Rydberg Series Research Articles

Extracting doubly excited state lifetimes in helium directly in the time domain with attosecond noncollinear four-wave-mixing spectroscopy

The helium atom, with one nucleus and two electrons, is a prototypical system to study quantum many-body dynamics. Doubly excited states, or quantum states in which both electrons are excited by one photon, showcase electronic-correlation mediated effects. In this paper, the natural lifetimes of the doubly excited 1Po2snp Rydberg series and the 1Se2p2 dark state in helium in the 60–65 eV region are measured directly in the time domain with extreme-ultraviolet/near-infrared noncollinear attosecond four-wave-mixing (FWM) spectroscopy. The measured lifetimes agree with lifetimes deduced from spectral linewidths and theoretical predictions, and the roles of specific decay mechanisms are considered. While complex spectral line shapes in the form of Fano resonances are common in absorption spectroscopy of autoionizing states, the background-free and thus homodyned character of noncollinear FWM results exclusively in Lorentzian spectral features in the absence of strong-field effects. The onset of strong-field effects that would affect the extraction of accurate natural lifetimes in helium by FWM is determined to be approximately 0.3 Rabi cycles. This study provides a systematic understanding of the FWM parameters necessary to enable accurate lifetime extractions, which can be utilized in more complex quantum systems in the future. Published by the American Physical Society 2024

Engineering Rydberg-pair interactions in divalent atoms with hyperfine-split ionization thresholds

Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in Sr87, we study an intrinsic Förster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials. Published by the American Physical Society 2024

Rydberg excitons in cuprous oxide: A two-particle system with classical chaos.

When an electron in a semiconductor gets excited to the conduction band, the missing electron can be viewed as a positively charged particle, the hole. Due to the Coulomb interaction, electrons and holes can form a hydrogen-like bound state called the exciton. For cuprous oxide, a Rydberg series up to high principle quantum numbers has been observed by Kazimierczuk et al. [Nature 514, 343 (2014)] with the extension of excitons up to the μm-range. In this region, the correspondence principle should hold and quantum mechanics turn into classical dynamics. Due to the complex valence band structure of Cu2O, classical dynamics deviates from a purely hydrogen-like behavior. The uppermost valence band in cuprous oxide splits into various bands resulting in yellow and green exciton series. Since the system exhibits no spherical symmetry, the angular momentum is not conserved. Thus, the classical dynamics becomes non-integrable, resulting in the possibility of chaotic motion. Here, we investigate the classical dynamics of the yellow and green exciton series in cuprous oxide for two-dimensional orbits in the symmetry planes as well as fully three-dimensional orbits. Our analysis reveals substantial differences between the dynamics of the yellow and green exciton series. While it is mostly regular for the yellow series, large regions in phase space with classical chaos do exist for the green exciton series.

Resonance ionization spectroscopy of neodymium for determining a highly efficient two-step ionization scheme

Two-color two-step resonance ionization spectroscopy of neodymium (Nd) was performed to identify more than 120 even-parity autoionizing levels and their candidate J-values. The analysis of the observed autoionizing Rydberg series yielded a value of 44,560.11 (43)stat (2)sys cm−1 as a more accurate ionization potential of Nd. The saturation method was used to measure the transition cross-sections for some intense ionization transitions. From the measured cross-sections, the ionization efficiencies of some two-step ionization schemes were evaluated using the scheme cross-section formula to obtain several promising schemes.

An energy-modified quantum defect method for the analysis of Rydberg spectra: Application to 2-butyne.

The high resolution Rydberg absorption spectrum of 2-butyne C4H6 recorded previously at the SOLEIL synchrotron facility has been interpreted using multichannel quantum defect theory (MQDT). The calculations are based on the continuum scattering calculations of Xu et al., J. Chem. Phys. 136, 154303 (2012) and of Jacovella et al., J. Phys. Chem. A 119, 12339 (2015) pertaining to the dipole-allowed excited state symmetries in absorption from the ground state. In contrast to the traditional approach of calculating low-lying electronic states first and then attempting to extend the calculations to ever higher energy, here the analysis proceeds through the extension of these detailed calculations of the electronic continuum scattering down into the discrete region of the spectrum. The continuum reaction matrices and dipole transition moments are adapted to the discrete Rydberg region via the use of an energy-modified formulation of MQDT theory and associated energy dependences of the quantum defects. The analysis reproduces more than 40 Rydberg states from n ≈ 10 down to the 3d and 4s levels with an rms error of better than 20 cm-1. These belong to five Rydberg series with three different molecular symmetries. While the approach predicts many additional series, most of these are calculated and observed to carry only little oscillator strength. The analysis shows that the Rydberg spectrum is dominated by the excitation of an e″ symmetry electron of fδ and gπ type, in line with what previous studies of the above-threshold shape resonance of 2-butyne have shown. The present study is intended to serve as an example showing how first principles continuum calculations may be useful for the interpretation of highly bound discrete states in a range that poses problems for the standard abinitio techniques. The quantitative treatment of the dipole absorption cross sections is deferred to a future paper.

