Two-photon Ionization Process Research Articles

High-resolution attosecond imaging of an atomic electron wave function in momentum space

An electron wave function is characterized by the phase and amplitude distributions over position or momentum space. Recent attosecond technologies allow us to obtain the phase information of photoelectrons using interference between several optical transition pathways. We demonstrate that by employing a two-path photoionization interference process, the complex wave function of the photoelectron is fully mapped in two-dimensional momentum space. We ionize neon gas by an extreme ultraviolet (XUV) attosecond pulse train consisting of both odd and even harmonics in the presence of an infrared (IR) laser field. By controlling the generation process of the attosecond pulse train, we isolate two ionization pathways for interfering with the photoelectrons: one is the two-photon ionization process due to the odd harmonic excitation with one IR photon absorption, and the other is the one-photon ionization by an even harmonic. We record the photoelectron momentum distributions via velocity map imaging as a function of the XUV and IR delay. Using three different experimental conditions, we show that the detailed structure of the amplitude and phase distributions of photoelectrons can be resolved in the two-dimensional momentum space within the bandwidth determined by the attosecond XUV pulse. We separate the measured photoelectron wave function into those produced by each ionization pathway. Our method will be applicable to more complex molecules.

Electronic coherences in argon through interfering one- and two-photon ionization processes in the vicinity of Feshbach resonances

The role of Rydberg autoionizing states in interfering one- and two-photon ionization paths is theoretically investigated in atomic Ar. The angularly resolved photoionization cross sections for each individual path is provided. By varying the relative optical phase between the two pulses the phase difference between the two interfering paths is extracted. The retrieved phase difference and the photoelectron angular distributions exhibit a strong dependence on the photon energy in the vicinity of the resonant states. In contrast to previous results obtained in atomic Ne, the phase difference features a smooth dependence with photoelectron emission angle.

Non-dipole effects on angular distribution of photoelectrons in sequential two-photon double ionization of Ar atom and K<sup>+</sup> ion

Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.

Temporal coherent control of resonant two-photon double ionization of the hydrogen molecule via doubly excited states

We use time-delayed, counter-rotating, circularly polarized few-cycle attosecond nonoverlapping pulses to study the temporal coherent control of the resonant process of two-photon double ionization (TPDI) of hydrogen molecule via doubly excited states for pulse propagation direction along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$ either parallel or perpendicular to the molecular axis $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\parallel}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a pulse carrier frequency of 36 eV resonantly populating the ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$ doubly excited state as well as other $^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}$ doubly excited states, we find that the indirect ionization pathway through these doubly excited states changes the character of the kinematical vortex-shaped momentum distribution produced by the two direct ionization pathways from fourfold to twofold rotational symmetry. This result is similar to what found in TPDI of the He atom involving $^{1}P_{\ifmmode\pm\else\textpm\fi{}1}^{o}$ doubly excited states [Ngoko Djiokap and Starace, J. Opt. 19, 124003 (2017)]; however, angular distributions exhibiting a quantum beat effect between the ground state and a doubly excited state seen for the He atom are observed here for its molecular counterpart with an anomaly in shape and magnitude, not in frequency. The sixfold differential probability integrated over the azimuthal angle of the photoelectron pair shows that this anomaly is due to autoionization decays and quantum beats between doubly excited states. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\perp}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a broadband pulse carrier frequency of 30 eV populating the ${Q}_{1}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(1)$, ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, and ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(2)$ doubly excited states, the momentum distribution is shown to exhibit dynamical electron vortices with four spiral arms, which originates from the interplay between the $^{1}\mathrm{\ensuremath{\Delta}}_{g}^{+}$, $^{1}\mathrm{\ensuremath{\Pi}}_{g}^{+}$, and $^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ dynamical ionization amplitudes. Our treatment within either the adiabatic-nuclei approximation or fixed-nuclei approximation shows that the latter provides a very good account for this correlated process.

