Interferences of ultrashort free electron wave packets

Femtosecond Polarization Shaping of Free-Electron Laser Pulses

We demonstrate the generation of extreme-ultraviolet (XUV) free-electron laser (FEL) pulses with time-dependent polarization. To achieve polarization modulation on a femtosecond timescale, we combine two mutually delayed counterrotating circularly polarized subpulses from two cross-polarized undulators. The polarization profile of the pulses is probed by angle-resolved photoemission and above-threshold ionization of helium; the results agree with solutions of the time-dependent Schrödinger equation. The stability limit of the scheme is mainly set by electron-beam energy fluctuations, however, at a level that will not compromise experiments in the XUV. Our results demonstrate the potential to improve the resolution and element selectivity of methods based on polarization shaping and may lead to the development of new coherent control schemes for probing and manipulating core electrons in matter.

Time domain double slit interference of electron produced by XUV synchrotron radiation

We present a new realization of the time-domain double-slit experiment with photoelectrons, demonstrating that spontaneous radiation from a bunch of relativistic electrons can be used to control the quantum interference of single-particles. The double-slit arrangement is realized by a pair of light wave packets with attosecond-controlled spacing, which is naturally included in the spontaneous radiation from two undulators in series. Photoelectrons emitted from helium atoms are observed in the energy-domain under the condition of detecting them one by one, and the stochastic buildup of the quantum interference pattern on a detector plane is recorded.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

All-optical attosecond time domain interferometry

Interferometry, a key technique in modern precision measurements, has been used for length measurement in engineering metrology and astronomy. An analogous time-domain interferometric technique would represent a significant complement to spatial domain applications and require the manipulation of interference on extreme time and energy scales. Here, we report an all-optical interferometer using laser-driven high order harmonics as attosecond temporal slits. By controlling the phase of the temporal slits with an external field, a time domain interferometer that preserves both attosecond temporal resolution and hundreds of meV energy resolution is implemented. We apply this exceptional temporal resolution to reconstruct the waveform of an arbitrarily polarized optical pulse, and utilize the provided energy resolution to interrogate the abnormal character of the transition dipole near the Cooper minimum in argon. This novel attosecond interferometry paves the way for high precision measurements in the time-energy domain using all-optical approaches.

Quantum state holography to reconstruct the molecular wave packet using an attosecond XUV-XUV pump-probe technique

An attosecond molecular interferometer is proposed by using a XUV-XUV pump-probe scheme. The interferograms resulting in the photoelectron distributions enable the full reconstruction of the molecular wave packet associated to excited states using a quantum state holographic approach that, to our knowledge, has only been proposed for simple atomic targets combining attosecond XUV pulses with IR light. In contrast with existing works, we investigate schemes where one- and two-photon absorption paths contribute to ionize the hydrogen molecule and show that it is possible to retrieve the excitation dynamics even when imprinted in a minority channel. Furthermore, we provide a systematic analysis of the time-frequency maps that reveal the distinct, but tightly coupled, motion of electrons and nuclei.

Coherent Control of Internal Conversion in Strong-Field Molecular Ionization

We demonstrate coherent control over internal conversion during strong-field molecular ionization with shaped, few-cycle laser pulses. The control is driven by interference in different neutral states, which are coupled via non-Born-Oppenheimer terms in the molecular Hamiltonian. Our measurements highlight the preservation of electronic coherence in nonadiabatic transitions between electronic states.

Holographic imaging of electromagnetic fields via electron-light quantum interference

Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and the phase of that signal. With electrons, the extension of holography to the ultrafast time domain remains a challenge, although it would yield the highest possible combined spatiotemporal resolution. Here, we show that holograms of local electromagnetic fields can be obtained with combined attosecond/nanometer resolution in an ultrafast transmission electron microscope (UEM). Unlike conventional holography, where signal and reference are spatially separated and then recombined to interfere, our method relies on electromagnetic fields to split an electron wave function in a quantum coherent superposition of different energy states. In the image plane, spatial modulation of the electron energy distribution reflects the phase relation between reference and signal fields. Beyond imaging applications, this approach allows implementing quantum measurements in parallel, providing an efficient and versatile tool for electron quantum optics.

