Frustrated Tunneling Ionization Research Articles

Correlation analysis of frustrated tunneling ionization

We visualize frustrated tunneling ionization (FTI) using the correlation function analysis outlined in our preceding works [I. Ivanov and K. T. Kim, J. Phys. B 55, 055001 (2022); Sci. Rep. 12, 19533 (2022)]. We apply this technique to the hydrogen atom subjected to a strong laser field. Our analysis supports the basic premises of the theory of FTI and demonstrates its sensitive dependence on the laser pulse duration and carrier envelope phase.

Editorial: Strong field physics and attosecond science

emission from Rydberg atoms. Substantial neutral atoms can be excited after tunneling in a strong laser 14 field, in the process known as frustrated tunneling ionization. The generation of coherent emission from 15 the excited-state atoms produced by the frustrated tunneling ionization is demonstrated to be dependent on 16 the chirp of the laser pulse. This chirp dependence also provides a new way to investigate the dynamics 17 of Rydberg states. Kong et al. (Kong et al., 2022) explored the influence of mechanical strains on the 18 high-order harmonic generation in the monolayer hexagonal boron nitride crystal by using time-dependent 19 density functional theory. They found the band structure is sensitive to the structural deformation modulated 20 by strains. This result may be useful in probing lattice deformations in crystals and heuristic to enhance the 21 optoelectronic efficiency of solid-state nano-devices. In conclusion, the Research Topic is created to present the latest advances and trends concerning the 62 strong field physics and attosecond science. Our special thanks to the Frontiers in Physics team for the 63 technical assistance with publishing. Much more efforts are still ongoing in this fascinating area. We expect 64 that this field will attract more and more attentions and benefit potential applications.

Rydberg state excitation in molecules manipulated by bicircular two-color laser pulses

Multiphoton resonant excitation and frustrated tunneling ionization, manifesting the photonic and optical nature of the driving light via direct excitation and electron recapture, respectively, are complementary mechanisms to access Rydberg state excitation (RSE) of atoms and molecules in an intense laser field. However, clear identification and manipulation of their individual contributions in the light-induced RSE process remain experimentally challenging. Here, we bridge this gap by exploring the dissociative and nondissociative RSE of H2 molecules using bicircular two-color laser pulses. Depending on the relative field strength and polarization helicity of the two colors, the RSE probability can be boosted by more than one order of magnitude by exploiting the laser waveform-dependent field effect. The role of the photon effect is readily strengthened with increasing relative strength of the second-harmonic field of the two colors regardless of the polarization helicity. As compared to the nondissociative RSE forming H2 * , the field effect in producing the dissociative RSE channel of ( H + , H * ) is moderately suppressed, which is primarily accessed via a three-step sequential process separated by molecular bond stretching. Our work paves the way toward a comprehensive understanding of the interplay of the underlying field and photon effects in the strong-field RSE process, as well as facilitating the generation of Rydberg states optimized with tailored characteristics.

Dynamics of frustrated tunneling ionization driven by inhomogeneous laser fields

We theoretically investigated frustrated tunneling ionization (FTI) driven by spatially inhomogeneous strong laser fields induced by surface plasmon resonance within a bow-tie metal nanostructure. The results show that the FTI probability and the principal quantum number distribution exhibit similar oscillatory behavior as a function of the pulse duration. Our analysis reveals that the periodic defocusing and refocusing of the electron spatial distribution due to the inhomogeneous laser field is responsible for the oscillatory structures. In addition, the initial tunneling coordinates and the angular momentum distributions of the FTI events and theirs pulse duration dependence are also explored. Moreover, our results show that the frequency of the oscillatory structures depends sensitively on the electron quiver amplitude and the inhomogeneity strength. Thus, the electron quiver amplitude and the size of the gap between bow-tie nanostructure are useful and efficient knobs for controlling the yield and properties of exited Rydberg states.

Coherent control of extreme ultraviolet emission generated through frustrated tunneling ionization

Coherent extreme ultraviolet (EUV) line emissions can be generated from an atom excited through frustrated tunneling ionization (FTI). The phase variation of the EUV emission in a generation medium along the propagation direction is a critical parameter that determines the phase-matching condition of this new light source. Here we show that the EUV emission sensitively depends on the intensity and phase of a driving laser pulse and the target position. Angle-resolved EUV spectra measured at different target positions and the carrier-envelope phases of the laser pulse exhibit an intensity modulation, showing similar behavior to that of a long-trajectory high harmonic radiation. The four-step model developed for the FTI emission accurately describes the coherent control of the EUV emission. These findings are essential ingredients for developing coherent extreme ultraviolet sources with high photon flux and for utilizing the FTI emission in time-resolved spectroscopy.