Universality of the Dynamic Characteristic Relationship of Electron Correlation in the Two-Photon Double Ionization Process of a Helium-Like SystemSupported by the National Natural Science Foundation of China (Grant Nos. 91850209, 11774129, and 11774411), and the National Key Research and Development Program of China (Grant Nos. 2019YFA0307700 and 2016YFA0401100).

Universality of the dynamic characteristic relationship between the characteristic time t c and the two-electron Coulomb interaction energy of the ground state in the two-photon double ionization process is investigated via changing the parameters of the two-electron atomic system and the corresponding laser conditions. The numerical results show that the product keeps constant around 4.1 in the cases of changing the nucleus charge, the electron charge, the electron mass, and changing simultaneously the nucleus charge and the electron charge. These results demonstrate that the dynamic characteristic relationship in the two-photon double ionization process is universal. This work sheds more light on the dynamic characteristic relationship in ultrafast processes and may find its application in measurements of attosecond pulses.

Observation of Binary Spectral Jumps in Color Centers in Diamond

AbstractOptical “blinking” normally refers to a switching behavior of fluorescence for quantum emissions between “ON” and “OFF” state. For quantum dots, single molecules, and nitrogen‐vacancy centers in diamond, it usually stems from conversions between two different charge states, with one emitting strong and bright fluorescence while the other scattering weak or no fluorescence. Here, a different type of blinking from single emitters in ion implanted diamond is reported, with both blinking states exhibiting detectable photoluminescence under nonresonant excitation. Thanks to the low jumping rates, the dynamics of the emission can be directly monitored. The quadratic power dependence of the conversion rates suggests the possibility of two‐photon ionization process in quantum jumps. This work provides extra insights into the photodynamics of the spectral jumps on defect‐based single‐photon emitters hosted in wide‐bandgap semiconductors.

Resonance-enhanced two-photon ionization of hydrogen atom in intense laser field investigated by Bohmian-mechanics**Project supported by Jilin Province Science and Technology Development Plan Project–Excellent Youth Talents Fund Project, China (Grant No. 20180520174JH) and the National Natural Science Foundation of China (Grant Nos. 11704145 11904050, 11774129, 11747007, and 11534004).

Resonance enhanced two-photon ionization process of hydrogen atom via the resonant laser pulse is studied by Bohmian mechanics (BM) method. By analyzing the trajectories and energies of Bohmian particles (BPs), we find that under the action of high frequency and low intensity multi-circle resonant laser pulses, the ionized BPs first absorb one photon completing the excitation, and then absorb another photon, completing the ionization after staying in the first excited state for a period of time. The analysis of work done by the forces shows that the electric field force and quantum force play a major role in the whole ionization process. At the excitation moment and in the excitation-ionization process, the effect of the quantum force is greater than that of the electric field force. Finally, we discuss the principle of work and energy for BPs, and find that the electric field force and quantum force are non-conservative forces whose work is equal to the increment of mechanical energy of the system. In addition, it is proved that the quantum potential energy actually comes from the kinetic energy of the system and the increment of kinetic energy is equal to that of the kinetic energy of the system.

Ultrafast time delay as a control parameter in resonant ionization by two XUV ultrashort pulses

We predict quantitatively that it is possible to use few-femtosecond positive or negative time delays, between two XUV Gaussian few-femtosecond pulses of moderate intensities and central frequencies and in order to control the probability of ionization at clearly defined exit energies corresponding to the sums of photon frequencies (), (), and ( or ). The phenomenon is demonstrated quantitatively by obtaining and using nonperturbative solutions of the time-dependent Schrödinger equation for a time-dependent scheme involving the process of two-photon resonant ionization of Helium via the (58.4 nm) and (52.22 nm) excited states. The calculations used wavefunctions which are state-specific for the discrete spectrum, (up to the Rydberg state), as well as for the energy-normalized continuous spectrum, (up to 2.0 a.u. above threshold with angular momenta = 0, 1, 2, 3, 4). For this system, using as a control knob, the effects on the photoelectron spectrum of the combination of the transition amplitudes via the two paths and their interference are determined clearly for pulses with field-cycles ranging from about 15 to about 80 cycles. The analysis has included the comparison of the nonperturbative results, obtained by implementing the state-specific expansion approach, with those obtained from the application of second order time-dependent perturbation theory with two Gaussian pulses of finite duration.

