Coherent Electron Wave Packets Research Articles

Probing ultrafast excited-state dynamics using EUV-IR six-wave-mixing emission spectroscopy.

Non-linear processes such as four-wave-mixing have become instrumental in attosecond EUV spectroscopy. Using EUV high harmonics in conjunction with collinear near-infrared and mid-infrared fields, we extended this approach to high-order-mixing between three colors. Specifically, we find that atomic resonances in neon exhibit a significant cross section for six-wave mixing. The MIR probe frequency tunability in our multicolor scheme is employed to access several optically dark resonances and probe the quantum beat of a coherent electronic wavepacket using background-free EUV emission as a diagnostic. This technique can be easily extended to other atomic and molecular systems, and opens the door to multi-dimensional non-linear spectroscopy.

Real-Time Observation of Electron-Hole Coherence Induced by Strong-Field Ionization

We introduce and demonstrate a new approach to measure the electron-hole dynamics and coherence induced by strong-field ionization using hole-assisted high-harmonic spectroscopy. The coherent driving of the infrared and XUV pulses correlates the dynamics of the core-hole and the valence-hole by coupling multiple continua, which leads to the otherwise forbidden absorption and emission of high harmonics. An analytical model is developed based on the strong-field approximation by taking into account the essential multielectron configurations. The emission spectra from the core-valence transition and the core-hole recombination are found to modulate strongly as functions of the time delay between the two pulses, suggesting that the coherent electron wave packets in multiple continua can be utilized to temporally resolve the core-valence transition in attoseconds.

Nuclear-Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation.

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear–electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron–nuclear dynamics are imprinted on top of electron–electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

Exploration of magnetic field generation of by direct ionization and coherent resonant excitation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12074146 and 12074142).

Coherent electronic dynamics are of great significance in photo-induced processes and molecular magnetism. We theoretically investigate electronic dynamics of triatomic molecule by circularly polarized pulses, including electron density distributions, induced electronic currents, and ultrafast magnetic field generation. By comparing the results of the coherent resonant excitation and direct ionization, we found that for the coherent resonant excitation, the electron is localized and the coherent electron wave packet moves periodically between three protons, which can be attributed to the coherent superposition of the ground A′ state and excited E+ state. Whereas, for the direct single-photon ionization, the induced electronic currents mainly come from the free electron in the continuum state. It is found that there are differences in the intensity, phase, and frequency of the induced current and the generated magnetic field. The scheme allows one to control the induced electronic current and the ultrafast magnetic field generation.

Complete phase retrieval of photoelectron wavepackets

Coherent, broadband pulses of extreme ultraviolet light provide a new and exciting tool for exploring attosecond electron dynamics. Using photoelectron streaking, interferometric spectrograms can be generated that contain a wealth of information about the phase properties of the photoionization process. If properly retrieved, this phase information reveals attosecond dynamics during photoelectron emission such as multielectron dynamics and resonance processes. However, until now, the full retrieval of the continuous electron wavepacket phase from isolated attosecond pulses has remained challenging. Here, after elucidating key approximations and limitations that hinder one from extracting the coherent electron wavepacket dynamics using available retrieval algorithms, we present a new method called absolute complex dipole transition matrix element reconstruction (ACDC). We apply the ACDC method to experimental spectrograms to resolve the phase and group delay difference between photoelectrons emitted from Ne and Ar. Our results reveal subtle dynamics in this group delay difference of photoelectrons emitted form Ar. These group delay dynamics were not resolvable with prior methods that were only able to extract phase information at discrete energy levels, emphasizing the importance of a complete and continuous phase retrieval technique such as ACDC. Here we also make this new ACDC retrieval algorithm available with appropriate citation in return.

Time resolved mechanism of the isotope selectivity in the ultrafast light induced dissociation in N2.

The time evolution of a vacuum ultraviolet excited N2 molecule is followed all the way from an ultrafast excitation to dissociation by a quantum mechanical simulation. The primary aim is to discern the role of the excitation by a pulse short compared to the vibrational period, to discern the different coupling mechanisms between different electronic states, nonadiabatic, spin orbit, and to analyze the origin of any isotopic effect. We compare the picture in the time and energy domains. The initial ultrafast excitation pumps the molecule to a coherent electronic wave packet to which several singlet bound electronic states contribute. The total nonstationary wave function is given as a coherent sum of nuclear wave packets on each electronic state times the stationary electronic wave function. When the wave packets on different electronic states overlap, they are coupled in a mass-dependent manner whether one uses an adiabatic or a diabatic electronic basis. A weak spin-orbit coupling acts as a bottleneck between the bound singlet part of phase space and the triplet manifold of states in which dissociation takes place. To describe the spin-orbit perturbation that is ongoing in time, an energy-resolved eigenstate representation appears to be more intuitive. In the eigenstate basis, the singlet-to-triplet population transfer is large only between those vibronic eigenstates that are quasiresonant in energy. The states in resonance are different for different excitation energy ranges. The resonances are mass dependent, which explains the control of the isotope effect through the profile of the pulse.

