General theory of carrier-envelope phase effects

Ultra-Nonlinear Subcycle Photoemission of Few-Electron States from Sharp Gold Nanotapers

The generation of ultrashort electron wavepackets is crucial for the development of ultrafast electron microscopes. Recent studies on Coulomb-correlated few-electron number states, photoemitted from sharp metallic tapers, have shown emission nonlinearities in the multiphoton photoemission regime which scale with the electron number. Here, we study few-electron photoemission from gold nanotapers triggered by few-cycle near-infrared pulses, demonstrating extreme 20th-order nonlinearities for electron triplets. We report interferometric autocorrelation traces of the electron yield that are quenched to a single emission peak with subfemtosecond duration due to these high nonlinearities. The modulation of the emission yield by the carrier-envelope phase suggests that electron emission predominantly occurs during a single half cycle of the driving laser field. When applying a bias voltage to the tip, recollisions in the electron trajectories are suppressed and coherent subcycle electron beams are generated with promising prospects for ultrafast electron microscopy with subcycle time resolution.

Efficient Control of Electron Localization and Probability Modulation with Synthesized Two-Color Intense Laser Pulses

A coupled electron-nuclear dynamical study at attosecond time scale is performed on the HD+ and H2+ molecular ions under the influence of synthesized intense two-color electric fields. We have employed ω - 2ω and also, ω - 3ω two-color fields in the infrared/mid-infrared regime to study the different fragmentation processes originating from the interference of n - (n + i) (i = 1, 2) photon absorption pathways. The branching ratios corresponding to different photofragments are controlled by tuning the relative phase as well as intensity of the two-color pulses, while the effect of the initial nuclear wave function is also studied by taking an individual vibrational eigenstate or a coherent superposition of several eigenstates of HD+ and H2+. By comprehensive analysis, the efficacy of the two different types of synthesized two-color pulses (ω - 2ω and ω - 3ω) are analyzed with respect to one-color intense pulses in terms of controlling the probability modulation and electron localization asymmetry and compared with previous theoretical calculations and experimental findings. Through the detailed investigation, we have addressed which one is the major controlling knob to have better electron localization as well as probability modulation.

Vibronic Correlations in Molecular Strong-Field Dynamics

We investigate the ultrafast vibronic dynamics triggered by intense femtosecond infrared pulses in small molecules. Our study is based on numerical simulations performed with 2D model molecules and analyzed in the perspective of the renowned Lochfrass and bond-softening models. We give a new interpretation of the observed nuclear wave packet dynamics with a focus on the phase of the bond oscillations. Our simulations also reveal intricate features in the field-induced nuclear motion that are not accounted for by existing models. Our analyses assign these features to strong dynamical correlations between the active electron and the nuclei, which significantly depend on the carrier envelope phase of the pulse, even for relatively "long" pulses, which should make them experimentally observable.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

Post-Ionization Dynamics of the Polar Molecule OCS in Asymmetric Laser Fields

We have investigated the dissociation mechanisms of the prototypical heavy polar molecule OCS into the two break-up channels of the dication, OCS²⁺ → O⁺ + CS⁺ and OC⁺ + S⁺, in phase-locked two-color intense laser fields. The branching ratio of the breaking of the C–O and C–S bonds followed a pronounced 2π-oscillation with a modulation depth of 11%, depending on the relative phase of the two-color laser fields. The fragment ejection direction of both break-up channels reflects the anisotropy of the tunneling ionization rate, following a 2π-periodicity, as well. The two dissociation pathways in the C–S bond breaking channel show different phase dependencies of the fragment ejection direction, which are assigned to post-ionization dynamics. These observations, resulting from the excitation with asymmetric two-color intense laser fields, supported by state-of-the-art theoretical simulations, reveal the importance of post-ionization population dynamics in addition to tunneling ionization in the molecular fragmentation processes, even for heavy polar molecules.

Dissociative ionization of the H2 molecule under a strong elliptically polarized laser field: carrier-envelope phase and orientation effect

A coupled electron–nuclear dynamical study is performed to investigate the sub-cycle dissociation and ionization of the H2 molecule in a strong 750 nm 4.5 fs elliptically polarized laser pulse.

