Quantum path interferences in high-order harmonic generation from aligned diatomic molecules
S. Chatziathanasiou, I. Liontos, E. Skantzakis, S. Kahaly, M. Upadhyay Kahaly, N. Tsatrafyllis, O. Faucher, B. Witzel, N. Papadakis, D. Charalambidis, P. Tzallas
Electron quantum path interferences in strongly laser-driven aligned molecules and their dependence on the molecular alignment is an essential open problem in strong-field molecular physics. Here, we demonstrate an approach which provides direct access to the observation of these interference processes. The approach is based on the combination of the time-gated-ion-microscopy technique with a pump-probe arrangement used to align the molecules and generate high-order harmonics. By spatially resolving the interference pattern produced by the spatiotemporal overlap of the harmonics emitted by the short and long electron quantum paths, we have succeeded in measuring in situ their phase difference and disclose their dependence on molecular alignment. The findings constitute a vital step towards an understanding of strong-field molecular physics and the development of attosecond spectroscopy approaches without the use of auxiliary atomic references.
In the present paper, we investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong field approximation (SFA) model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum, and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these in…
We calculate angle-resolved above-threshold ionization spectra for diatomic molecules in linearly polarized laser fields, employing the strong-field approximation. The interference structure resulting from the individual contributions of the different scattering scenarios is discussed in detail, with respect to the dependence on the internuclear distance and molecular orientation. We show that, in general, the contributions from the processes in which the electron is freed at one center and rescatters off the other obscure the interference maxima and minima obtained from single-center processe…
We study ionization dynamics of aligned diatomic molecules N$_2$ in strong elliptical laser fields experimentally and theoretically. The alignment dependence of photoelectron momentum distributions (PMDs) of N$_2$ measured in experiments is highlighted with comparing to Ar measured synchronously. Our results show that the PMDs of N$_2$ depend strongly on the alignment of the molecule, relative to the main axis of the laser ellipse. In particular, the most-probable electron-emission angle which is often used in attosecond measurement, differs remarkably when changing the molecular alignment. We…
We address the influence of the orbital symmetry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to the electron emission at spatially separated centers. The interference patterns survive the in…
We investigate high-order harmonic spectra from aligned diatomic molecules in intense driving fields whose components have orthogonal polarizations. We focus on how the driving-field ellipticity influences structural interference patterns in a macroscopic medium. In a previous publication [Phys. Rev. A 88, 023404 (2013)] we have shown that the non-vanishing ellipticity introduces an effective dynamic shift in the angle for which the two-center interference maxima and minima occur, with regard to the existing condition for linearly polarized fields. In this work we show through simulation that …
We investigate the influence of intense, elliptically polarized driving fields on high-order harmonic spectra from aligned diatomic molecules. We derive a generalized two-center interference condition for elliptically polarized fields, which accounts for s-p mixing and the orbital symmetry, within the strong-field and the single-active electron approximation. We show that the non-vanishing ellipticity introduces an effective dynamic shift in the angle for which the two-center interference maxima and minima occur, with regard to the existing condition for linearly polarized fields. This shift d…
We perform a detailed analysis of high-order harmonic generation in diatomic molecules within the strong-field approximation, with emphasis on quantum-interference effects. Specifically, we investigate how the different types of electron orbits, involving one or two centers, affect the interference patterns in the spectra. We also briefly address the influence of the choice of gauge, and of the initial and final electronic bound states on such patterns. For the length-gauge SFA and undressed bound states, there exist additional terms, which can be interpreted as potential energy shifts. If, on…
The generation of high harmonics (HHG) in atomic systems by the highly non-linear response to an intense laser field is a prominent pathway to the synthesis of ever shorter laser pulses at increasingly higher photon energies. Extensions of this process to molecules add to the complexity but also offers novel opportunities as multi-center effects and the coupling to nuclear degrees of freedom can influence HHG. In this work we theoretically explore the impact of coherent vibronic excitations of diatomic molecules on the HHG spectrum within the framework of time-dependent density functional theo…
