Coherent Electron Wave Packets Research Articles

Electronic dynamics by ultrafast pump photoelectron detachment probed by ionization: a dynamical simulation of negative-neutral-positive in LiH(-).

The control of electronic dynamics in the neutral electronic states of LiH before the onset of significant nuclei motion is investigated using a negative-neutral-positive (NeNePo) ultrafast IR pump-attoescond pulse train (APT) probe scheme. Starting from the ground state of the anion (LiH(-)), multiphoton ultrafast electron detachment and subsequent excitation of the neutral by a few femtosecond intense IR pulse produces a non-equilibrium electronic density in neutral LiH. The coherent electronic wave packet is then probed by angularly resolved photoionization to the cation by an APT generated from a replica of the pump IR pulse at several time delays. Realistic parameters for the pump and the APT are used. Several NeNePo schemes are simulated using different IR carrier frequencies, showing that the delay between the successive attosecond pulses in the train can be used as a filter to probe the different pairs of states present in the coherent electronic wave packet produced by the pump pulse. The dynamical simulations include the pump and the probe pulses to all orders by solving the time-dependent Schrödinger equation using a coupled equation scheme for the manifolds of the anion, neutral, and cation subspaces. We show that an incomplete molecular orientation of the molecule in the laboratory frame does not prevent probing the electronic density localization by angularly resolved photoelectron maps.

Nonadiabatically Coupled π-Electron Rotation and Molecular Vibration in Aromatic Molecules Excited by Polarized UV/Vis Laser Pulses

We review our theoretical studies on laser-driven ultrafast π-electron rotation (ring current) and vibronically coupled molecular vibrations in aromatic molecules with quasi-degenerate excited states. The main focus of discussion is on the role of laser polarization in controlling the coherent vibronic dynamics. We first present general formulations of the coherent electronic wave packet and expectation value of electronic angular momentum for arbitrary laser polarization within a frozen-nuclei model. We show that the relative quantum phase of the superposed quasi-degenerate states, which determines the oscillating behavior of angular momentum, can be manipulated by the ellipticity and orientation of the incident laser. The controllability of π-electron rotation is demonstrated by electronic wave packet simulations for a model molecule. The results of nuclear wave packet simulations on effective potential energy surfaces of the molecule have revealed that the angular momentum is gradually reduced by nonadiabatic transitions. The amplitude of induced molecular vibration depends significantly on the direction of linear polarization vectors but is insensitive to the helicity of circular polarization. The characteristic feature in vibrational amplitudes is attributed to the interference between nuclear wave packets that acquire different quantum phases in nonadiabatic transition. This feature offers a new strategy for laser control of molecular vibrations through the wave packet interference in nonadiabatic transition.

High-Harmonic Probing of Electronic Coherence in Dynamically Aligned Molecules

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 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 packet, we demonstrate an unprecedented sensitivity that arises from optical interference between coherent and incoherent pathways. This mechanism converts a 0.1% excitation fraction into a ∼20% signal modulation.

Carrier-envelope phase effects on the strong-field photoemission of electrons from metallic nanostructures

Sharp metallic nanotapers irradiated with few-cycle laser pulses are emerging as a source of highly confined coherent electron wavepackets with attosecond duration and strong directivity. The possibility to steer, control or switch such electron wavepackets by light is expected to pave the way towards direct visualization of nanoplasmonic field dynamics and real-time probing of electron motion in solid state nanostructures. Such pulses can be generated by strong-field induced tunneling and acceleration of electrons in the near-field of sharp gold tapers within one half-cycle of the driving laser field. Here, we show the effect of the carrier-envelope phase of the laser field on the generation and motion of strong-field emitted electrons from such tips. This is a step forward towards controlling the coherent electron motion in and around metallic nanostructures on ultrashort length and time scales.

