The aim of the FAMU experiment is to realize the first measurement of the hyperfine splitting (hfs) in the 1S state of muonic hydrogen $ΔE^{hfs}_{1S}$, by using the RIKEN-RAL intense pulsed muon beam and a high-energy mid-infrared tunable laser. This requires a detailed study of the muon transfer mechanism at different temperatures and hence at different epithermal states of the muonic system. The experimental setup involves a cryogenic pressurized gas target and a detection system based on silicon photomultipliers-fiber beam hodoscopes and high purity Germanium detectors and Cerium doped Lant…
We experimentally investigate the generation of above-threshold harmonics completely from argon atoms on an excited state using mid-infrared femtosecond laser pulses. The highly nonlinear dependences of the observed signal on the pulse energy and polarization of the driver laser pulses indicate its non-perturbative characteristic.
One key parameter in the high-order harmonic generation (HHG) phenomenon is the exact frequency of the generated harmonic field. Its deviation from perfect harmonics of the laser frequency can be explained considering (i) the single-atom laser-matter interaction and (ii) the spectral changes of the driving laser. In this work, we perform an experimental and theoretical study of the causes that generate spectral changes in the HHG radiation. We measured the driving laser spectral shift after high harmonic generation in long medium using a correction factor to take into account the multiple poss…
We investigate the harmonic response of neon atoms to mid-IR laser fields (2000-3000nm) using a single-active electron (SAE) model and the fully ab initio all-electron R-Matrix with Time-dependence (RMT) method. The laser peak intensity and wavelength are varied to find suitable parameters for high-harmonic imaging in the water window. Comparison of the SAE and RMT results shows qualitative agreement between them as well as parameters such as the cutoff frequency predicted by the classical three-step model. However, there are significant differences in the details, particularly in the predicte…
We present the generation of high order harmonics in crystalline silicon subjected to intense near-infrared 30fs laser pulse. The harmonic spectrum extends from the near infrared to the extreme ultraviolet spectral region. Depending on the pulsed laser intensity, we distinguish two regimes of harmonic generation: (i) perturbative regime: electron-hole pairs born during each half-cycle of the laser pulse via multiphoton and tunnel transitions are accelerated in the laser electric field and gain kinetic energy; the electron-hole pairs then recombine in the ground state by emitting a single high-…
We present calculation of photoexcitation and high-harmonic generation in bulk diamond induced by intense near-infrared laser pulse of photon energy 1.55 eV, time duration of 15 fs and peak field strength $F=$ 0.4 V/Å. Depending on the laser polarization direction, the pulsed irradiation creates electron-hole pairs and transient density fluctuations in a localized region of the crystal momentum space. As a consequence energetic inter- and intra-band harmonics are generated with alternating phase during each half-cycle of the driving pulse. The corresponding inter- and intra-band currents are i…
We study the temporal and spatial dynamics of the large amplitude and frequency modulation that can be induced in an intense, few cycle laser pulse as it propagates through a rapidly ionizing gas. Our calculations include both single atom and macroscopic interactions between the non-linear medium and the laser field. We analyze the harmonic generation by such pulses and show that it is spatially separated from the ionization dynamics which produce a large dynamical blue shift of the laser pulse. This means that small changes in the initial laser focusing conditions can lead to large difference…
The generation of harmonics by atoms or ions in a two-color, coplanar field configuration with commensurate frequencies is investigated through both, an analytical calculation based on the Lewenstein model and the numerical ab initio solution of the time-dependent Schroedinger equation of a two-dimensional model ion. Through the analytical model, selection rules for the harmonic orders in this field configuration, a generalized cut-off for the harmonic spectra, and an integral expression for the harmonic dipole strength is provided. The numerical results are employed to test the predictions of…
In present paper we develop an analytic theory for the harmonic generation of symmetric diatomic molecular ions beyond two-level model, emphasizing the influence of charge-resonance (CR) states those are strongly coupled to electromagnetic fields for large internuclear distance. With taking into account the continuum states that is ignored in the two-level model and become important for intense laser case, our model is capable to produce spectrum for the whole range of harmonic orders consisting of a molecular plateau due to the CR transition and an atomic-like plateau for a long-wavelength ex…
We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements.