Rotation Active Sensors Based on Ultrafast Fibre Lasers

Gyroscopes merit an undeniable role in inertial navigation systems, geodesy and seismology. By employing the optical Sagnac effect, ring laser gyroscopes provide exceptionally accurate measurements of even ultraslow angular velocity with a resolution up to 10-11 rad/s. With the recent advancement of ultrafast fibre lasers and, particularly, enabling effective bidirectional generation, their applications have been expanded to the areas of dual-comb spectroscopy and gyroscopy. Exceptional compactness, maintenance-free operation and rather low cost make ultrafast fibre lasers attractive for sensing applications. Remarkably, laser gyroscope operation in the ultrashort pulse generation regime presents a promising approach for eliminating sensing limitations caused by the synchronisation of counter-propagating channels, the most critical of which is frequency lock-in. In this work, we overview the fundamentals of gyroscopic sensing and ultrafast fibre lasers to bridge the gap between tools development and their real-world applications. This article provides a historical outline, highlights the most recent advancements and discusses perspectives for the expanding field of ultrafast fibre laser gyroscopes. We acknowledge the bottlenecks and deficiencies of the presented ultrafast laser gyroscope concepts due to intrinsic physical effects or currently available measurement methodology. Finally, the current work outlines solutions for further ultrafast laser technology development to translate to future commercial gyroscopes.

Coupled nuclear and electron dynamics in the vicinity of a conical intersection

Ultrafast optical techniques allow us to study ultrafast molecular dynamics involving both nuclear and electronic motion. To support interpretation, theoretical approaches are needed that can describe both the nuclear and electron dynamics. Hence, we revisit and expand our ansatz for the coupled description of the nuclear and electron dynamics in molecular systems (NEMol). In this purely quantum mechanical ansatz, the quantum-dynamical description of the nuclear motion is combined with the calculation of the electron dynamics in the eigenfunction basis. The NEMol ansatz is applied to simulate the coupled dynamics of the molecule NO₂ in the vicinity of a conical intersection (CoIn) with a special focus on the coherent electron dynamics induced by the non-adiabatic coupling. Furthermore, we aim to control the dynamics of the system when passing the CoIn. The control scheme relies on the carrier envelope phase of a few-cycle IR pulse. The laser pulse influences both the movement of the nuclei and the electrons during the population transfer through the CoIn.

High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau

Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

Controlling the Ultrafast Dynamics of HD+ by the Carrier-Envelope Phases of an Ultrashort Laser Pulse: A Quasi-Classical Dynamics Study

A theoretical study on the coupled electron-nuclear dynamics of HD⁺ molecular ions under ultrashort, intense laser pulses is performed by employing a well-established quasi-classical model. The influence of the laser carrier-envelope phase on various channel (H + D⁺, D + H⁺, and H⁺ + D⁺) probabilities is investigated at different laser field intensities. The carrier-envelope phase is found to govern the dissociation (H + D⁺ and D + H⁺) and Coulomb explosion (H⁺ + D⁺) channel probabilities. The kinetic energy release distributions of the fragments are also found to be sensitive to the carrier-envelope phase of the laser pulse. Our results are in agreement with the previously reported quantum dynamics studies and experiments.

Generalized Phase Sensitivity of Directional Bond Breaking in the Laser-Molecule Interaction

We establish a generalized picture of the phase sensitivity of laser-induced directional bond breaking using the H_{2} molecule as the example. We show that the well-known proton ejection anisotropy measured with few-cycle pulses as a function of their carrier-envelope phases arises as an amplitude modulation of an intrinsic anisotropy that is sensitive to the laser phase at the ionization time and determined by the molecule's electronic structure. Our work furthermore reveals a strong electron-proton correlation that may open up a new approach to experimentally accessing the laser-sub-cycle intramolecular electron dynamics also in larger molecules.

Controlling Electron Dynamics with Carrier-Envelope Phases of a Laser Pulse

A theoretical study on the ionization dynamics of carbon atom irradiated with a few-cycle, intense laser field is performed within a quasiclassical model to get mechanistic insights into an earlier reported carrier-envelope phase dependency of ionization probabilities of an atom [ Phys. Rev. Lett. 2013, 110, 083602]. The carrier-envelope phase of the laser pulse is found to govern the overall dynamics, reflecting its importance in controlling electronic motion. To understand the origin of this effect, individual trajectories were analyzed at a particular laser intensity. We found that a variation in the carrier-envelope phase affects the angle of ejection of the electrons and subsequently the attainment of the desired final state.