Frustrated tunneling dynamics in ultrashort laser pulses

We study a model for frustrated tunneling ionization using ultrashort laser pulses. The model is based on the strong field approximation and it employs the saddle point approximation to predict quasiclassical trajectories that are captured on Rydberg states. We present a classification of the saddle-point solutions and explore their behavior as functions of angular momentum of the final state, as well as the carrier-envelope phase (CEP) of the laser pulse. We compare the final state population computed by the model to results obtained by numerical propagation of the time-dependent Schrödinger equation (TDSE) for the hydrogen atom. While we find qualitative agreement in the CEP dependence of the populations in principal quantum numbers, n, the populations to individual angular momentum channels, ℓ, are found to be inconsistent between model and TDSE. Thus, our results show that improvements of the quasiclassical trajectories are in order for a quantitative model of frustrated tunneling ionization.

Electron dynamics in laser-driven atoms near the continuum threshold

Strong-field ionization and Rydberg-state excitation (RSE) near the continuum threshold exhibit two phenomena that have attracted a lot of recent attention: the low-energy structure (LES) just above and frustrated tunneling ionization just below the threshold. The former becomes apparent for longer laser wavelengths, while the latter has been especially investigated in the near infrared; both have been treated as separate phenomena so far. Here we present a unified perspective based on electron trajectories, which emphasizes the very important role of the electron-ion Coulomb interaction as expected in this energy region. Namely, those trajectories that generate the LES can also be recaptured into a Rydberg state. The coherent superposition of the contributions of such trajectories with different travel times (each generating one of the various LES peaks) causes an oscillation in the intensity dependence of the RSE yield, which is especially noticeable for longer wavelengths. The theory is illustrated by RSE experiments at 1800 nm, which agree very well with the theory with respect to position and period of the oscillation. The wavelength scaling of the RSE oscillation is also discussed. Our work establishes a solid relationship between processes below and above the threshold and sheds new light on atomic dynamics driven by intense laser fields in this critical energy region.

Frustrated tunneling ionization in strong circularly polarized two-color laser fields

We study the frustrated tunneling ionization (FTI) in counter-rotating and co-rotating circularly polarized two-color (CPTC) laser fields using a classical electron ensemble method. We find that the FTI probability depends sensitively on the relative helicity and the field amplitude ratio of the two-color laser fields. The FTI probability in the counter-rotating CPTC laser fields is three orders higher than that in the co-rotating fields. In the counter-rotating CPTC laser fields, the maximal FTI probability appears at the field amplitude ratio of ∼2.0, while in the co-rotating CPTC laser fields it appears at the ratio of ∼3.6. Tracing the electron trajectories, we find that recollision-assisted recapture plays an important role for the FTI in the CPTC laser fields. We further show that the angular momentum of the Rydberg state from the FTI events can be controlled by changing the field amplitude ratio of the counter-rotating CPTC laser fields, while it is nearly unchanged in the co-rotating CPTC laser fields.

Ellipticity dependence of excitation and ionization of argon atoms by short-pulse infrared radiation

When atoms or molecules are exposed to strong short-pulse infrared radiation, ionization as well as "frustrated tunneling ionization" (FTI) can occur, in which a portion of the almost ionized electrons recombine into the initial ground or an excited bound state. We analyze the ellipticity dependence of the relative signals that are predicted in a single-active electron approximation (SAE), the validity of which is checked against a parameter-free multi-electron \hbox{$R$-matrix} (close-coupling) with time dependence approach. We find good agreement between the results from both models, thereby providing confidence in the SAE model potential to treat the process of interest. Comparison of the relative excitation probabilities found in our numerical calculations with the predictions of Landsman {\it et al.}\ (New Journal of Physics {\bf 15} (2013) 013001) and Zhao {\it et al.}\ (Optics Express {\bf 27} (2019) 21689) reveals good agreement with the former for short pulses. For longer pulses, the ellipticity dependence becomes wider than that obtained from the Landsman {\it et al.} formula, but we do not obtain the increase compared to linearly polarized radiation predicted by Zhao {\it et al.}

Frustrated tunneling ionization in the elliptically polarized strong laser fields.

