Direct Experimental Access to the Nonadiabatic Initial Momentum Offset upon Tunnel Ionization

Spatiotemporal imaging and shaping of electron wave functions using novel attoclock interferometry

Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Characterizing and shaping the electron wave function on its natural timescale is of paramount importance for understanding and controlling ultrafast electron dynamics in atoms, molecules and condensed matter. Here we propose a novel attoclock interferometry to shape and image the electron wave function in atomic photoionization. Using a combination of a strong circularly polarized second harmonic and a weak linearly polarized fundamental field, we spatiotemporally modulate the atomic potential barrier and shape the electron wave functions, which are mapped into a temporal interferometry. By analyzing the two-color phase-resolved and angle-resolved photoelectron interference, we are able to reconstruct the spatiotemporal evolution of the shaping on the amplitude and phase of electron wave function in momentum space within the optical cycle, from which we identify the quantum nature of strong-field ionization and reveal the effect of the spatiotemporal properties of atomic potential on the departing electron. This study provides a new approach for spatiotemporal shaping and imaging of electron wave function in intense light-matter interactions and holds great potential for resolving ultrafast electronic dynamics in molecules, solids, and liquids.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400 nm laser pulse, the ionization probability is reduced if another relatively weak 800 nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800 nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Orbital-resolved photoelectron momentum distributions of F- ions in a counter-rotating bicircular field

We present a theoretical study of the orbital-resolved photoelectron momentum distributions (PMDs) of F^- ions by a two-color counter-rotating circularly polarized field. We show that the PMDs of F^- ions can be modulated from an isotropic symmetric distribution into a three-lobe one by adding a weak fundamental counter-rotating field to the intense second harmonic circularly polarized field, and this modulation strongly depends on the initial atomic orbital. The PMDs simulated by the strong-field approximation method show good agreement with those obtained by solving the time-dependent Schrödinger equation. Based on the strong-field approximation method, we find that the radial momentum shift of PMDs for different orbitals is the fingerprint of orbital-dependent initial momentum at the tunnel exit. More importantly, we demonstrate that the lobes in PMDs appear in sequential order, highlighting that the scheme can be viewed as controllable rotating temporal Young's two-slit interferometer.

Nonadiabatic strong field ionization of noble gas atoms in elliptically polarized laser pulses

We present theoretically obtained photoelectron momentum distributions (PMDs) for the strong field ionization of argon in an elliptically polarized laser field at a central wavelength of 400 nm. Three different theoretical approaches, namely, a numerical solution of the time-dependent Schrödinger equation (TDSE), a nonadiabatic model, and a classical-trajectory Monte Carlo (CTMC) model are adopted in our calculations. From the TDSE calculations, it is found that the attoclock offset angle (most probable electron emission angles with respect to the minor axis of the laser's polarization ellipse) in the PMD increases with rising ATI order. While this result cannot be reproduced by the CTMC model, the nonadiabatic model achieves good agreement with the TDSE result. Analysis shows that the nonadiabatic corrections of the photoelectron initial momentum distribution (in both longitudinal and transverse directions with respect to the tunneling direction) and nonadiabatic correction of the tunneling exit are responsible for the ATI order-dependent angular shift.

Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit

If the time evolution of a quantum state leads back to the initial state, a geometric phase is accumulated that is known as the Berry phase for adiabatic evolution or as the Aharonov-Anandan (AA) phase for nonadiabatic evolution. We evaluate these geometric phases using Floquet theory for systems in time-dependent external fields with a focus on paths leading through a degeneracy of the eigenenergies. Contrary to expectations, the low-frequency limits of the two phases do not always coincide. This happens as the degeneracy leads to a slow convergence of the quantum states to adiabaticity, resulting in a nonzero finite or divergent contribution to the AA phase. Steering the system adiabatically through a degeneracy provides control over the geometric phase as it can cause a π shift of the Berry phase. On the other hand, we revisit an example of degeneracy crossing proposed by AA. We find that, at suitable driving frequencies, both geometric-phase definitions give the same result and the dynamical phase is zero due to the symmetry of time evolution about the point of degeneracy, providing an advantageous setup for manipulation of quantum states.

Nonadiabatic Strong Field Ionization of Atomic Hydrogen

We present experimental data on the nonadiabatic strong field ionization of atomic hydrogen using elliptically polarized femtosecond laser pulses at a central wavelength of 390 nm. Our measured results are in very good agreement with a numerical solution of the time-dependent Schrödinger equation (TDSE). Experiment and TDSE show four above-threshold ionization peaks in the electron's energy spectrum. The most probable emission angle (also known as "attoclock offset angle" or "streaking angle") is found to increase with energy, a trend that is opposite to standard predictions based on Coulomb interaction with the ion. We show that this increase of deflection angle can be explained by a model that includes nonadiabatic corrections of the initial momentum distribution at the tunnel exit and nonadiabatic corrections of the tunnel exit position itself.

