Entanglement in photo-ionization process.

We report a study of the entanglement between the quantized photon field and an atom arising in the photo-ionization process. Our approach is based on an ab initio solution of the time-dependent Schrödinger equation (TDSE) describing the quantum evolution of a bipartite system consisting of the atom and the quantized electromagnetic field. Using the solution of the TDSE, we calculate the reduced photon density matrix, which we subsequently use to compute entanglement entropy. We explain some properties of the entanglement entropy and propose an approximate formula for the entanglement entropy based on the analysis of the density matrix and its eigenvalues. We present the results of a comparative study of the entanglement in the photo-ionization process for various ionization regimes, including the tunneling and the multiphoton ionization regimes.

Tailoring octave-spanning ultrashort laser pulses using multiple prisms.

We demonstrate a novel pulse shaper in which an incident laser beam is angularly dispersed by a first prism, and then it is split into separate beams using multiple prisms. Since this new pulse shaper offers independent control of the amplitude and phase of the separate beams, it can produce pulses having desired temporal shapes. Furthermore, it imposes a significant amount of negative group delay dispersion (GDD) over an octave spectrum near visible, which can compensate for a positive GDD accumulated in the process of spectral broadening. Consequently, single-cycle or few-cycle laser pulses can be produced without the need for chirped mirrors.

High-harmonic generation from a flat liquid-sheet plasma mirror.

High-harmonic radiation can be generated when an ultra-intense laser beam is reflected from an over-dense plasma, known as a plasma mirror. It is considered a promising technique for generating intense attosecond pulses in the extreme ultraviolet and X-ray wavelength ranges. However, a solid target used for the formation of the over-dense plasma is completely damaged by the interaction. Thus, it is challenging to use a solid target for applications such as time-resolved studies and attosecond streaking experiments that require a large amount of data. Here we demonstrate that high-harmonic radiation can be continuously generated from a liquid plasma mirror in both the coherent wake emission and relativistic oscillating mirror regimes. These results will pave the way for the development of bright, stable, and high-repetition-rate attosecond light sources, which can greatly benefit the study of ultrafast laser-matter interactions.

Joint probability calculation of the lateral velocity distribution in strong field ionization process.

We describe an approach to the description of the time-development of the process of strong field ionization of atoms based on the calculation of the joint probability of occurrence of two events, event B being finding atom in the ionized state after the end of the laser pulse, event A being finding a particular value of a given physical observable at a moment of time inside the laser pulse duration. As an example of such an physical observable we consider lateral velocity component of the electron's velocity. Our approach allows us to study time-evolution of the lateral velocity distribution for the ionized electron during the interval of the laser pulse duration. We present results of such a study for the cases of target atomic systems with short range Yukawa and Coulomb interactions.

Interference patterns in ionization of Kramers-Henneberger atom.

We combine IR pump and XUV probe laser pulses to visualize the Kramers-Henneberger (KH) state of the potassium atom. We demonstrate that ionization of such an atom exhibits some molecular-like features such as low order interference maxima in photoelectron momentum spectra. The locations of these maxima allow to estimate spatial dimensions of the KH atom and can be used for accurate calibration of high intensity laser fields. At the same time, we show that an analogy between the KH atom and a homo-nuclear diatomic molecule cannot be extended too far. In particular, higher order interference maxima are very difficult to observe in the case of the KH state. We attribute this to a particular structure of the KH potential which does not confine electron motion to a well-defined potential well unlike in real diatomic molecules.

Effect of the finite speed of light in ionization of extended molecular systems.

We study propagation effects due to the finite speed of light in ionization of extended molecular systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shrödinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the [Formula: see text] molecular ion and the [Formula: see text] dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily accessible than the ground breaking synchrotron measurement by Grundmann et al. (Science 370:339, 2020).

Reconstruction algorithm for tunneling ionization with a perturbation for the time-domain observation of an electric-field.