We theoretically investigated frustrated tunneling ionization (FTI) in the interaction of atoms with elliptically polarized laser pulses by a semiclassical ensemble model. Our results show that the yield of frustrated tunneling ionization events exhibits an anomalous behavior which maximizes at the nonzero ellipticity. By tracing back the initial tunneling coordinates, we show that this anomalous behavior is due to the fact that the initial transverse velocity at tunneling of the FTI events is nonzero in the linear laser pulses and it moves across zero as the ellipticity increases. The FTI yield maximizes at the ellipticity when the initial transverse momentum for being trapped is zero. Moreover, the angular momentum distribution of the FTI events and its ellipticity dependence are also explored. The anomalous behavior revealed in our work is very similar to the previously observed ellipticity dependence of the near- and below-threshold harmonics, and thus our work may uncover the mechanism of the below-threshold harmonics which is still a controversial issue.

Strong-field-approximation model for coherent extreme-ultraviolet emission generated through frustrated tunneling ionization

An atom can be excited through tunneling when it is exposed to a strong laser field. This excitation process is known as frustrated tunneling ionization (FTI). Recently it has been reported that coherent extreme-ultraviolet emission can be achieved through FTI. In the present work we extend the strong-field-approximation (SFA) model developed by Lewenstein et al. to derive a quantum mechanical description of the FTI emission. An analytic expression is derived to describe FTI emission as four steps: tunneling of an electron from the ground state of an atom, acceleration of the electron in the continuum, recombination into the exited state of the parent atom, and free induction decay. The coherence property of FTI emission is studied using the attosecond lighthouse method, in which a spatially chirped laser beam generates FTI emissions in different directions. The spatial distribution of the FTI emission in the far field is analyzed using both the extended SFA model and the time-dependent Schr\odinger equation model. The results obtained from the two models agree well, thereby confirming the validity of our extended SFA model.

Frustrated Coulomb explosion of small helium clusters

Almost ten years ago, energetic neutral hydrogen atoms were detected after a strong-field double ionization of H$_2$. This process, called 'frustrated tunneling ionization', occurs when an ionized electron is recaptured after being driven back to its parent ion by the electric field of a femtosecond laser. In the present study we demonstrate that a related process naturally occurs in clusters without the need of an external field: we observe a charge hopping that occurs during a Coulomb explosion of a small helium cluster, which leads to an energetic neutral helium atom. This claim is supported by theoretical evidence. As an analog to 'frustrated tunneling ionization', we term this process 'frustrated Coulomb explosion'.

Angular momentum distribution in strong-field frustrated tunneling ionization

Using the classical-trajectory Monte Carlo model, we have theoretically studied the angular momentum distribution of frustrated tunneling ionization (FTI) of atoms in strong laser fields. Our results show that the angular momentum distribution of the FTI events exhibits a double-hump structure. With this classical model, we back traced the tunneling coordinates, i.e., the tunneling time and initial transverse momentum at tunneling ionization. It is shown that for the events tunneling ionized at the rising edge of the electric field, the final angular momentum exhibits a strong dependence on the initial transverse momentum at tunneling. While for the events ionized at the falling edge, there is a relatively harder recollision between the returning electron and the parent ion, leading to the angular momentum losing the correlation with the initial transverse momentum. Our study suggests that the angular momentum of the FTI events could be manipulated by controlling the initial coordinates of the tunneling ionization.

Excitation of Rydberg wave packets in the tunneling regime

In the tunneling regime for strong laser field ionization of atoms, experimental studies have shown that a substantial fraction of atoms survive the laser pulse in many Rydberg states. To explain the origin of such trapping of population into Rydberg states, two mechanisms have been proposed: the first involves ac-Stark-shifted multiphoton resonances, and the second, called frustrated tunneling ionization, leads to the recombination of tunneled electrons into Rydberg states. We use a very accurate spectral method based on complex Sturmian functions to solve the time-dependent Schr\odinger equation for hydrogen in a linearly polarized infrared pulse and to calculate the tunneling probability in terms of the atomic ground-state width. We examine the probability of excitation into Rydberg states as a function of the peak intensity for various pulse durations and two wavelengths, 800 and 1800 nm, and we try to explain the results in light of the two aforementioned mechanisms. For long pulses of 800 nm wavelength, the extreme sensitivity of the trapping of population into high-lying Rydberg states to the peak intensity, the well-defined value, and parity of the angular momentum of the populated Rydberg states and the presence of Freeman resonances can be explained using a multiphotonic excitation mechanism. For strong pulses of 1800 nm wavelength, in the so-called adiabatic or quasistatic tunneling regime, the oscillations of the excitation probability as a function of intensity are in phase opposition to the ionization probability, and we observe a migration toward high values of the angular momentum with different distributions in the angular momentum at the maxima and minima of the oscillations. We also present a detailed study of how the excited-state wave packet builds up in time during the interaction of the atom with the pulse.