Weak-field coherent control of photodissociation in polyatomic molecules

A coherent control scheme is suggested to modify the output of photodissociation in a polyatomic system. The performance of the scheme is illustrated by applying it to the ultrafast photodissociation of CH₃I in the A-band. The control scheme uses a pump laser weak field that combines two pulses of a few femtoseconds delayed in time. By varying the time delay between the pulses, the shape of the laser field spectral profile is modulated, which causes a change in the initial relative populations excited by the pump laser to the different electronic states involved in the photodissociation. Such a change in the relative populations produces different photodissociation outputs, which is the basis of the control achieved. The degree of control obtained over different photodissociation observables, like the branching ratio between the two dissociation channels of CH₃I yielding I(²P_3/2) and I*(²P_1/2) and the fragment angular distributions associated with each channel, is investigated. These magnitudes are found to oscillate strongly with the time delay, with the branching ratio changing by factors between two and three. Substantial variations of the angular distributions also indicate that the scheme provides a high degree of control. Experimental application of the scheme to general polyatomic photodissociation processes should be straightforward.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Electron Vortices in Femtosecond Multiphoton Ionization

Multiphoton ionization of potassium atoms with a sequence of two counter-rotating circularly polarized femtosecond laser pulses produces vortex-shaped photoelectron momentum distributions in the polarization plane describing Archimedean spirals. The pulse sequences are produced by polarization shaping and the three-dimensional photoelectron distributions are tomographically reconstructed from velocity map imaging measurements. We show that perturbative ionization leads to electron vortices with c_{6} rotational symmetry. A change from c_{6} to c_{4} rotational symmetry of the vortices is demonstrated for nonperturbative interaction.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

Communication: Control of the fragment state distributions produced upon decay of an isolated resonance state

Control of the fragment state distributions produced upon decay of a resonance state is achieved by using a weak laser field consisting of two pulses with a varying time delay between them. It is shown that specific product fragment states can be significantly favored or quenched. The efficiency and flexibility of the control method are found to increase with increasing resonance width. The control scheme is completely independent of the specific system to which it is applied, which makes its applicability universal.

Unravelling the role of quantum interference in the weak-field laser phase modulation control of photofragment distributions

The role played by quantum interference in the laser phase modulation coherent control of photofragment distributions in the weak-field regime is investigated in detail in this work. The specific application involves realistic wave packet calculations of the transient vibrational populations of the Br2(B,vf) fragment produced upon predissociation of the Ne-Br2(B) complex, which is excited to a superposition of overlapping resonance states using different fixed bandwidth pulses where the linear chirps are varied. The postpulse transient phase modulation effects observed on fragment populations for a long time window are explained in terms of the mechanism of interference between overlapping resonances. A detailed description of how the interference mechanism affects the magnitude and the time window of the phase control effects is also provided. In the light of the results, the conditions to maximize phase modulation control on fragment distributions are discussed.

Quantum interference control of an isolated resonance lifetime in the weak-field limit

Resonance states play an important role in a large variety of physical and chemical processes. Thus, controlling the resonance behavior, and particularly a key property like the resonance lifetime, opens up the possibility of controlling those resonance mediated processes. While such a resonance control is possible by applying strong-field approaches, the development of flexible weak-field control schemes that do not alter significantly the system dynamics still remains a challenge. In this work, one such control scheme within the weak-field regime is proposed for the first time in order to modify the lifetime of an isolated resonance state. The basis of the scheme suggested is quantum interference between two pathways induced by laser fields, that pump wave packet amplitude to the target resonance under control. The simulations reported here show that the scheme allows for both enhancement and quenching of the resonance survival lifetime, being particularly flexible to achieve large lifetime enhancements. Control effects on the resonance lifetime take place only while the pulse is operating. In addition, the conditions required to generate the two interfering quantum pathways are found to be rather easy to meet for general systems, which makes the experimental implementation straightforward and implies the wide applicability of the control scheme.

Electron vortices in photoionization by circularly polarized attosecond pulses

Single ionization of He by two oppositely circularly polarized, time-delayed attosecond pulses is shown to produce photoelectron momentum distributions in the polarization plane having helical vortex structures sensitive to the time delay between the pulses, their relative phase, and their handedness. Results are obtained by both ab initio numerical solution of the two-electron time-dependent Schrödinger equation and by a lowest-order perturbation theory analysis. The energy, bandwidth, and temporal duration of attosecond pulses are ideal for observing these vortex patterns.

Frequency-resolved optical gating technique for retrieving the amplitude of a vibrational wavepacket

We propose a novel method to determine the complex amplitude of each eigenfunction composing a vibrational wavepacket of / molecular ions evolving with a ~10 fs time scale. We find that the two-dimensional spectrogram of the kinetic energy release (KER) of H⁺/D⁺ fragments plotted against the time delay of the probe pulse is equivalent to the spectrogram used in the frequency-resolved optical gating (FROG) technique to retrieve the complex amplitude of an ultrashort optical pulse. By adapting the FROG algorithm to the delay-KER spectrogram of the vibrational wavepacket, we have successfully reconstructed the complex amplitude. The deterioration in retrieval accuracy caused by the bandpass filter required to process actual experimental data is also discussed.