Time-dependent perturbation theory beyond the dipole approximation for two-photon ionization of atoms

SynopsisWe develop a time-dependent perturbation theory beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. Subse-quent applications of the PT method in the nonresonant regime allow us to analyze one of the most important nondipole effects, i.e., the linear-momentum-transfer law in the two-photon ionization process and to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction.

Photoelectron circular dichroism with Lissajous-type bichromatic fields: One-photon versus two-photon ionization of chiral molecules

Angular distribution of photoelectrons released by the ionization of randomly-oriented molecules with two laser fields of carrier frequencies $\omega$ and $2\omega$, which are linearly polarized in two mutually-orthogonal directions, is analyzed in the perturbation limit for the case of one- vs two-photon ionization process. In particular, we focus on the recently predicted [Ph.V. Demekhin {\it et al.}, Phys. Rev. Lett. \textbf{121}, 253201 (2018)] forward-backward asymmetry in the photoelectron emission, which is induced by the interference of two fields and depends on the external relative phase between them. The present theoretical analysis proves a chiral origin of the effect and suggests that a molecule introduces an additional internal relative phase between two ionizing fields.

The probe of electron correlation along the He isoelectronic sequence by intense and short laser pulses

The two-photon double ionization process along the He isoelectronic sequence (He − Ne8+) is investigated by solving the full-dimensional time-dependent Schrödinger equation in an intense laser field. The ionization is triggered from the ground state of each system with photons of energy higher than its second ionization potential, in which case the sequential two-electron ejection is allowed. The results of the total two-photon double ionization probability and the energy distribution of ejected electrons demonstrate the important effect of the nuclear charge Z on the dynamics of the interaction between the two ejected electrons.

Structural Rearrangement by Isomer-Specific Infrared Excitation in the Neutral Isolated Dihydrated Cluster of 3-Hydroxyflavone.

Isomer-specific, IR-induced reactions in the electronic ground state (S0) can be of great interest to control reaction pathways. Here we show a first example of these reactions with isomer-specific excitation and formation of a new isomer under isolated conditions in a molecular beam experiment. The investigated dihydrated cluster of 3-hydroxyflavone forms two isomers, I and D, in the S0 state. We show that only a mode-specific excitation of isomer I leads to a structural rearrangement yielding an isomer that has not been identified so far. This isomer is assigned in comparison to quantum chemical calculations. The experiments are performed by applying an IR/IR method in combination with a mass-selective resonant two-photon ionization (R2PI) process. Usually these kinds of IR/IR/R2PI methods are chosen to discriminate isomers; here it is demonstrated that this powerful method can also be applied for analysis of IR-induced reactions probed by an IR/R2PI process.

Direct and Sequential Two-Photon Double Ionization of Two-Electron Quantum Dots.

In this work we study the double ionization yields and kinetic energy spectra of a two-electron spherical quantum dot (QD) exposed in laser fields. The theoretical description is based on an ab initio nonperturbative configuration interaction theory capable of describing the two-electron QD dynamics in THz and mid-IR ultrashort laser fields. The QD's confinement potential is approximated to have a Gaussian-like spatial dependence. We have found that significant variations of the two-electron kinetic energy patterns and two-photon double ionization yields occur as we vary the QD's size. For a given laser pulse, the double ionization yield increases by orders of magnitude when the dot size is reduced. The size of the QD determines the sequential or direct character of the two-photon double ionization process. Provided that it is energetically allowed, the sequential two-photon double ionization process, requiring minimal interelectronic correlations, becomes dominant over the direct one. In the sequential regime, the corresponding two-electron kinetic energy spectrum changes from a broadened single-peaked to a doubly peaked one. Moreover, we also have identified features in the spectrum that are distinctively different than those in its atomic counterpart.