We present a reconstruction algorithm developed for the temporal characterization method called tunneling ionization with a perturbation for the time-domain observation of an electric field (TIPTOE). The reconstruction algorithm considers the high-order contribution of an additional laser pulse to ionization, enabling the use of an intense additional laser pulse. Therefore, the signal-to-noise ratio of the TIPTOE measurement is improved by at least one order of magnitude compared to the first-order approximation. In addition, the high-order contribution provides additional information regarding the pulse envelope. The reconstruction algorithm was tested with ionization yields obtained by solving the time-dependent Schrödinger equation. The optimal conditions for accurate reconstruction were analyzed. The reconstruction algorithm was also tested using experimental data obtained using few-cycle laser pulses. The reconstructed pulses obtained under different dispersion conditions exhibited good consistency. These results confirm the validity and accuracy of the reconstruction process.

Distribution of absorbed photons in the tunneling ionization process.

We describe a procedure that allows us to solve the three-dimensional time-dependent Schrödinger equation for an atom interacting with a quantized one-mode electromagnetic field. Atom-field interaction is treated in an ab initio way prescribed by quantum electrodynamics. We use the procedure to calculate probability distributions of absorbed photons in the regime of tunneling ionization. We analyze evolution of the reduced photon density matrix describing the state of the field. We show that non-diagonal density matrix elements decay quickly, as a result of the decoherence process. A stochastic model, viewing ionization as a Markovian birth-death process, reproduces the main features of the calculated photon distributions.

Attosecond streaking using a rescattered electron in an intense laser field.

When an atom or molecule is exposed to a strong laser field, an electron can tunnel out from the parent ion and moves along a specific trajectory. This ultrafast electron motion is sensitive to a variation of the laser field. Thus, it can be used as a fast temporal gate for the temporal characterization of the laser field. Here, we demonstrate a new type of attosecond streaking wherein a rescattered electron trajectory is manipulated by an ultrashort laser pulse. The vector potential of the laser pulse is directly recorded in the photoelectron spectra of the rescattered electron. In contrast to high harmonic generation methods, our approach has no directional ambiguity in space, leading to complete in situ temporal characterization. In addition, it provides timing information on ionization and re-scattering events. Therefore, our approach can be a useful tool for the investigation of strong-field processes triggered by rescattering, such as non-sequential double ionization and laser-induced electron diffraction.

Temporal characterization of femtosecond laser pulses using tunneling ionization in the UV, visible, and mid-IR ranges.

To generalize the applicability of the temporal characterization technique called "tunneling ionization with a perturbation for the time-domain observation of an electric field" (TIPTOE), the technique is examined in the multicycle regime over a broad wavelength range, from the UV to the IR range. The technique is rigorously analyzed first by solving the time-dependent Schrödinger equation. Then, experimental verification is demonstrated over an almost 5-octave wavelength range at 266, 1800, 4000 and 8000 nm by utilizing the same nonlinear medium - air. The experimentally obtained dispersion values of the materials used for the dispersion control show very good agreement with the ones calculated using the material dispersion data and the pulse duration results obtained for 1800 and 4000 nm agree well with the frequency-resolved optical gating measurements. The universality of TIPTOE arises from its phase-matching-free nature and its unprecedented broadband operation range.

Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities.

We present a detailed experimental and theoretical study on the relativistic nondipole effects in strong-field atomic ionization by near-infrared linearly polarized few-cycle laser pulses in the intensity range of 10^{14}-10^{15} W/cm^{2}. We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly ab initio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counterintuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between the experimental results and theoretical predictions.

Generation of a single-cycle pulse using a two-stage compressor and its temporal characterization using a tunnelling ionization method.