The single ionization of noble gas atoms by the combined action of XUV attopulses and an infrared laser field is theoretically investigated by means of a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret the angular distributions as two-center interferences where the separation between the centers is governed by the infrared laser field. Angular distributions are compared to the available experimental data showing a good agreement. Finally, we deduce the conditio…
We address the influence of the molecular orbital geometry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules for different molecular species, namely $\mathrm{N}_2$ and $\mathrm{Li}_2$. We focus on the recollision excitation with subsequent tunneling ionization (RESI) mechanism, in which the first electron, upon return, promotes the second electron to an excited state, from where it subsequently tunnels. We show that the electron-momentum distributions exhibit interference maxima and minima due to t…
We analyze the influence of different recombination scenarios, involving one or two centers, on high-order harmonic generation (HHG) in diatomic molecules, for different values of the internuclear separation. We work within the strong-field approximation, and employ modified saddle-point equations, in which the structure of the molecule is incorporated. We find that the two-center interference patterns, attributed to high-order harmonic emission at spatially separated centers, are formed by the quantum interference of the orbits starting at a center $C_{j}$ and finishing at a different center …
The elastic scattering of twisted electrons by diatomic molecules is studied within the framework of the non-relativistic first Born approximation. In this process, the coherent interaction of incident electrons with two molecular centers may cause interference patterns in the angular distributions of outgoing particles. We investigate how this Young-type interference is influenced by the complex internal structure of twisted beams. In particular, we show that the corkscrew-like phase front and the inhomogeneous intensity profile of the incident beam can strongly modify the angular distributio…
We investigate theoretically the dissociative ionization of a H2+ molecule using two ultrashort laser (pump-probe) pulses. The pump pulse prepares a dissociating nuclear wave packet on an ungerade surface of H2+. Next, an UV (or XUV) probe pulse ionizes this dissociating state at large (R = 20 - 100 bohr) internuclear distance. We calculate the momenta distributions of protons and photoelectrons which show a (two-slit-like) interference structure. A general, simple interference formula is obtained which depends on the electron and protons momenta, as well as on the pump-probe delay on the puls…
We investigate laser-induced nonsequential double ionization from aligned diatomic molecules, using the strong-field approximation in its length and velocity gauge formulations. Throughout, we consider that the first electron dislodges the second by electron-impact ionization. Employing modified saddle-point equations, we single out the contributions of different scattering scenarios to the maxima and minima observed in the differential electron momentum distributions. We show that the quantum interference between the electron orbits starting and ending at a specific center $C_{j}$%, and those…
The double-slit interference in single-photon ionization of the diatomic molecular ion $\mathrm{H}_2^+$ is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned $\mathrm{H}_2^+$ and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from $\mathrm{H}_2^+$: (i) the photon-momentum transfer and (ii) the finite speed of light. While both effects could modify the maxima of the interference fringes, we show tha…
The direct above-threshold ionization (ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet (IR+XUV) laser fields is investigated by the frequency-domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ioni…
Diatomic molecules (e.g., O$_2$) in intense laser field exhibit a peculiar suppressed ionization behavior compared to their companion atoms. Several physical models have been proposed to account for this suppression while no consensus has been achieved. In this letter, we aim to clarify the underlying mechanisms behind this molecular ionization suppression. Experimental data recorded at midinfrared laser wavelength and its comparison with that at near-infrared wavelength revealed a peculiar wavelength and intensity dependence of the suppressed ionization of O$_2$ with respect to its companion …
We analyze the imprint of nodal planes in high-order harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semi-analytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole op…