Hydrogen bond induced HF elimination from photoionized fluorophenol dimers in the gas phase.

In this paper, we report finding of a remarkable chemical effect of hydrogen bonding, elimination of hydrogen fluoride (HF) from the hydrogen bonded dimers of 2-fluorophenol (2-FP) and 3-fluorophenol (3-FP), in a supersonic jet expansion upon multi-photon ionization using 4th harmonic wavelength (266 nm) of a Q-switched Nd:YAG laser, and the reaction has been probed by time-of-flight mass spectrometry. No HF elimination is observed to occur by such means from the monomer of 3-FP, but it occurs with a small yield from the monomer of 2-FP. On the other hand, upon dimerization the reaction is triggered on for 3-FP, and for 2-FP it becomes so facile that no intact dimer cation survives and only the HF eliminated product ion appears in the mass spectra. Electronic structure calculation shows that in the cationic ground (D0) state, although the reaction for 2-FP dimer is exothermic, the associated barrier is significantly high (2.75 eV) and for its occurrence, absorption of three photons (2+1 type) is required. However, the reaction is predicted barrierless in the intermediate S1 state of this dimer, and HF loss dimer cation mass peak could appear in the mass spectrum due to an effective two-photon (1+1) ionization process. In the case of 3-FP dimer, the energy barriers both in S1 (neutral) and D0 (ionic) states are high, and it is suggested that for occurrence of HF elimination, dimer cation needs to absorb an additional photon. For facilitation of HF loss from this dimer cation, a rearrangement of the geometry and formation of an intermediate adduct have been suggested, and it is argued that the latter could be produced by nucleophilic attack of the neutral moiety at the ortho site of the cationic counterpart.

State-selective preparation of Ar2+ and Kr2+ by resonantly enhanced two-photon double ionization via intermediate Rydberg states using high-order harmonics

Simultaneous two-electron emission processes of Ar induced by high-order harmonics of near-infrared femtosecond laser pulses were investigated by coincidence photoelectron spectroscopy. Two-photon double ionization processes via the $3s3{p}^{6}np\phantom{\rule{0.16em}{0ex}}(n\ensuremath{\sim}25)$ intermediate resonances of Ar were observed, which selectively created the $3s3{p}^{5}\phantom{\rule{0.16em}{0ex}}^{1}P$ state of $\mathrm{A}{\mathrm{r}}^{2+}$. The similar double ionization processes were also observed in Kr. The selective creation indicates that the core electron configuration of the doubly ionized state tends to be the same as that of the intermediate state and that the emitted two electrons tend to form the singlet state.

Two-electron processes in multiple ionization under strong soft-x-ray radiation

In a combined experimental and theoretical study we have investigated the ionization of atomic argon upon irradiation with intense soft-x-ray pulses of 105 eV photon energy from the free-electron laser FLASH. The measured ion yields show charge states up to ${\mathrm{Ar}}^{7+}$. The comparison with the theoretical study of the underlying photoionization dynamics highlights the importance of excited states in general and of processes governed by electron correlation in particular, namely, ionization with excitation and shake-off, processes usually inaccessible by measurements of ionic yields only. The ${\mathrm{Ar}}^{7+}$ yield shows a clear deviation from the predictions of the commonly used model of sequential ionization via single-electron processes and the observed signal can only be explained by taking into account the full multiplet structure of the involved configurations and by inclusion of two-electron processes. The competing process of two-photon ionization from the ground state of ${\mathrm{Ar}}^{6+}$ is calculated to be orders of magnitude smaller.