A single-cycle laser pulse was generated using a two-stage compressor and characterized using a pulse characterization technique based on tunnelling ionization. A 25-fs, 800-nm laser pulse was compressed to 5.5 fs using a gas-filled hollow-core fibre and a set of chirped mirrors. The laser pulse was further compressed, down to the single-cycle limit by propagation through multiple fused-silica plates and another set of chirped mirrors. The two-stage compressor mitigates the development of higher-order dispersion during spectral broadening. Thus, a single-cycle pulse was generated by compensating the second-order dispersion using chirped mirrors. The duration of the single-cycle pulse was 2.5 fs, while its transform-limited duration was 2.2 fs. A continuum extreme ultraviolet spectrum was obtained through high-harmonic generation without applying any temporal gating technique. The continuum spectrum was shown to have a strong dependence on the carrier-envelope phase of the laser pulse, confirming the generation of a single-cycle pulse.

Exit point in the strong field ionization process.

We analyze the process of strong field ionization using the Bohmian approach. This allows retention of the concept of electron trajectories. We consider the tunnelling regime of ionization. We show that, in this regime, the coordinate distribution for the ionized electron has peaks near the points in space that can be interpreted as exit points. The interval of time during which ionization occurs is marked by a quick broadening of the coordinate distribution. The concept of the exit point in the tunneling regime, which has long been assumed for the description of strong field ionization, is justified by our analysis.

Full characterization of an attosecond pulse generated using an infrared driver.

The physics of attosecond pulse generation requires using infrared driving wavelength to reach the soft X-rays. However, with longer driving wavelength, the harmonic conversion efficiency drops significantly. It makes the conventional attosecond pulse measurement using streaking very difficult due to the low photoionization cross section in the soft X-rays region. In-situ measurement was developed for precisely this purpose. We use in-situ measurement to characterize, in both space and time, an attosecond pulse produced by ultrafast wavefront rotation of a 1.8 µm fundamental beam. We confirm what models suggest - that each beamlet is an isolated attosecond pulse in the time domain. We get almost constant flat wavefront curvature through the whole photon energy range. The measurement method is scalable to the soft X-ray spectral region.

Resolving multiple molecular orbitals using two-dimensional high-harmonic spectroscopy.

High-harmonic radiation emitted from molecules in a strong laser field contains information on molecular structure and dynamics. When multiple molecular orbitals participate in high-harmonic generation, resolving the contribution of each orbital is crucial for understanding molecular dynamics and for extending high-harmonic spectroscopy to more complicated molecules. We show that two-dimensional high-harmonic spectroscopy can resolve high-harmonic radiation emitted from the two highest-occupied molecular orbitals, HOMO and HOMO-1, of aligned molecules. By the application of an orthogonally polarized two-color laser field that consists of the fundamental and its second-harmonic fields to aligned CO2 molecules, the characteristics attributed to the two orbitals are found to be separately imprinted in odd and even harmonics. Two-dimensional high-harmonic spectroscopy may open a new route to investigate ultrafast molecular dynamics during chemical processes.

Controlling attosecond angular streaking with second harmonic radiation.

High harmonic generation, which produces a coherent burst of radiation every half cycle of the driving field, has been combined with ultrafast wavefront rotation to create a series of spatially separated attosecond pulses, called the attosecond lighthouse. By adding a coherent second harmonic beam with polarization parallel to the fundamental, we decrease the generating frequency from twice per optical cycle to once. The increased temporal separation increases the pulse contrast. By scanning the carrier envelope phase, we see that the signal is 2π periodic.

Creating high-harmonic beams with controlled orbital angular momentum.

A beam with an angular-dependant phase Φ = ℓϕ about the beam axis carries an orbital angular momentum of ℓℏ per photon. Such beams are exploited to provide superresolution in microscopy. Creating extreme ultraviolet or soft-x-ray beams with controllable orbital angular momentum is a critical step towards extending superresolution to much higher spatial resolution. We show that orbital angular momentum is conserved during high-harmonic generation. Experimentally, we use a fundamental beam with |ℓ| = 1 and interferometrically determine that the harmonics each have orbital angular momentum equal to their harmonic number. Theoretically, we show how any small value of orbital angular momentum can be coupled to any harmonic in a controlled manner. Our results open a route to microscopy on the molecular, or even submolecular, 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.