Anomalous Photon-Induced Near-Field Electron Microscopy.

We reveal the classical and quantum regimes of free electron interaction with radiation, common to the general variety of radiation sources (e.g., a Smith-Purcell radiation), the dielectric laser accelerator, and photo-induced near-field electron microscopy (PINEM). Modeling the electron with initial conditions of a coherent quantum electron wave packet, its topology in phase space uniquely defines a universal distinction of three interaction regimes: point-particle-like acceleration, a quantum wave function (PINEM), and a newly reported regime of anomalous PINEM (APINEM). The quantum interference beat of APINEM is capable of improving the spectral resolution of postselective electron microscopy. The particle-wave duality transition between regimes reveals the history-dependent nature of quantum electron interaction with light.

Control of Nuclear Dynamics through Conical Intersections and Electronic Coherences.

The effect of nuclear dynamics and conical intersections on electronic coherences is investigated employing a two-state, two-mode linear vibronic coupling model. Exact quantum dynamical calculations are performed using the multiconfiguration time-dependent Hartree method. It is found that the presence of a nonadiabatic coupling close to the Franck-Condon point can preserve electronic coherence to some extent. Additionally, the possibility of steering the nuclear wave packets by imprinting a relative phase between the electronic states during the photoionization process is discussed. It is found that the steering of nuclear wave packets is possible given that a coherent electronic wave packet embodying the phase difference passes through a conical intersection. A conical intersection close to the Franck-Condon point is thus a necessary prerequisite for control, providing a clear path towards attochemistry.

Attosecond transient absorption of a bound wave packet coupled to a smooth continuum

We investigate the possibility of using transient absorption of a coherent bound electron wave packet in hydrogen as an attosecond pulse characterization technique. In a recent work, we have shown that photoionization of such a coherent bound electron wave packet opens up for pulse characterization with unprecedented temporal accuracy—independent of the atomic structure—with maximal photoemission at all kinetic energies given a wave packet with zero relative phase (Pabst and Dahlström Phys. Rev. A 94 13411 (2016)). Here, we perform numerical propagation of the time-dependent Schrödinger equation and analytical calculations based on perturbation theory to show that the energy-resolved maximal absorption of photons from the attosecond pulse does not uniquely occur at a zero relative phase of the initial wave packet. Instead, maximal absorption occurs at different relative wave packet phases, distributed as a non-monotonous function with a smooth shift across the central photon energy (given a Fourier-limited Gaussian pulse). Similar results are also found in helium. Our finding is surprising, because it implies that the energy-resolved photoelectrons are not mapped one-to-one with the energy-resolved absorbed photons of the attosecond pulse.

Interference of electron wave packets in photoionization of by attosecond ultraviolet laser pulses

We study molecular photoionization of aligned by a sequence of two attosecond ultraviolet laser pulses at frequencies and from numerical solutions of time-dependent Schördinger equations. Results exhibit signature of interference effects of coherent electron wave packets, which is shown to be sensitive to the time delay between the two pulses. It is found that for the photoionization with identical frequencies , same interference distributions are produced in the positive and negative momentum regions whereas for the case of , photoelectron momentum distributions are asymmetric. Influence of the pulse carrier envelope phase is also presented. The attosecond perturbation theory is used to describe these interference phenomena.

Monitoring coherent electron wave packet excitation dynamics by two-color attosecond laser pulses.

We propose a method to monitor coherent electron wave packet (CEWP) excitation dynamics with two-color attosecond laser pulses. Simulations are performed on aligned H2+ by numerically solving the three-dimensional time-dependent Schrödinger equation with combinations of a resonant linearly polarized λl= 100/70 nm pump pulse and a circularly polarized λc=5 nm attosecond probe pulse. It is found that time dependent diffraction patterns in molecular frame photoelectron angular distributions (MFPADs) produced by the circular probe pulse exhibit sensitivity to the molecular alignments and time-dependent geometry of the CEWPs during and after the coherent excitation between the ground and excited states induced by the linear pump pulse. The time dependent MFPADs are described by an ultrafast diffraction model for the ionization of the bound CEWPs.