Photoelectron angular distributions in molecular above threshold ionization by two colour circularly polarized ultrashort UV laser pulses

Photoionization of an aligned molecular ion H has been investigated with two colour circularly polarized ultrashort UV laser pulses by numerically solving the corresponding time dependent Schrödinger equation. Photoelectron angular distributions (PADs) in molecular above threshold ionization (MATI) exhibit: (i) asymmetry resulting from interference of coherent electron wave packets from multiple pathway ionization, which depends critically on the relative carrier envelope phase (CEP) between the two colour laser pulses and photoelectron kinetic energies; (ii) rotation with respect to the molecular symmetry axes due to effects of the nonspherical two center Coulomb potential. Such features are described by multi-photon perturbative theoretical ionization models. The ionization probability is functions of both the CEP and the angle between the electron emission and the molecular axis. The influence of pulse intensity and ellipticity on PADs in MATI is also investigated. It is found that the asymmetry depends on the pulse intensity whereas the rotation angle is shown to be sensitive to the pulse ellipticity, both reflecting the orientation dependence of molecular ionization probabilities.

Coherent femtosecond low-energy single-electron pulses for time-resolved diffraction and imaging: A numerical study

We numerically investigate the properties of coherent femtosecond single electron wave packets photoemitted from nanotips in view of their application in ultrafast electron diffraction and non-destructive imaging with low-energy electrons. For two different geometries, we analyze the temporal and spatial broadening during propagation from the needle emitter to an anode, identifying the experimental parameters and challenges for realizing femtosecond time resolution. The simple tip-anode geometry is most versatile and allows for electron pulses of several ten of femtosecond duration using a very compact experimental design, however, providing very limited control over the electron beam collimation. A more sophisticated geometry comprising a suppressor-extractor electrostatic unit and a lens, similar to typical field emission electron microscope optics, is also investigated, allowing full control over the beam parameters. Using such a design, we find ∼230 fs pulses feasible in a focused electron beam. The main limitation to achieve sub-hundred femtosecond time resolution is the typical size of such a device, and we suggest the implementation of more compact electron optics for optimal performance.

Laser-Polarization Effects on Coherent Vibronic Excitation of Molecules with Quasi-Degenerate Electronic States

The laser-polarization effects on nonadiabatically coupled π-electron rotation (ring current) and molecular vibration have been theoretically analyzed for aromatic molecules with quasi-degenerate excited states irradiated by an ultrashort laser pulse of arbitrary polarization. We first derived general formulations of the coherent electronic wave packet and expectation value of electronic angular momentum within a frozen-nuclei model. The relative quantum phase of the superposed quasi-degenerate states, which determines the oscillating behavior of angular momentum, can be manipulated by the ellipticity and orientation of the incident laser. Nuclear wave packet simulations with a model molecule confirmed the controllability of π-electron rotation, although the angular momentum is gradually reduced by nonadiabatic couplings. The amplitude of molecular vibration depends prominently on the orientation of linear polarization vectors rather than the helicity of circular polarization. The characteristic feature in vibrational amplitudes is attributed to the interference in nonadiabatic transition governed by the relative quantum phase between nuclear wave packets. This offers a new strategy for laser control of molecular vibrations through the wave packet interference in nonadiabatic transition.

High-order-harmonic generation from coherent electron wave packets in atoms and molecules as a tool for monitoring attosecond electrons

We study numerically pump-probe schemes for monitoring electron-nuclear motion in a dissociating molecule using a midinfrared, intense few-femtosecond probe laser pulse which generates molecular high-order harmonics (MHOHG) from a coherent superposition of electron-nuclear wave packets prepared by a weak femtosecond UV pump pulse from an initial bound state. We show that by varying the time delay between the intense probe pulse and the UV pump pulse by a few hundred attoseconds one alters the MHOHG signal intensity by many orders of magnitude. The periodicity of the MHOHG intensity variations as function of the time delay is equal to the period of the electron oscillation in the coherent superposition which varies with internuclear distance. We use the strong field approximation (SFA) and three-step model to explain this high sensitivity of the harmonic intensity to pulse delay time and to the overlap of nuclear wave packets. We also solve numerically the three-dimensional (3D) time-dependent Schr\odinger equation describing harmonic generation for a hydrogen atom prepared in a superposition of its two lowest atomic states, in order to investigate the dependence of the same effect (in a simpler system but in 3D) on the probe-pulse carrier-envelope phase (CEP) and on the probe duration. We also relate these strong effects in the intensity of harmonics to the correlation between the velocity of the recolliding electron wave packet and the electron velocity in the coherent superposition of the electron bound states.