We investigate the high harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schrödinger equations (TDSE) are solved numerically by using B-spline basis sets in coordinate space. The energy band structure and wave vectors can be directly retrived from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$ space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly w…
The strong-field approximation for high-harmonic generation in near-infrared and infrared laser pulses is formulated in the accelerated Kramers-Henneberger frame. The accompanying physical picture is discussed and the nature of the leading-order term is contrasted with that of the three-step model following the strong-field-approximation formulation in the length or velocity gauges. The theory is illustrated by high-harmonic generation spectra for atomic hydrogen.
The present work reports on the generation of short-pulse coherent extreme ultraviolet radiation of controlled polarization. The proposed strategy is based on high-order harmonics generated in pre-aligned molecules. Field-free molecular alignment produced by a short linearly-polarized infrared laser pulse is used to break the isotropy of a gas medium. Driving the aligned molecules by a circularly-polarized infrared pulse allows to transfer the anisotropy of the medium to the polarization of the generated harmonic light. The ellipticity of the latter is controlled by adjusting the angular distr…
We studied the high-harmonic generation by the interaction of sub-cycle laser pulses with the He atom. The sub-cycle pulses are modeled using the complex source vector beam model, which is an exact solution to Maxwell's equations and accurately models the sub-cycle field profiles. We observed that the harmonic cutoff could be extended with the variation of the sub-cycle pulse duration, mainly because of the inherent blueshift associated with shorter pulses. The scaling laws for the harmonic yield and harmonic cutoff energy with pulse duration and fundamental driver wavelengths are also deduced…
We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrodinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. T…
Present photoionization experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) from the outermost valence electrons of molecules. We show that details of the MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides…
A theoretical model is developed describing high-order harmonic generation (HHG) from a gas of multiply-charged ions driven by a laser field of relativistic intensity. Macroscopic propagation of harmonics is investigated in a relativistic HHG setup where the relativistic drift is suppressed by means of x-ray field assistance of the driving laser field. The possibility of phase-matched emission of the harmonics is shown. The laser field geometry is optimized to maximize the HHG yield with the corresponding phase-matching schemes. Crucial issues determining the macroscopic HHG yield are discusse…
We develop a numerical scheme to investigate the high-order harmonic generation (HHG) in intense laser-matter interactions. Tracing the time evolution of every electronic laser-field-free state, we "observe" the HHG in a time-integrated quantum transition picture. Our full-quantum simulations reveal that continuum electrons with a broad energy distribution contribute equally to one harmonic and the excited state also plays an important role in the molecular HHG. These results imply a laser-intensity-dependent picture of intramolecular interference in the HHG.
We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is p…
We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted parallel and perpendicular to the direction of the {\em same} returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmoni…
Quantum-mechanical investigation is presented to study single attosecond pulse generation by gating high-order harmonic emission from H$_2^+$ molecule in intense laser pulses with time-dependent ellipticity. The high-order harmonic generation from H$_2^+$ molecule in superposition of a left and a right-hand circularly polarized Gaussian pulse is studied and the effect of time duration and carrier-envelope phase of laser field on single attosecond pulse generation is investigated. Using laser field formed by combination of a left and a right-hand elliptically polarized Gaussian pulse, the effec…
It is demonstrated by single-atom simulations that X-ray signals in the 3.4 to 4 keV region from an 8 micron laser driven high harmonic generation can be increased by more than two orders of magnitude when a single-cycle pulse centered at 800 nm is added. The ionization probability of a helium atom by the two-pulse field is set to 4.56x10^-5, which is needed for balancing the index of refraction of free electrons with that of neutral helium atoms to achieve phase matching.
Two different induced effects of a laser falling edge on high-order harmonic generation are resolved by solving numerically full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. The harmonic spectrum of H$_2^+$ and T$_2^+$ isotopes are compared to see the effects of a 4-cycle falling edge of a 800 nm, 15-cycle trapezoidal laser pulse of $I=$3 $\times 10^{14}$ Wcm$^{-2}$ intensity on harmonic emission spectrum. The harmonic emission at the laser falling part is negligible for H$_2^+$ due to ionization suppression, but considerable for T$_2^+$…
We present numerical simulations of high-order harmonic generation in helium using a temporally synthesised and spatially non-homogeneous strong laser field. The combination of temporal and spatial laser field synthesis results in a dramatic cut-off extension far beyond the usual semiclassical limit. Our predictions are based on the convergence of three complementary approaches: resolution of the three dimensional Time Dependent Schrödinger Equation, time-frequency analysis of the resulting dipole moment and classical trajectories extraction. Employing a combination of temporally and spatially…