Photoionization of hydrogen halides using the R-matrix method

Abstract In this study, we use the UK Molecular R-matrix (UKRMol) codes in the close-coupling approximation to examine the photoionization of hydrogen halides (hydrogen fluoride, hydrogen chloride, and hydrogen bromide). This article reports the total and partial photoionization cross sections for the X2Π, A2Σ+, and B2Σ+ ionic states of these halides. The calculated cross sections are compared with the available literature, which does not accurately represent the effective cross sections near the threshold region, which is dominated by the Rydberg series autoionization resonances converging to the A2Σ+ ionic state. There seems to have been minimal effort to investigate the Rydberg-bound states of these halides. Meanwhile, the R-matrix approaches have traditionally excelled at characterizing such studies. This indicates the effectiveness of this method for molecular photoionization as well as for understanding the resonant contribution to the photoionization cross sections. The detailed cross sections calculated comprise the complex autoionizing resonance structures capable of significantly contributing to the computations of total photoionization rates, which are necessary to maintain a steady state of ionization in astrophysical plasmas. Comparisons with the experimental measurements and the theoretical data generally show reasonable agreement across the reported energy range.

Mixing of Hot Shocked Plasma with Cold Gas in Nova YZ Ret 2020

The origin of bright X-ray emission lines that appear late in a nova eruption remains largely a puzzle. We present two high-resolution X-ray grating spectra of the classical nova YZ Ret, observed 77 and 115 days post-eruption, using XMM-Newton and Chandra, respectively. Both spectra feature resolved emission lines blueshifted by v = –1500 km s−1 and broadened by σ v = 500 km s−1. The two spectra are well described by a collisionally ionized plasma of kT ∼ 70 eV that dimmed by a factor of ∼40 between the two exposures. The spectra also show narrow radiative recombination continua (RRCs) of C+4, C+5, and N+5, indicating the interaction of the hot ionized plasma with cold electrons of kT ∼ 2 eV. The high-n Rydberg series of C+4 is anomalously bright, allowing us to measure the electron density through continuum lowering, which is in agreement with the He-like N+5 density diagnostic of n e = (1.7 ± 0.4) × 1011 cm−3. The high population of these high-n levels constitutes the best evidence to date of charge exchange (CX) with neutral H in an astrophysical ionized plasma. The remarkable fact that the velocity and plasma temperature are the same after 38 days, despite the high density and decreasing flux, is evidence for ongoing heating. We suggest the heating is due to a reverse shock in the nova ejecta, which forms a thin X-ray shell. The narrow RRCs and CX are attributed to direct mixing with cold gas, which overtakes the hot plasma either from the shock front or through the contact discontinuity.

Energy levels and characteristic features in photoionization of Cl III using the R-matrix method

We report study of Cl III for its large number of fine structure bound levels, 890, with n ≤ 10 and l ≤ 9, and 1/2 ≤ j ≤ 19/2 of even and odd parities with spectroscopic designation and photoionization cross sections (σPI) of the levels revealing various characteristic features. Various resonant structures and the shapes of the background, and their interference in σPI are illustrated for the ground, excited equivalent electron, low and high lying excited levels with single valence electron, and effects of fine structure couplings. σPI of the ground level shows Rydberg series of resonances on smooth background, and of equivalent electron levels producing strong closely spaced Rydberg series of resonances belonging to the low lying core ion excitation thresholds. They will impact applications in low temperature plasma. For the single valence electron excited levels, we find that σPI of low lying excited states are dominated by Rydberg series of resonances and of high lying excited states exhibit prominent broad feature of Seaton resonances. Partial photoionization cross sections of the ground level for leaving the core ion in the ground and various excited levels are also presented for applications in plasma modeling. The study was carried out in relativistic Breit–Pauli R-matrix method using a large close coupling wave function expansion of 45 levels of the core ion configurations 3 s23 p2, 3 s3 p3, 3 s23 p3 d, 3 s23 p4 s, 3 s3 p23 d, and 3 p4 with closed 1s, 2s, 2p orbitals. They belong to the optimized set of 13 configurations of Cl IV, 3 s23 p2, 3 s3 p3, 3 s23 p3 d, 3 s23 p4 s, 3 s23 p4 p, 3 s23 p4 d, 3 s3 p23 d, 3 s3 p24 s, 3 s3 p24 p, 3 p4, 3 p33 d, 3 p34 s, and 3 p34 p. Cl III energies are in good agreement with measured values. σPI features of low lying levels were benchmark with observation carried out at Advanced Light Source at LBNL with very good agreement. The present set of high accuracy data should complete for any practical applications.