Atomic excitation and acceleration in strong laser fields

Atomic excitation in the tunneling regime of a strong-field laser–matter interaction has been recently observed. It is conveniently explained by the concept of frustrated tunneling ionization (FTI), which naturally evolves from the well-established tunneling picture followed by classical dynamics of the electron in the combined laser field and Coulomb field of the ionic core. Important predictions of the FTI model such as the n distribution of Rydberg states after strong-field excitation and the dependence on the laser polarization have been confirmed in experiments. The model also establishes a sound basis to understand strong-field acceleration of neutral atoms in strong laser fields. The experimental observation has become possible recently and initiated a variety of experiments such as atomic acceleration in an intense standing wave and the survival of Rydberg states in strong laser fields. Furthermore, the experimental investigations on strong-field dissociation of molecules, where neutral excited fragments after the Coulomb explosion of simple molecules have been observed, can be explained. In this review, we introduce the subject and give an overview over relevant experiments supplemented by new results.

Correspondence of below-threshold high-order-harmonic generation and frustrated tunneling ionization

Among many of the nonlinear phenomena induced by strong laser pulses, two of the important processes are the harmonic generation and the creation of neutral atoms in the Rydberg states. We carry out a joint study of the below-threshold high-order-harmonic (BTH) generation and the production of low-lying Rydberg atoms driven by an intense few-cycle midinfrared laser pulse. Our results are based on the numerical solution to the three-dimensional time-dependent Schr\odinger equation within the single active electron approximation and a semiclassical simulation. The yields of BTH and low-lying Rydberg atoms are found to have a similar carrier envelope phase dependence. We find that both processes can be faithfully described semiclassically in the deep tunneling regime. The trajectory analysis shows that these two processes share the same series of trajectories and can be simultaneously manipulated by the driving pulse shape. Our finding bridges the below-threshold high-order-harmonic generation and the frustrated tunneling ionization.

Excited state distribution and spin-effects in strong-field excitation of neutral Helium

SynopsisWe investigated the principal quantum number n distribution of excited states resulting from the interaction of Helium with strong, short laser pulses. We find excellent agreement with predictions of the semiclassical frustrated tunneling ionization (FTI) model [1] as well as fully quantum mechanical calculations. Furthermore, the excitation process directly populates triplet excited states due to the breakdown of the Russel-Saunders coupling scheme for high orbital angular momentum l states of Helium, which are predominantly populated in the strong laser field.

Enhanced high-order harmonic generation from excited argon

We experimentally demonstrate an effective scheme to generate the enhanced high-order harmonics from a coherent superposition state of ground state and excited states in Argon. By controlling the time delay between the pump and probe laser pulses, a surprising enhancement plateau of high-order harmonic generation is observed, with a half lifetime of dozens of picoseconds. In the plateau, the harmonic intensity is enhanced by nearly one order of magnitude compared to the case without pre-excitation. Moreover, the gradual enhancement process is also presented when the pump intensity is increasing for improving the population of excited states, which can be attributed to the Rydberg states created by frustrated tunneling ionization.

Strong-field excitation of helium: bound state distribution and spin effects.

Using field ionization combined with the direct detection of excited neutral atoms we measured the distribution of principal quantum number n of excited He Rydberg states after strong-field excitation at laser intensities well in the tunneling regime. Our results confirm theoretical predictions from semiclassical and quantum mechanical calculations and simultaneously underpin the validity of the semiclassical frustrated tunneling ionization model. Moreover, since our experimental detection scheme is spin sensitive in the case of He atoms, we show that strong-field excitation leads to strong population of triplet states. The origin of it lies in the fact that high angular momentum states are accessible in strong-field excitation. Thus, singlet-triplet transitions become possible due to the increased importance of spin-orbit interaction rather than due to direct laser induced spin-flip processes.

Publisher's Note: Rescattering and frustrated tunneling ionization of atoms in circularly polarized laser fields [Phys. Rev. A89, 013422 (2014)

Publisher's Note: Rescattering and frustrated tunneling ionization of atoms in circularly polarized laser fields [Phys. Rev. A89, 013422 (2014)