Eliminating the dipole phase in attosecond pulse characterization using Rydberg wave packets

We propose a new technique to fully characterize the temporal structure of extreme ultraviolet pulses by ionizing a bound coherent electronic wavepacket. The populated energy levels make it possible to interfere different spectral components leading to quantum beats in the photoelectron spectrum as a function of the delay between ionization and initiation of the wavepacket. The influence of the dipole phase, which is the main obstacle for state-of-the-art pulse characterization schemes, can be eliminated by angle integration of the photoelectron spectrum. We show that particularly atomic Rydberg wavepackets are ideal and that wavepackets involving multiple electronic states provide redundant information which can be used to cross-check the consistency of the phase reconstruction.

Photoelectron momentum distributions of molecules in bichromatic circularly polarized attosecond UV laser fields

We theoretically investigate molecular photoelectron momentum distributions (MPMDs) by bichromatic [frequencies $({\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2})]$ circularly polarized attosecond UV laser pulses. Simulations performed on aligned single-electron ${\mathrm{H}}_{2}{}^{+}$ by numerically solving the corresponding three-dimensional time-dependent Schr\odinger equation within a static nucleus frame show that MPMDs exhibit a spiral structure for both co-rotating and counter-rotating schemes. Results are analyzed by attosecond perturbation ionization models. Coherent electron wave packets created, respectively, by the two color pulses in the continuum interfere with each other. Photoionization distributions are functions of the photoelectron momentum $p$ and the ejection angle $\ensuremath{\theta}$, thus leading to spiral MPMDs. The dependence of spiral MPMDs on the time delay between the bicircular pulses and their relative phases is also presented. The spiral interference patterns are determined by the helicities and frequencies $({\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2})$ of the bicircular fields. It is also found that the spiral patterns are sensitive to the molecular alignment and suppressed by two-center ionization interference, thus offering new tools for imaging molecular geometry.

Interference asymmetry of molecular frame photoelectron angular distributions in bichromatic UV ionization processes

We investigate molecular photoionization by ultrafast bichromatic linearly polarized UV laser pulses at frequencies perpendicular to the internuclear axis R involving π orbital excitation. Results from numerical solutions of time dependent Schrödinger equations for aligned show that molecular frame photoelectron angular distributions (MFPADs) exhibit signatures of asymmetry perpendicular to the molecular symmetry axis, arising from interference of coherent electron wave packets created by respectively one and two-photon absorption. A resonant excitation process between the ground state and the excited state is triggered by the pulse. The asymmetry of MFPADs varies periodically with pulse intensity I0 and duration T, which we attribute to coherent resonant Rabi oscillations in electronic state population. A perturbative model is adopted to qualitatively describe and analyze these effects in both resonant and nonresonant photoionization processes.

Observation of autoionization dynamics and sub-cycle quantum beating in electronic molecular wave packets

The coherent interaction with ultrashort light pulses is a powerful strategy for monitoring and controlling the dynamics of wave packets in all states of matter. As light presents an oscillation period of a few femtoseconds (T = 2.6 fs in the near infrared spectral range), an external optical field can induce changes in a medium on the sub-cycle timescale, i.e. in a few hundred attoseconds. In this work, we resolve the dynamics of autoionizing states on the femtosecond timescale and observe the sub-cycle evolution of a coherent electronic wave packet in a diatomic molecule, exploiting a tunable ultrashort extreme ultraviolet pulse and a synchronized infrared field. The experimental observations are based on measuring the variations of the extreme ultraviolet radiation transmitted through the molecular gas. The different mechanisms contributing to the wave packet dynamics are investigated through theoretical simulations and a simple three level model. The method is general and can be extended to the investigation of more complex systems.

Strong-field-induced wave packet dynamics in carbon dioxide molecule.