Two-Dimensional Control of Electron Localization in H2 Dissociation with Elliptically Polarized Few-Cycle Pulses

We demonstrate two-dimensional control over the chargelocalization in H2 dissociation using elliptically polarized laser pulses. The influences of the CEP and the laser phase at the instant of ionization are investigated.

Observing electron localization in a dissociating H2+ molecule in real time

Dissociation of diatomic molecules with odd number of electrons always causes the unpaired electron to localize on one of the two resulting atomic fragments. In the simplest diatomic molecule H₂⁺ dissociation yields a hydrogen atom and a proton with the sole electron ending up on one of the two nuclei. That is equivalent to breaking of a chemical bond-the most fundamental chemical process. Here we observe such electron localization in real time by performing a pump-probe experiment. We demonstrate that in H₂⁺ electron localization is complete in just 15 fs when the molecule's internuclear distance reaches 8 atomic units. The measurement is supported by a theoretical simulation based on numerical solution of the time-dependent Schrödinger equation. This observation advances our understanding of detailed dynamics of molecular dissociation.

Carrier-envelope phase dependent photoelectron energy spectra in low intensity regime

We study the carrier-envelope phase (CEP) dependent photoelectron energy spectra from above-threshold ionization by numerically solving the time-dependent Schrödinger equation of hydrogen atom in a few-cycle laser field at intensities in the range of (2-10) × 10¹³ W/cm². Depending on the electron energy and the laser intensity, the yield of the photoelectron reveals clear oscillations with respect to the CEP. At high laser intensities (larger than ~3 × 10¹³ W/cm²), the yield of the high-energy photoelectrons (larger than 2U_p, with U_p being the ponderomotive potential) shows two kinds of oscillations with the CEP for different electron energies. There is a clear phase jump for those two kinds of oscillations. In contrast, at low laser intensities (smaller than ~3 × 10¹³ W/cm²), the phase of the oscillation for the high-energy photoelectron yield with the CEP is nearly independent on the electron energy, which will reduce the sensitivity of the retrieval of single-shot CEP using the method reported by T. Wittmann et al. [Nat. Phys. 5, 357 (2009)] at low laser intensities. We further show that the low-energy photoelectrons display distinct CEP-dependent intercycle interference fringes, providing an alternative approach to retrieve the CEP with high sensitivity in a few-cycle laser field with low intensity.

Selective bond breaking of CO2 in phase-locked two-color intense laser fields: laser field intensity dependence

One of the two equivalent C–O bonds of CO₂ can be selectively broken by phase-locked two-color intense laser fields.

Carrier-envelope phase dependence of the directional fragmentation and hydrogen migration in toluene in few-cycle laser fields

The dissociative ionization of toluene initiated by a few-cycle laser pulse as a function of the carrier envelope phase (CEP) is investigated using single-shot velocity map imaging. Several ionic fragments, CH3 (+), H2 (+), and H3 (+), originating from multiply charged toluene ions present a CEP-dependent directional emission. The formation of H2 (+) and H3 (+) involves breaking C-H bonds and forming new bonds between the hydrogen atoms within the transient structure of the multiply charged precursor. We observe appreciable intensity-dependent CEP-offsets. The experimental data are interpreted with a mechanism that involves laser-induced coupling of vibrational states, which has been found to play a role in the CEP-control of molecular processes in hydrocarbon molecules, and appears to be of general importance for such complex molecules.

Carrier envelope phase shifter for broadband terahertz pulses

We demonstrated controlled shifting of the internal phase of broadband terahertz (THz) pulses. The internal phase of an ultrashort pulse is called the carrier envelope phase (CEP), which is an important parameter in the interaction of few-cycle light pulses and matter. Our CEP shifter utilizes the ultra-broadband feature of prism wave plates. We analytically derived the amount of CEP shift achievable by the CEP shifter using Jones matrixes. THz time-domain measurements clearly showed the shift of the CEP, and the results agreed well with the calculated values. The CEP shift was as high as 2π, indicating that any CEP values can be chosen using our CEP shifter.