Single molecules filmed dancing on a table top

By ripping an electron away from a molecule and then slamming it back again, the motion of nuclei in a molecule has been tracked with extremely high temporal and spatial resolution. See Letter p.194 Molecular imaging, or the determination of the positions of atoms in molecules, is an important technique in the physical, chemical and biological sciences. But going beyond mere structure determination, recent technical developments offer the tantalizing prospect of access to ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. One approach uses laser-ionized bursts of coherent electron wave packets to self-interrogate the parent molecular structure. Here, Blaga et al. use this laser-induced electron diffraction (LIED) method to map the structural responses of oxygen and nitrogen molecules to ionization. By measuring a 0.1-angstrom displacement in the oxygen bond length occurring in a time interval of about 5 femtoseconds, the authors establish LIED as a promising approach for imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

Imaging ultrafast molecular dynamics with laser-induced electron diffraction

Establishing the structure of molecules and solids has always had an essential role in physics, chemistry and biology. The methods of choice are X-ray and electron diffraction, which are routinely used to determine atomic positions with sub-ångström spatial resolution. Although both methods are currently limited to probing dynamics on timescales longer than a picosecond, the recent development of femtosecond sources of X-ray pulses and electron beams suggests that they might soon be capable of taking ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. The past decade has also witnessed the emergence of an alternative imaging approach based on laser-ionized bursts of coherent electron wave packets that self-interrogate the parent molecular structure. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction (LIED), to image molecular structures with sub-ångström precision and exposure times of a few femtoseconds. We apply the method to oxygen and nitrogen molecules, which on strong-field ionization at three mid-infrared wavelengths (1.7, 2.0 and 2.3 μm) emit photoelectrons with a momentum distribution from which we extract diffraction patterns. The long wavelength is essential for achieving atomic-scale spatial resolution, and the wavelength variation is equivalent to taking snapshots at different times. We show that the method has the sensitivity to measure a 0.1 Å displacement in the oxygen bond length occurring in a time interval of ∼5 fs, which establishes LIED as a promising approach for the imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

Imaging of ultrafast electron motion in molecules

We probe the attosecond electron motion in [Formula: see text], at short internuclear distances, by exact numerical solution of the 3D time-dependent Schrödinger equation in the Born–Oppenheimer approximation. We simulate a pump-probe experiment to calculate the energy distributions of ionized electrons. We start the experiment with a pump pulse that creates a coherent electronic wavepacket combination of the 1sσg and 2pσu states. We let the electronic wavepacket oscillate during a time delay Δt. In the second step of the experiment, we submit the wavepacket to an intense attosecond X-ray laser pulse. We observe an asymmetry in the energy distributions of ionized electrons that allows the mapping of the attosecond electron motion in [Formula: see text].

Dynamics of electron in a surface quantum well

This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with autocorrelation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanics is shown explicitly in the system.

On the feasibility of an ultrafast purely electronic reorganization in lithium hydride

Excitation of a coherent electronic wave packet, a linear combination of several electronic stationary states, is discussed with a computational example, the A and B low lying excited states of LiH. Such linear combination results in the electron executing a rotation-like motion in the xz plane with a period of 4 fs. The excitation needs to be shorter than this purely electronic reorganization time and yet the mean energy of the photon should be relatively low so that the A and B states are coherently accessed. These two requirements limit the wave form of the few cycle pump pulse.

Ultrafast Fiske Effect in Semiconductor Superlattices

The current flowing across a semiconductor superlattice in tilted electric and magnetic fields is known to exhibit resonant enhancement, when Landau states of neighboring wells align at certain ratios of the field strengths. We show that the ultrafast version of this effect, in which coherent electron wave packets are involved, has a profound analogy to the Fiske effect in superconductor Josephson junctions and superfluid weak links, in that the coupling of the tunneling-induced charge oscillations (magneto-Bloch versus Josephson oscillations) to another oscillator (in-plane cyclotron oscillations versus external oscillator modes) opens an elastic rectifying transport channel. We explore the superlattice effect both theoretically and experimentally, and find that the transient self-induced current can be adequately modeled if the damping of both types of coupled electron oscillations is properly taken into account.