Resonance Energies of Autoionizing Rydberg Series from the Single Photoionization of the 4s24p2 (3P1) and 4s24p2 (1D2) Excited States of the Br3+ Ion

Resonance Energies of Autoionizing Rydberg Series from the Single Photoionization of the 4s24p2 (3P1) and 4s24p2 (1D2) Excited States of the Br3+ Ion

Resonant laser ionization of neptunium: investigation on excitation schemes and the first ionization potential

The atomic structure of neptunium (Np) was investigated by two-step resonance ionization spectroscopy. The study involved exploring ground-state transitions as well as following transitions to high-lying states just below the ionization potential (IP) or auto-ionizing states above the IP. That resulted in the identification of two-step ionization schemes, suitable for trace analysis and nuclear structure investigations. The lifetimes of two excited states located at 25,342.48 cm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\, \ ext {cm}^{-1} $$\\end{document} and 25,277.64 cm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\, \ ext {cm}^{-1} $$\\end{document} were determined as 230(12) ns and 173(9) ns, respectively. Because of the absence of Rydberg series in wide-ranging spectra recorded, the first IP was determined through the field ionization of high-lying, weakly-bound states using a well-controlled static electric field. By applying the saddle-point model, an IP value of 50,535.54(15) cm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} [6.265608(19) eV] was derived. This value agrees with the current literature value of 50,535(2) cm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}, while providing a more than ten times higher precision.Graphic abstract

Atomic-scale visualization of the interlayer Rydberg exciton complex in moiré heterostructures

Excitonic systems, facilitated by optical pumping, electrostatic gating or magnetic field, sustain composite particles with fascinating physics. Although various intriguing excitonic phases have been revealed via global measurements, the atomic-scale accessibility towards excitons has yet to be established. Here, we realize the ground-state interlayer exciton complexes through the intrinsic charge transfer in monolayer YbCl3/graphite heterostructure. Combining scanning tunneling microscope and theoretical calculations, the excitonic in-gap states are directly profiled. The out-of-plane excitonic charge clouds exhibit oscillating Rydberg nodal structure, while their in-plane arrangements are determined by moiré periodicity. Exploiting the tunneling probe to reflect the shape of charge clouds, we reveal the principal quantum number hierarchy of Rydberg series, which points to an excitonic energy-level configuration with unusually large binding energy. Our results demonstrate the feasibility of mapping out the charge clouds of excitons microscopically and pave a brand-new way to directly investigate the nanoscale order of exotic correlated phases.

Ion-core switching in Rydberg series of XeKr

We investigate XeKr in high Rydberg states by mass-resolved optical-optical double resonance excitation spectroscopy. We excite XeKr via two-photon absorption to the v* = 0 and v* = 2 vibrational levels of an intermediate electronically excited state of Xe*Kr correlated to Xe*6p[5/2]2 and excite Xe*Kr further via one-photon absorption to the high Rydberg states of Xe**Kr in the energy range of 93200–97400 cm−1. The potential energy curves and the quantum defects of the d-Rydberg and s-Rydberg series of Xe**Kr, converging the A 2Π3/2 state of XeKr+ are determined. From the kinetic energy release in the predissociation process, we conclude that the ion-core switching occurs by the interaction between the bound electronic states of Xe**Kr converging to the A 2Π3/2 state of XeKr+ and the repulsive electronic states of low-lying electronic states of XeKr**. Based on numerical simulations, we interpret the dependence of the yield of the ion-core switching on the excitation energy in terms of the population transfer from the bound electronic states of the high Rydberg states Xe**Kr, converging to the A 2Π3/2 state of XeKr+, to those converging to the electronic ground X2 Σ 1 / 2 + state of XeKr + .