For a molecule, the two-center interference and the molecular scattering phase of the electron are important for almost all the processes that may occur in a laser field. In this study, we investigate their effects in the transfer of linear photon momentum to the ionized electron by absorbing a single photon. The time-dependent Schrödinger equation of H$_2^+$ is numerically solved in {the multipolar} gauge in which the electric quadrupole term and the magnetic dipole term are explicitly expressed. This allows us to separate the contributions of the two terms in the momentum transfer. For diffe…
Laser-induced electron diffraction is an evolving tabletop method, which aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-Ångström spatial and femtosecond temporal resolution. Here, we provide the general foundation for the retrieval of multiple bond lengths from a polyatomic molecule by simultaneously measuring the C-C and C-H bond lengths in aligned acetylene. Our approach takes the method beyond the hitherto achieved imaging of simple diatomic molecules and is based upon the combination of a 160 kHz mid-IR few-cycle laser source with full three-dimension…
By using Bohmian trajectory method, we investigate the dynamic interference in diatomic molecular high-order harmonic generation progress. It is demonstrated that the main characteristics of the molecular harmonic spectrum can be well reproduced by only two Bohmain trajectories which are located respectively at the two ions. This is because these two localized trajectories can receive and store the whole collision information coming from all of the other recollision trajectories. Therefore, the amplitudes and frequencies of these two trajectories represent the intensity and frequency distribut…
We extend a model of two-center interference to include the superposition of opposite orientations in aligned polar molecules. We show that the position of the minimum in the harmonic spectrum from both aligned and oriented CO depends strongly on the relative recombination strength at different atoms, not just the relative phase. We reinterpret the minimum in aligned CO as an interference between opposite orientations, and obtain good agreement with numerical calculations. Inclusion of the first-order Stark effect shifts the position of the interference minimum in aligned CO even though aligne…
Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation, Feshbach resonances and bimolecular collisions, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By phot…
We study single-photon ionization of aligned H$_2^+$ in a high-frequency low-intensity laser field. We focus on the case where the laser frequency is not far larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. By developing a theory model applicable for high-frequency laser field, we show that the interference patterns can not be explained by the interference of the electronic wave with the observed momentum between these two atomic centers of …
We explore the feasibility of optically forming long-range tetratomic and larger polyatomic molecules in their ground electronic state from ultracold pairs of polar molecules aligned by external fields. Depending on the relative orientation of the interacting diatomic molecules, we find that a tetratomic can be formed either as a weakly bound complex in a very extended halo state or as a pure long-range molecule composed of collinear or nearly-collinear diatomic molecules. The latter is a novel type of tetratomic molecule comprised of two diatomic molecules bound at long intermolecular range a…
We investigate direct above-threshold ionization in diatomic molecules, with particular emphasis on how quantum interference is altered by a driving field of non-vanishing ellipticity. This interference may be either temporal, i.e., related to ionization events occurring at different times, or spatial, i.e., related to the electron emission at different centers in the molecule. Employing the strong-field approximation and saddle-point methods, we find that, in general, for non-vanishing ellipticity, there will be a blurring of the temporal and spatial interference patterns. The former blurring…
We theoretically investigate the interference effect of high-order harmonics generated from molecules at different alignment angles. It is shown that the interference of the harmonic emissions from molecules aligned at different angles can significantly modulate the spectra and result in the anomalous harmonic cutoffs observed in a recent experiment [ Nature Phys. 7, 822 (2011) ]. The shift of the spectral minimum position with decreasing the degree of alignment is also explained by the interference effect of the harmonic emissions.
Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected l…
Quantum interference effects in inter-conversion between cold atoms and diatomic molecules are analysed. Within the framework of Fano's theory, continuum-bound anisotropic dressed state formalism of atom-molecule quantum dynamics is presented. This formalism is applicable in photo- and magneto-associative strong-coupling regimes. The significance of Fano effect in ultracold atom-molecule transitions is discussed. Quantum effects at low energy atom-molecule interface are important for exploring coherent phenomena in hither-to unexplored parameter regimes.