Angular distribution and circular dichroism in the two-colour XUV+NIR above-threshold ionization of helium

The photoelectron angular distribution and the circular dichroism in two-colour XUV+NIR above-threshold ionization of helium atoms have been investigated both experimentally and theoretically. Circularly polarized XUV pulses from the free electron laser FERMI have been spatially and temporally overlapped with circularly polarized optical pulses in the interaction region with an atomic helium jet. The emitted electrons were energy and angle analyzed by means of a velocity map imaging spectrometer. Asymmetry parameters of the angular distribution were determined and compared to theoretical predictions based on the strong field approximation and perturbation theory, respectively. For low NIR intensities, the ratio of the partial waves in the two-photon ionization process and their relative phase could be deduced. For high NIR intensities, the influence of multi-photon processes is discussed. Circular dichroism was revealed in both cases and is in good agreement with the results of the strong field approximation.

Ionization efficiency of Doppler-broadened atoms by transform-limited and broadband nanosecond pulses: one-photon resonant two-photon ionization of muoniums

We theoretically study the ionization efficiency of Doppler-broadened atoms through a one-photon resonant two-photon ionization process using nanosecond pump and ionizing laser pulses. Under the presence of significant (> tens of GHz) Doppler broadening, the bandwidth of the transform-limited nanosecond pump pulse is far smaller than the Doppler width, and the use of the broadband nanosecond pulse rather than the transform-limited nanosecond pulse seems to be much more efficient to pump and eventually ionize atoms. It turns out, however, that the transform-limited nanosecond pump pulse with sufficient high intensity can outperform the broadband nanosecond pump pulse in the high intensity regime for the ionizing pulse, at which the other broadening mechanisms because of the strong pump and fast ionization play more important roles than the bandwidth of the pump pulse. Using a set of density matrix equations, we present specific numerical results for muoniums (μ+e−) with enormous Doppler widths (80 and 230 GHz), which support the above argument.

Resonant and nonresonant multiphoton ionization processes in the mass spectrometry of explosives.

Multiphoton ionization processes were studied for three types of explosives using a line-tunable ultraviolet femtosecond laser. When peroxides such as triacetone triperoxide (TATP) and hexamethylene triperoxide diamine (HMTD) were ionized through a nonresonant two-photon process, a molecular ion was dominantly observed by reducing the excess energy remaining in the ion. However, an aromatic nitro compound such as 2,4,6-trinitrotoluene (TNT) produced large signals arising from molecular and fragment ions by resonant two-photon ionization. In addition, only fragment ions were produced from a nonaromatic nitro compound such as 1,3,5-trinitroperhydro-1,3,5-triazine (RDX), even when a resonant two-photon ionization process was employed, suggesting that a further reduction in excess energy would be necessary if a molecular ion were to be observed.

Theoretical study of pulse delay effects in the photoelectron angular distribution of near-thresholdEUV+IRtwo-photon ionization of atoms

We study theoretically the photoelectron angular distributions (PADs) from two-color two-photon near-threshold ionization of hydrogen and noble gas (He, Ne, and Ar) atoms by a combined action of femtosecond extreme ultraviolet (EUV) and near-infrared (IR) laser pulses. By using second-order time-dependent perturbation theory, we clarify how the two-photon ionization process depends on the EUV-IR pulse delay and how it is connected to the interplay between resonant and nonresonant ionization paths. Furthermore, by solving the time-dependent Schr\"odinger equation, we calculate the anisotropy parameters ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$ as well as the amplitude ratio and relative phase between partial waves characterizing the PADs. We show that, in general, these parameters notably depend on the time delay between the EUV and IR pulses, except for He. This dependence is related to the varying relative role of resonant and nonresonant paths of photoionization. Our numerical results for H, He, Ne, and Ar show that the pulse-delay effect is more pronounced for $p$-shell ionization than for $s$-shell ionization.