Resonant Auger decay of dissociating CH3I near the I 4d threshold.

Resonant Auger processes provide a unique perspective on electronic interactions and excited vibrational and electronic states of molecular ions. Here, new data are presented on the resonant Auger decay of excited CH3I in the region just below the I 4d-1 ionization threshold. The resonances include the Rydberg series converging to the five spin-orbit and ligand-field split CH3I (I 4d-1) thresholds, as well as resonances corresponding to excitation from the I 4d5/2,3/2 orbitals into the σ* lowest unoccupied molecular orbital. This study focuses on participator decay that populates the lowest lying states of CH3I+, in particular, the X̃2E3/2 and 2E1/2 states, and on spectator decay that populates the lowest-lying (CH3I2+)σ* states of CH3I+. The CH3I (I 4d-1)σ* resonances are broad, and dissociation to CH3 + I competes with the autoionization of the core-excited states. Auger decay as the molecule dissociates produces a photoelectron spectrum with a long progression (up to v3+ ∼ 25) in the C-I stretching mode of the X̃2E3/2 and 2E1/2 states, providing insights into the shape of the dissociative core-excited surface. The observed spectator decay processes indicate that CH3I+ is formed on the repulsive wall of the lower-lying (CH3I2+)σ* potentials, and the photon-energy dependence of the processes provides insights into the relative slopes of the (4d-1)σ* and (CH3I2+)σ* potential surfaces. Data are also presented for the spectator decay of higher lying CH3I (I 4d-1)nl Rydberg resonances. Photoelectron angular distributions for the resonant Auger processes provide additional information that helps distinguish these processes from the direct ionization signal.

Self-organization in the avalanche, quench and dissipation of a molecular ultracold plasma

Spontaneous avalanche to plasma begins in the core of an ellipsoidal Rydberg gas of nitric oxide. Ambipolar expansion of NO $^+$ draws energy from avalanche-heated electrons. Then, cycles of long-range resonant electron transfer from Rydberg molecules to ions equalize their relative velocities. This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes. These dynamics adiabatically sequester energy in a reservoir of mass transport, starting a process that anneals separating volumes to form an apparent glass of strongly coupled ions and electrons. Short-time electron spectroscopy provides experimental evidence for complete ionization. The long lifetime of this system, particularly its stability with respect to recombination and neutral dissociation, suggests that this transformation affords a robust state of arrested relaxation, far from thermal equilibrium. We see this most directly in the excitation spectrum of transitions to states in the initially selected Rydberg series, detected as the long-lived signal that survives a flight time of $500\ \mathrm {\mu }$ s to reach an imaging detector. The initial density of electrons produced by prompt Penning ionization, which varies with the selected initial principal quantum number and density of the Rydberg gas, determines a balance between the rising density of ions and the falling density of Rydberg molecules. This Penning-regulated ion-Rydberg molecule balance appears necessary as a critical factor in achieving the long ultracold plasma lifetime to produce spectral features detected after very long delays.

Computing Decay Widths of Autoionizing Rydberg States with Complex-Variable Coupled-Cluster Theory.

We compute autoionization widths of various Rydberg states of neon and N2 by equation-of-motion coupled-cluster theory combined with complex scaling and complex basis functions. This represents the first time that complex-variable methods are applied to Rydberg states represented in Gaussian basis sets. A new computational protocol based on Kaufmann basis functions is designed to make these methods applicable to atomic and molecular Rydberg states. As a first step, we apply our protocol to the neon atom and compute widths of the 3s, 3p, 4p and 3d Rydberg states. We then proceed to compute the widths of the 3sσg, 3dσg, and 3dπg Rydberg states of N2, which belong to the Hopfield series. Our results demonstrate a decrease in the decay width for increasing angular momentum and principal quantum number within both Rydberg series.

Conformational effects in the vibrational and electronic spectra of propionaldehyde: Experimental and theoretical studies.