Picometer-Resolved Photoemission Position within the Molecule by Strong-Field Photoelectron Holography

Laser-induced tunneling ionization is one of the fundamental light-matter interaction processes. An accurate description of the tunnel-ionized electron wave packet is central to understanding and controlling subsequent electron dynamics. Because of the anisotropic molecular structure, tunneling ionization of molecules involves considerable challenges in accurately describing the tunneling electron wave packet. Up to now, some basic properties of the tunneling electron from molecules still remain unexplored. Here, we demonstrate that the tunneling electron from a molecule is not always emitted from the geometric center of the molecule along the tunnel direction. Rather, the photoemission position depends on the molecular orientation. Using a photoelectron holographic technique, we determine the photoemission position for a nitrogen molecule relative to the molecular geometric center to be 95±21  pm when the molecular axis is oriented along the tunnel direction. Our Letter poses, and answers experimentally, a fundamental question as to where the molecular photoionization actually begins, which has significant implications for time-resolved probing of valence electron dynamics in molecules.

Probing the Spin-Orbit Time Delay of Multiphoton Ionization of Kr by Bicircular Fields

We study multiphoton ionization of Kr atoms by circular 400-nm laser fields and probe its photoelectron circular dichroism with the weak corotating and counterrotating circular fields at 800 nm. The unusual momentum- and energy-resolved photoelectron circular dichroisms from the ^{2}P_{1/2} ionic state are observed as compared with those from ^{2}P_{3/2} ionic state. We identify an anomalous ionization enhancement at sidebands related to the ^{2}P_{1/2} ionic state on photoelectron momentum distribution when switching the relative helicity of the two fields from corotating to counterrotating. By performing the two-color intensity-continuously-varying experiments and the pump-probe experiment, we find a specific mixed-photon populated resonant transition channel in counterrotating fields that contributes to the ionization enhancement. We then probe the time delay between the two spin-orbit coupled ionic states (^{2}P_{1/2} and ^{2}P_{3/2}) using bicircular fields and reveal that the resonant transition has an insignificant effect on the relative spin-orbit time delay.

Angular dependence of the Wigner time delay upon tunnel ionization of H2

When a very strong light field is applied to a molecule an electron can be ejected by tunneling. In order to quantify the time-resolved dynamics of this ionization process, the concept of the Wigner time delay can be used. The properties of this process can depend on the tunneling direction relative to the molecular axis. Here, we show experimental and theoretical data on the Wigner time delay for tunnel ionization of H₂ molecules and demonstrate its dependence on the emission direction of the electron with respect to the molecular axis. We find, that the observed changes in the Wigner time delay can be quantitatively explained by elongated/shortened travel paths of the emitted electrons, which occur due to spatial shifts of the electrons' birth positions after tunneling. Our work provides therefore an intuitive perspective towards the Wigner time delay in strong-field ionization.

Electric Nondipole Effect in Strong-Field Ionization

Strong-field ionization of atoms by circularly polarized femtosecond laser pulses produces a donut-shaped electron momentum distribution. Within the dipole approximation this distribution is symmetric with respect to the polarization plane. The magnetic component of the light field is known to shift this distribution forward. Here, we show that this magnetic nondipole effect is not the only nondipole effect in strong-field ionization. We find that an electric nondipole effect arises that is due to the position dependence of the electric field and which can be understood in analogy to the Doppler effect. This electric nondipole effect manifests as an increase of the radius of the donut-shaped photoelectron momentum distribution for forward-directed momenta and as a decrease of this radius for backwards-directed electrons. We present experimental data showing this fingerprint of the electric nondipole effect and compare our findings with a classical model and quantum calculations.

Nonadiabatic effects in the double ionization of atoms driven by a circularly polarized laser pulse

We study the double ionization of atoms subjected to circularly polarized (CP) laser pulses. We analyze two fundamental ionization processes: the sequential (SDI) and nonsequential (NSDI) double ionization in the light of the rotating frame (RF) which naturally embeds nonadiabatic effects in CP pulses. We use and compare two adiabatic approximations: The adiabatic approximation in the laboratory frame (LF) and the adiabatic approximation in the RF. The adiabatic approximation in the RF encapsulates the energy variations of the electrons on subcycle timescales happening in the LF and this, by fully taking into account the ion-electron interaction. This allows us to identify two nonadiabatic effects including the lowering of the threshold intensity at which over-the-barrier ionization happens and the lowering of the ionization time of the electrons. As a consequence, these nonadiabatic effects facilitate over-the-barrier ionization and recollision-induced ionizations. We analyze the outcomes of these nonadiabatic effects on the recollision mechanism. We show that the laser envelope plays an instrumental role in a recollision channel in CP pulses at the heart of NSDI.

Relative phase effect of nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields

Relative phase effect of nonsequential double ionization (NSDI) of aligned molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results show that NSDI yield in counter-rotating TCCP fields sensitively depends on the relative phase of the two components, which exhibits a sin-like behavior with the period of π/2. NSDI yield achieves its maximum at the relative phase π/8 and minimum at 3π/8. Back analysis indicates the recollision time and the return angle of the electron strongly depend on the relative phase of the two components, which results in the dominant emission direction of the electrons, is different for different relative phases. This indicates that the recollision process can be steered by changing the relative phase of the two components in counter-rotating TCCP laser fields. Meantime, it provides an avenue to obtain information about the recollision time and the return angle in the recollision process from the electron momentum distribution.

Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses

Strong-field photoelectron holography (SFPH), originating from the interference of the direct electron and the rescattering electron in tunneling ionization, is a significant tool for probing structure and electronic dynamics in molecules. We theoretically study SFPH by counter rotating two-color circularly (CRTC) polarized laser pulses. Different from the case of the linearly polarized laser field, where the holographic structure in the photoelectron momentum distribution (PEMD) is clustered around the laser polarization direction, in the CRTC laser fields, the tunneling ionized electrons could recollide with the parent ion from different angles and thus the photoelectron hologram appears in the whole plane of laser polarization. This property enables structural information delivered by the electrons scattering the molecule from different angles to be recorded in the two-dimensional photoelectron hologram. Moreover, the electrons tunneling at different laser cycles are streaked to different angles in the two-dimensional polarization plane. This property enables us to probe the sub-cycle electronic dynamics in molecules over a long time window with the multiple-cycle CRTC laser pulses.

Photoelectron Holographic Interferometry to Probe the Longitudinal Momentum Offset at the Tunnel Exit

Laser-induced electron tunneling underlies numerous emerging spectroscopic techniques to probe attosecond electron dynamics in atoms and molecules. The improvement of those techniques requires an accurate knowledge of the exit momentum for the tunneling wave packet. Here we demonstrate a photoelectron interferometric scheme to probe the electron momentum longitudinal to the tunnel direction at the tunnel exit by measuring the photoelectron holographic pattern in an orthogonally polarized two-color laser pulse. In this scheme, we use a perturbative 400-nm laser field to modulate the photoelectron holographic fringes generated by a strong 800-nm pulse. The fringe shift offers direct experimental access to the intermediate canonical momentum of the rescattering electron, allowing us to reconstruct the momentum offset at the tunnel exit with high accuracy. Our result unambiguously proves the existence of nonzero initial longitudinal momentum at the tunnel exit and provides fundamental insights into the nonquasistatic nature of the strong-field tunneling.

Nonsequential double ionization by co-rotating two-color circularly polarized laser fields

Nonsequential double ionization (NSDI) of Ar in co-rotating two-color circularly polarized (TCCP) laser fields is investigated with a three-dimensional classical ensemble model. Our numerical results indicate that co-rotating TCCP fields can induce NSDI by recollision process, while the yield is an order of magnitude lower than counter-rotating case. NSDI yield in co-rotating TCCP fields strongly depends on field ratio of the two colors and achieves its maximum at a ratio of 2.4. In co-rotating TCCP fields, the short recollision trajectory with traveling time smaller than one cycle is dominant. Moreover, the recollision time in co-rotating TCCP laser fields depends on the field ratio, which is mapped to the electron momentum distribution. This provides anavenue to obtain information about recollision time and access the subcycle dynamics of the recollision process.

Detecting and Characterizing the Nonadiabaticity of Laser-Induced Quantum Tunneling

The nonadiabaticity of quantum tunneling through an evolving barrier is relevant to resolving laser-driven dynamics of atoms and molecules at an attosecond timescale. Here, we propose and demonstrate a novel scheme to detect the nonadiabatic behavior of tunnel ionization studied in an attoclock configuration, without counting on the laser intensity calibration or the modeling of the Coulomb effect. In our scheme, the degree of nonadiabaticity for tunneling scenarios in elliptically polarized laser fields can be steered continuously simply with the pulse ellipticity, while the critical instantaneous vector potentials remain identical. We observe the characteristic feature of the measured photoelectron momentum distributions, which matches the distinctive prediction of nonadiabatic theories. In particular, our experiments demonstrate that the nonadiabatic initial transverse momentum at the tunnel exit is approximately proportional to the instantaneous effective Keldysh parameters in the tunneling regime, as predicted theoretically by Ohmi, Tolstikhin, and Morishita [Phys. Rev. A 92, 043402 (2015)PLRAAN1050-294710.1103/PhysRevA.92.043402]. Our study clarifies a long-standing controversy over the validation of the adiabatic approximation and will substantially advance studies of laser-induced ultrafast dynamics in experiments.

Universal Description of the Attoclock with Two-Color Corotating Circular Fields

We experimentally measure the laser-intensity-dependent photoelectron momentum distributions (PMDs) of Ar atoms with two-color (ω+2ω) corotating circularly polarized fields. The interference patterns on PMDs reveal complex structures with respect to the laser intensity ratio. The main above-threshold ionization peaks and sidebands on PMD distribute oppositely when the fundamental field is much weaker than the second-harmonic field, and the PMD reveals a characteristic single-lobe distribution when the two colors have comparable intensities. Using strong-field approximation, we analytically explain how the interference pattern on PMD evolves with respect to the relative laser intensity. By analyzing the interference pattern, we reveal the phase difference and the temporal evolution of the emitting electron wave packets. We show that, when monitoring the intensity ratio, the double-pointer attoclock geometry with corotating circular fields can be universally mimicked as the spatially rotating temporal double-slit experiments with the variable slit width, which can be used to probe and control strong-field ionization.