Temporal evolution of electronic and nuclear wave packets created in strong-field excitation of the carbon dioxide molecule is studied employing momentum-resolved ion spectroscopy and channel-selective Fourier analysis. Combining the data obtained with two different pump-probe set-ups, we observed signatures of vibrational dynamics in both, ionic and neutral states of the molecule. We consider far-off-resonance two-photon Raman scattering to be the most likely mechanism of vibrational excitation in the electronic ground state of the neutral CO2. Using the measured phase relation between the time-dependent yields of different fragmentation channels, which is consistent with the proposed mechanism, we suggest an intuitive picture of the underlying vibrational dynamics. For ionic states, we found signatures of both, electronic and vibrational excitations, which involve the ground and the first excited electronic states, depending on the particular final state of the fragmentation. While our results for ionic states are consistent with the recent observations by Erattupuzha et al. [J. Chem. Phys.144, 024306 (2016)], the neutral state contribution was not observed there, which we attribute to a larger bandwidth of the 8 fs pulses we used for this experiment. In a complementary measurement employing longer, 35 fs pulses in a 30 ps delay range, we study the influence of rotational excitation on our observables, and demonstrate how the coherent electronic wave packet created in the ground electronic state of the ion completely decays within 10 ps due to the coupling to rotational motion.

Attosecond-magnetic-field-pulse generation by coherent circular molecular electron wave packets

Attosecond-magnetic-field-pulse generation is investigated using numerical solutions of the time-dependent Schr\odinger equation for oriented ${{\mathrm{H}}_{2}}^{+}$ excited and ionized by intense $2\ifmmode\times\else\texttimes\fi{}{10}^{16} \mathrm{W}/{\mathrm{cm}}^{2}$ circularly polarized attosecond UV pulses. The results show that localized attosecond-magnetic-field pulses $B$ at the molecular center $(\mathbf{r}=\mathbf{0})$ decrease in intensity with increasing attosecond-pulse wavelength, following a classical model. Magnetic-field minima are obtained at a specific laser-pulse wavelength $\ensuremath{\lambda}=55$ nm, which is attributed to ionization suppression. It is found that spatially localized coherent circular electron currents and wave packets are created and induce magnetic-field minima. At $\ensuremath{\lambda}=55$ nm, coherent excitation between the ground state and Rydberg states is created, giving rise to partial Rabi oscillations in population and doublets in molecular above-threshold-ionization photoelectron energy spectra. Pulse intensities are shown to influence these effects on the attosecond time scale through population variations.

Coherent Electronic Wave Packet Motion inC60Controlled by the Waveform and Polarization of Few-Cycle Laser Fields

Strong laser fields can be used to trigger an ultrafast molecular response that involves electronic excitation and ionization dynamics. Here, we report on the experimental control of the spatial localization of the electronic excitation in the C_{60} fullerene exerted by an intense few-cycle (4fs) pulse at 720nm. The control is achieved by tailoring the carrier-envelope phase and the polarization of the laser pulse. We find that the maxima and minima of the photoemission-asymmetry parameter along the laser-polarization axis are synchronized with the localization of the coherent electronic wave packet at around the time of ionization.

Asymmetry of Photoelectron Angular Distributions in Molecules by Intense Attosecond Extreme Ultraviolet Laser Pulses

We present photoelectron angular distribution of the aligned molecular ion H2+ by intense ultrashort attosecond extreme ultraviolet laser pulses from numerical solutions of time-dependent Schrödinger equations. Photoionization from a superposition state of the ground 1sσg and the excited 2pσu states with pulses at photon energies above the ionization potential, ħω>Ip, and intensity 1014 W/cm2, yields pulse duration dependent asymmetry of photoelectron angular distributions. We attribute the asymmetry to the periodical oscillation of the coherent electron wave packets, resulting from the interference of the two electronic states. For the processes with long pulse durations, such duration dependence is absent and symmetric angular distributions are obtained.

Autler-Townes Effects in Attosecond Circular Polarization Molecular Photoionization

We present molecular photoionization simulations by intense (I ~ 1016 W/cm2) few cycle circularly polarized attosecond extreme ultraviolet laser pulses for aligned H2+ from numerical solutions of the corresponding time-dependent Schrodinger equation. With appropriate laser pulse parameters, circular attosecond coherent electron wave packets (CEWPs) are created in excited Rydberg states. Such CEWPs are spatially localized during ionization processes, thus resulting in sufficient population oscillations between the resonant excited Rydberg states and the initial ground state. Consequently Autler-Townes splitting in circular polarization energy spectra is predicted, which is shown to be critically sensitive to the pulse intensity, duration, and polarization. The resulting photoelectron angular distributions are rotated with respect to the molecular axis due to the nonspherical Coulomb potential of the molecule, resulting in different ionization rates at different laser polarization-molecular angles.