We investigate harmonic generation (HG) from ground-state Ar+ aligned with M=1 at a laser wavelength of 390-nm and intensity of 4x10(14) Wcm-2. Using time-dependent R-matrix theory, we find that an initial state with magnetic quantum number M=1 provides a 4-fold increase in harmonic yield over M=0. HG arises primarily from channels associated with the (3)Pe threshold of Ar2+, in contrast with M=0 for which channels associated with the excited, (1)De threshold dominate HG. Multichannel and multielectron interferences lead to a more marked suppression of HG for M=1 than M=0.
We present a theoretical investigation into the two-center interference in aligned H$_2^+$. The influence of the laser field on the recombination step is investigated by comparing laser-induced harmonic generation with harmonic generation from field-free collisions of Gaussian wave packets with the core. We find that for different Gaussian wave packets colliding with the molecule, the interference minimum occurs at the same alignment angle. The same result is obtained for the laser-induced spectrum when only a single electronic trajectory per harmonic contributes. When multiple electronic traj…
We study non-classical pathways and quantum interference in enhanced ionisation of diatomic molecules in strong laser fields using machine learning techniques. Quantum interference provides a bridge, which facilitates intramolecular population transfer. Its frequency is higher than that of the field, intrinsic to the system and depends on several factors, for instance the state of the initial wavepacket or the internuclear separation. Using dimensionality reduction techniques, namely t-distributed stochastic neighbour embedding (t-SNE) and principal component analysis (PCA), we investigate the…
We investigate how short and long electron trajectory contributions to high harmonic emission and their interferences give access to intra-molecular dynamics. In the case of unaligned molecules, we show experimental evidences that the long trajectory signature is more dependent upon the molecule than the short one, providing a high sensitivity to cation nuclear dynamics within 100's of as to few fs. Using theoretical approaches based on Strong Field Approximation and Time Dependent Schrodinger Equation, we examine how quantum path interferences encode electronic motion whilst molecules are ali…
We introduce and demonstrate a new approach to measuring coherent electron wave packets using high-harmonic spectroscopy. By preparing a molecule in a coherent superposition of electronic states, we show that electronic coherence opens previously unobserved high-harmonic-generation channels that connect distinct but coherently related electronic states. Performing the measurements in dynamically aligned nitric oxide (NO) molecules we observe the complex temporal evolution of the electronic coherence under coupling to nuclear motion. Choosing a weakly allowed transition to prepare the wave pack…
We study the generation of terahertz radiation from atoms and molecules driven by an ultrashort fundamental laser and its second harmonic field by solving time-dependent Schrödinger equation (TDSE). The comparisons between one-, two-, and three- dimensional TDSE numerical simulations show that initial ionized wave-packet and its subsequent acceleration in the laser field and rescattering with long-range Coulomb potential play key roles. We also present the dependence of the optimum phase delay and yield of terahertz radiation on the laser intensity, wavelength, duration, and the ratio of two-c…
We present a novel method for probing the alignment of the molecular axis of an ultracold, nonpolar dimer. These results are obtained using diatomic $^{87}\textrm{Rb}_2$ molecules in the vibrational ground state of the lowest triplet potential $a^3Σ_u^+$ trapped in a 3D optical lattice. We measure the molecular polarizabilities, which are directly linked to the alignment, along each of the $x$, $y$, and $z$ directions of the lab coordinate system. By preparing the molecules in various, precisely defined rotational quantum states we can control the degree of alignment of the molecular axis with…
High-order harmonic generation (HHG) results from strong-field laser matter interaction and it is one of the main processes that are used to extract electron structural and dynamical information about the atomic or molecular targets with sub-femtosecond temporal resolution. Moreover, it is the workhorse for the generation of attosecond pulses. Here we develop an analytical description of HHG, which extends the well established theoretical strong-field approximation (SFA). Our approach involves two innovative aspects: i) First, using a model non-local, but separable potential, we calculate the …
We made use of supersymmetric (SUSY) quantum mechanics to find a condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subject to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition, $Δω= \frac{ω^2}{4 (m+1)^2}$, connects values of the dimensionless parameters $ω$ and $Δω$ that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the $|\tilde{J}=m,m;ω,Δω>$ family of "stretched" states. The field-f…