Extracting phase and amplitude modifications of laser-coupled Fano resonances

Fano line shapes observed in absorption spectra encode information on the amplitude and phase of the optical dipole response. A change in the Fano line shape, e.g., by interaction with short-pulsed laser fields, allows us to extract dynamical modifications of the amplitude and phase of the coupled excited quantum states. We introduce and apply this physical mechanism to near-resonantly coupled doubly excited states in helium. This general approach provides a physical understanding of the laser-induced spectral shift of absorption-line maxima on a sub-laser-cycle time scale as they are ubiquitously observed in attosecond transient-absorption measurements.

Resonant detection of the signature of control of a resonance state lifetime using a pump–probe scheme

Realistic wave packet simulations demonstrate that the signature of control of the survival probability and lifetime of a specific resonance state can be observed and probed in typical time-resolved pump–probe experiments.

Selective coherent control of the lifetime of a resonance state with laser pulses

It is shown that new possibilities for control of the lifetime of a system in a resonance state emerge when the density of resonances overlapping and interfering with the target resonance increases. When using a control scheme combining two pump laser pulses, it is found that increasing the density of resonance states overlapping with the target one increases the selectivity of the scheme applied, and leads to achieve a remarkably higher degree of control. Lifetime enhancements by factors up to 20 are obtained when this selectivity is applied. The underlying reasons for such strong enhancements are analyzed and explained in the light of the equations of the model applied. Application of this strategy to control and enhance the lifetime of a system in excited states is envisioned.

Attosecond probe of valence-electron wave packets by subcycle sculpted laser fields

We experimentally and theoretically demonstrate a self-referenced wave-function retrieval of a valence-electron wave packet during its creation by strong-field ionization with a sculpted laser field. Key is the control over interferences arising at different time scales. Our work shows that the measurement of subcycle electron wave-packet interference patterns can serve as a tool to retrieve the structure and dynamics of the valence-electron cloud in atoms on a sub-10-as time scale.

Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics

Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.

CONTROLLING WAVE PACKET INTERFERENCE OF DISSOCIATING MOLECULES BY SHAPING LASER PULSES IN FREQUENCY DOMAIN

The interference of dissociating wave packets for the Br 2 molecule in femtosecond laser field is studied theoretically using time-dependent quantum wave packet method. The interference of dissociating wave packets can be determined by the spectrum of laser field. By shaping laser pulses in frequency domain, the corresponding R- and v-dependent density functions can be effectively controlled. Compared with the 2-pulse excitation scheme, the resolution of the interference patterns can be improved by using 3- and 4-pulse excitation schemes. The dissociating velocity can be steered by varying laser parameters.

QUANTUM INTERFERENCE AND LASER PULSE PHASE EFFECT ON THE PHOTOIONIZATION RATES OF EXCITED HYDROGEN ATOMS IN THE TUNNELING REGION

Using the generalized Keldysh theory, we investigate the quantum interference and the laser pulse phase effects by tunneling photoionization of an excited hydrogen atom. We assume that its initial state be a linear combination of 1s, 2s, 2p Stark-shifted atomic states. It is found that within the Keldysh approximation, quantum interference can take place among the 1s, 2s, and 2pz states, while this is not the case among 1s, 2s, 2pz and 2px, 2py, or 2px and 2py themselves. From the numerical calculations, we predict that the prominent destructive quantum interference takes place between 2s and 2pz atomic orbitals. In addition, we have found that in general, the laser pulse phase does not affect the individual photoionization rates while it does affect the quantum interference terms.

Zeptosecond precision pulse shaping

We investigate the temporal precision in the generation of ultrashort laser pulse pairs by pulse shaping techniques. To this end, we combine a femtosecond polarization pulse shaper with a polarizer and employ two linear spectral phase masks to mimic an ultrastable common-path interferometer. In an all-optical experiment we study the interference signal resulting from two temporally delayed pulses. Our results show a 2σ-precision of 300 zs = 300 × 10(-21) s in pulse-to-pulse delay. The standard deviation of the mean is 11 zs. The obtained precision corresponds to a variation of the arm's length in conventional delay stage based interferometers of 0.45 Å. We apply these precisely generated pulse pairs to a strong-field quantum control experiment. Coherent control of ultrafast electron dynamics via photon locking by temporal phase discontinuities on a few attosecond timescale is demonstrated.

Ultrafast relaxation dynamics observed through time-resolved photoelectron angular distributions

Time-resolved photoelectron imaging of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical anion is presented. Photoelectron angular distributions (PADs) are qualitatively analyzed in terms of the simple s-p model that is based on symmetry arguments. The internal conversion dynamics from the first excited state (1(2)B(3u)) to the ground state ((2)B(2g)) may be observed through temporal changes in the PADs of the spectrally overlapping photoelectron features arising from photodetachment of the ground state and the excited state. A formulism for extracting the population dynamics from the β(2) anisotropy parameter of overlapping spectroscopic features is presented. This is used to extract the lifetime of the first excited state, which is in good agreement with that observed in the time-resolved photoelectron spectra.