Carrier-envelope-phase insensitivity in high-order harmonic generation driven by few-cycle laser pulses

We present evidence for self-stabilization of the relative spectral phase of high-order harmonic emission against intensity variations of the driving field. Our results demonstrate that, near the laser focus, phase matching of the harmonic field from a macroscopic target can compensate for the intensity dependence of the intrinsic phase of the harmonics emitted by a single radiator. As a consequence, we show experimentally and theoretically the insensitivity of the harmonic spectra produced at the laser focus against variations of the carrier-envelope phase (CEP) of a sub-two-cycle driving field. In addition, the associated attosecond pulse trains exhibit phase locking against CEP changes of the few-cycle driver.

Coherent electronic wave packet motion in C(60) controlled 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 (4 fs) pulse at 720 nm. 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.

Identification of a previously unobserved dissociative ionization pathway in time-resolved photospectroscopy of the deuterium molecule

A femtosecond vacuum ultraviolet (VUV) pulse with high spectral resolution (<200  meV) is selected from the laser-driven high order harmonics. This ultrafast VUV pulse is synchronized with an infrared (IR) laser pulse to study dissociative ionization in deuterium molecules. At a VUV photon energy of 16.95 eV, a previously unobserved bond-breaking pathway is found in which the dissociation direction does not follow the IR polarization. We interpret it as corresponding to molecules predissociating into two separated atoms, one of which is photoionized by the following IR pulse. A time resolved study allows us to determine the lifetime of the intermediate predissociation process to be about 1 ps. Additionally, the dissociative ionization pathways show high sensitivity to the VUV photon energy. As the VUV photon energy is blueshifted to 17.45 eV, the more familiar bond-softening channel is opened to compete with the newly discovered pathway. The interpretation of different pathways is supported by the energy sharing between the electron and nuclei.

Two-dimensional directional proton emission in dissociative ionization of H(2)

An intense phase-controlled orthogonally polarized two-color ultrashort laser pulse is used to singly ionize and dissociate H_{2} into a neutral hydrogen atom and a proton. Emission-direction and kinetic-energy dependent asymmetric dissociation of H_{2} is observed as a function of the relative phase of the orthogonally polarized two-color pulse. Significant asymmetric proton emission is measured in the direction between two polarization axes. Our numerical simulations of the time-dependent Schrödinger equation reproduce many of the observed features. The asymmetry is attributed to the coherent superposition of two-dimensional nuclear wave packets with opposite parities, which have the same energies and overlap in the same emission directions.

Theoretical investigation of the competitive mechanism between dissociation and ionization of H₂⁺ in intense field

The competitive mechanism between dissociation and ionization of hydrogen molecular ion in intense field has been theoretically investigated by using an accurate non-Born-Oppenheimer method. The relative yield of fragments indicates that the dissociation and ionization channels are competitive with the increasing laser intensity from 5.0 × 10(13) to 2.0 × 10(14) W/cm(2). In the case of intensity lower than 1.0 × 10(14) W/cm(2), the dissociation channel is dominant, with a minor contribution from ionization. The mechanism of dissociation includes the contributions from the bond softening, bond hardening, below-threshold dissociation, and above-threshold dissociation, which are strongly dependent on the laser intensity and initial vibrational state. Furthermore, the ionization dominates over the dissociation channel at the highest intensity of 2.0 × 10(14) W/cm(2). The reasonable origin of ionization is ascribed as the above-threshold Coulomb explosion, which has been demonstrated by the space-time dependent ionization rate. Moreover, the competition mechanism between dissociation and ionization channels are displayed on the total kinetic energy resolved (KER) spectra, which could be tested at current experimental conditions.

Carrier-envelope-phase-dependent above-threshold ionization of xenon observed with multi-cycle laser pulses

Carrier-envelope-phase (CEP)-dependent modulation was measured in above-threshold ionization of xenon driven with 30-fs laser pulses. We showed the dependence from the asymmetry map obtained using a velocity map imaging spectrometer, up to 17 eV in photoelectron energy. The dependence appeared to be linear with a slope of one photon energy increase per CEP change of 2π and did not rely on the sign or the amount of laser chirp. Our results indicated the existence of the quantum interference between different multiphoton ionization paths.