Sub-cycle strong-field interferometry

A nonlinear interferometry scheme is described theoretically to induce and resolve electron wavefunction beating on time scales shorter than the optical cycle of the time-delayed pump and probe pulses. By employing two moderately intense few-cycle laser fields with a stable carrier-envelope phase, a large range of the entire electronic level structure of a quantum system can be retrieved. In contrast to single-photon excitation schemes, the retrieved electronic states include levels that are both dipole- and non-dipole-accessible from the ground electronic state. The results show that strong-field interferometry can reveal both high-resolution and broad-band spectral information at the same time with important consequences for quantum-beat spectroscopy on attosecond time scales.

Wave packet interferometry with attosecond precision and picometric structure

Wave packet (WP) interferometry is applied to the vibrational WPs of the iodine molecule. Interference fringes of quantum waves weave highly regular space-time images called "quantum carpets." The structure of the carpet has picometre and femtosecond resolutions, and changes drastically depending on the amplitudes and phases of the vibrational eigenstates composing the WP. In this review, we focus on the situation where quantum carpets are created by two counter-propagating nuclear vibrational WPs. Such WPs can be prepared with either a single or double femtosecond (fs) laser pulse. In the single pulse scheme, the relevant situation appears around the half revival time. Similar situations can be generated with a pair of fs laser pulses whose relative phase is stabilized on the attosecond time scale. In the latter case we can design the quantum carpet by controlling the timing between the phase-locked pulses. We demonstrate this carpet design and visualize the designed carpets by the fs pump-probe measurements, tuning the probe wavelength to resolve the WP density-distribution along the internuclear axis with ~3 pm spatial resolution and ~100 fs temporal resolution.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Actively tailored spatiotemporal images of quantum interference on the picometer and femtosecond scales

Interference fringes of quantum waves weave highly regular space-time images, which could be seen in various wave systems such as wave packets in atoms and molecules, Bose-Einstein condensates, and fermions in a box potential. We have experimentally designed and visualized spatiotemporal images of dynamical quantum interferences of two counterpropagating nuclear wave packets in the iodine molecule; the wave packets are generated with a pair of femtosecond laser pulses whose relative phase is locked within the attosecond time scale. The design of the image has picometer and femtosecond resolutions, and changes drastically as we change the relative phase of the laser pulses, providing a direct spatiotemporal control of quantum interferences.

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.

Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.

Attosecond double-slit experiment

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.

FEMTOSECOND LASER PHOTOELECTRON SPECTROSCOPY ON ATOMS AND SMALL MOLECULES: Prototype Studies in Quantum Control

▪ Abstract  We review prototype studies in the area of quantum control with femtosecond lasers. We restrict this discussion to atoms and diatomics under gas-phase collision-free conditions to allow for a comparison between theory and experiment. Both the perturbative regime and the nonperturbative regime of the light-matter interaction are addressed. To that end, atomic/molecular beam techniques are combined together with femtosecond laser techniques and energy-resolved photoelectron spectroscopy and ion detection. Highly detailed information on the laser-induced quantum dynamics is extracted with the help of kinetic energy-resolved photoelectron spectroscopy.

Femtosecond lasers in gas phase chemistry

This critical review is intended to provide an overview of the state-of-the-art in femtosecond laser technology and recent applications in ultrafast gas phase chemical dynamics. Although "femtochemistry" is not a new subject, there have been some tremendous advances in experimental techniques during the last few years. Time-resolved photoelectron spectroscopy and ultrafast electron diffraction have enabled us to observe molecular dynamics through a wider window. Attosecond laser sources, which have so far only been exploited in atomic physics, have the potential to probe chemical dynamics on an even faster timescale and observe the motions of electrons. Huge progress in pulse shaping and pulse characterisation methodology is paving the way for exciting new advances in the field of coherent control.

Ponderomotive shearing for spectral interferometry of extreme-ultraviolet pulses

We propose a novel method for completely characterizing ultrashort pulses at extreme-ultraviolet (XUV) wavelengths by adapting the technique of spectral phase interferometry for direct electric-field reconstruction to this spectral region. Two-electron wave packets are coherently produced by photoionizing atoms with two time-delayed replicas of the XUV pulse. For one of the XUV pulses, photoionization occurs in the presence of a strong infrared pulse that ponderomotively shifts the binding energy, thereby providing the spectral shear needed for reconstruction of the spectral phase of the XUV pulse.