Carrier-envelope phase control over pathway interference in strong-field dissociation of H2+

The dissociation of an H2+ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4×10(14) W/cm2 with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H+ fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net zero-photon and one-photon interference predominantly contributes at H+ + H kinetic energy releases of 0.2-0.45 eV, and net two-photon and one-photon interference contributes at 1.65-1.9 eV. These measurements of the benchmark H2+ molecule offer the distinct advantage that they can be quantitatively compared with ab initio theory to confirm our understanding of strong-field coherent control via the carrier-envelope phase.

Coherent control at its most fundamental: carrier-envelope-phase-dependent electron localization in photodissociation of a H2(+) molecular ion beam target

Measurements and calculations of the absolute carrier-envelope-phase (CEP) effects in the photodissociation of the simplest molecule, H2(+), with a 4.5-fs Ti:sapphire laser pulse at intensities up to (4±2)×10(14)  W/cm2 are presented. Localization of the electron with respect to the two nuclei (during the dissociation process) is controlled via the CEP of the ultrashort laser pulses. In contrast to previous CEP-dependent experiments with neutral molecules, the dissociation of the molecular ions is not preceded by a photoionization process, which strongly influences the CEP dependence. Kinematically complete data are obtained by time- and position-resolved coincidence detection. The phase dependence is determined by a single-shot phase measurement correlated to the detection of the dissociation fragments. The experimental results show quantitative agreement with ab initio 3D time-dependent Schrödinger equation calculations that include nuclear vibration and rotation.

Weak-field, multiple-cycle carrier envelope phase effects in laser excitation

Although the absolute or carrier envelope phase (CEP) of a laser pulse is usually assumed to be effective for ultrashort and/or ultrastrong pulses only, it is demonstrated that these limitations can eventually be removed. Therefore, the excitation of a model positively charged homonuclear diatomic molecule, in which four electronic states are coupled by the laser field, is studied. In an initial step, nuclear wave packets in two dissociative states are prepared. Upon reaching the fragment channel, a weak pulse interacts with the system and prepares CEP-dependent asymmetries associated with electron density localized on one or the other fragmentation product.

Enhancing the intense field control of molecular fragmentation

We describe a pump-probe scheme with which the spatial asymmetry of dissociating molecular fragments-as controlled by the carrier-envelope phase of an intense few-cycle laser pulse-can be enhanced by an order of magnitude or more. We illustrate the scheme using extensive, full-dimensional calculations for dissociation of H(2)(+) and include the averaging necessary for comparison with experiment.

Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses

The steering of electron motion in molecules is accessible with waveform-controlled few-cycle laser light and may control the outcome of light-induced chemical reactions. An optical cycle of light, however, is much shorter than the duration of the fastest dissociation reactions, severely limiting the degree of control that can be achieved. To overcome this limitation, we extended the control metrology to the midinfrared studying the prototypical dissociative ionization of D(2) at 2.1 μm. Pronounced subcycle control of the directional D(+) ion emission from the fragmentation of D(2)(+) is observed, demonstrating unprecedented charge-directed reactivity. Two reaction pathways, showing directional ion emission, could be observed and controlled simultaneously for the first time. Quantum-dynamical calculations elucidate the dissociation channels, their observed phase relation, and the control mechanisms.

Theoretical study of the photodissociation of Li(2)+ in one-color intense laser fields

A theoretical treatment of the photodissociation of the molecular ion Li(2) (+) in one-color intense laser fields, using the time-dependent wave packet approach in a Floquet Born-Oppenheimer representation, is presented. Six electronic states 1,2 (2)Σ(g)(+), 1,2 (2)Σ(u)(+), 1 (2)Π(g), and 1 (2)Π(u) are of relevance in this simulation and have been included. The dependences of the fragmental dissociation probabilities and kinetic energy release (KER) spectra on pulse width, peak intensity, polarization angle, wavelength, and initial vibrational level are analyzed to interpret the influence of control parameters of the external field. Three main dissociation channels, 1 (2)Σ(g)(+) (m = -1), 2 (2)Σ(g)(+) (m = -2), and 2 (2)Σ(u)(+) (m = -3), are seen to dominate the dissociation processes under a wide variety of laser conditions and give rise to well separated groups of KER features. Different dissociation mechanisms for the involved Floquet channels are discussed.