We report here investigations on conformational effects in the vibrational and electronic spectra of the propionaldehyde (propanal) molecule using FTIR (600-3200cm-1) and vacuum ultraviolet (VUV) synchrotron radiation photoabsorption (52 500-85 000cm-1) spectroscopy respectively. Detailed theoretical calculations (using DFT and TDDFT methodologies) on ground and excited states of the cis and gauche conformers of propanal are performed; a comprehensive spectral analysis of the IR and VUV spectra is presented. A reinvestigation of the IR spectrum reveals several new bands assigned to the gauche conformer based on theoretical calculations. The VUV spectrum exhibits rich Rydberg series structure assigned to ns, np and nd series converging to the first ionization potentials of the two conformers. Earlier assignments of the 3s cis and gauche origins are revised in addition to extending Rydberg series analysis to several higher members. Vibronic bands accompanying the 3s, 4s and 4p Rydberg states are assigned using estimated vibrational frequencies of cis and gauche conformers in the cationic ground state. Simulated potential energy curves of the first few excited states (singlets and triplets) of cis and gauche conformers of propanal help in gaining insights into photodissociation mechanisms and possible conformational effects therein.

Photoionization of ground and excited states of Cr VIII with Rydberg series analysis of resonances involved

Photoionization of ground and excited states of Cr VIII with Rydberg series analysis of resonances involved

New atomic data for C i Rydberg states compared with solar UV spectra

ABSTRACT We use the Breit–Pauli R-matrix method to calculate accurate energies and radiative data for states in C i up to n = 30 and with l ≤ 3. We provide the full data set of decays to the five 2s2 2p2 ground configuration states 3P0,1,2, 1D2, and 1S0. This is the first complete set of data for transitions from n ≥ 5. We compare oscillator strengths and transition probabilities with the few previously calculated values for such transitions, finding generally good agreement (within 10 per cent) with the exception of values recently recommended by National Institute of Standards and Technology, where significant discrepancies are found. We then calculate spectral line intensities originating from the Rydberg states using typical chromospheric conditions and assuming local thermal equilibrium, and compare them with well-calibrated Solar and Heliospheric Observatory Solar Ultraviolet Measurements of Emitted Radiation ultraviolet (UV) spectra of the quiet Sun. The relative intensities of the Rydberg series are in excellent agreement with observation, which provides firm evidence for the identifications and blends of nearly 200 UV lines. Such comparison also resulted in a large number of new identifications of C i lines in the spectra. We also estimate optical depth effects and find that these can account for much of the absorption noted in the observations. The atomic data can be applied to model a wide range of solar and astrophysical observations.

Electron impact scattering and electronic excitation in glycolaldehyde: The first ever detected sugar in space

Detailed theoretical investigations on structural, spectroscopic and electron scattering cross sections of glycolaldehyde, the first ever detected sugar in space are reported in this work. Spectroscopic calculations are performed on the ground and excited states of glycolaldehyde using density functional theory (DFT) and time-dependent density functional theory (TDDFT), respectively. The optimized geometrical parameters and vibrational spectrum are in good agreement with the earlier reported work. Vertical excited state (VES) energies at the TDDFT/B3LYP/aug-cc-PVQZ level of theory along with detailed assignments are reported up to 30 transitions. The TDDFT predicted Rydberg series energies are compared with the Rydberg series of glycolaldehyde converging to its first IP, computed using the standard Rydberg formula and are found to be in good agreement. In the absence of sufficient experimental data on excited states of glycolaldehyde, the theoretical results are validated by comparison of VES calculations performed at the same level of theory with the available experimental data for an analogous molecule viz. acetaldehyde. Triplet excited-state energies for glycolaldehyde are reported here for the first time. Electron impact cross section calculations in the energy range 0.1 to 20 eV are carried out using ab-initio R-matrix method. We have detected one π* shape resonance in all the three models viz. SE, SEP and CC, which may also lead to a possible fragmentation channel wherein a hydrogen atom is removed from the molecule forming a glycolaldehyde dehydrogenated anionic radical (C2H3O2−). The π* shape resonance is correlated with the corresponding molecular orbital electronic structure calculations. Additionally, differential, electronic excitation, ionization and total cross sections are reported here for the first time.

Mean Lifetimes of ns, np, nd, & nf Levels of N V

Nitrogen is one of the key elements in the evolution and formation of stellar objects. Earth's atmosphere contains 21% oxygen and 78% nitrogen; these two gases give rise to aurora when ions of the solar wind in the ionosphere collide with them. Some aerosols made of nitrogen and oxygen are also found in the atmosphere. Nitrogen, hydrogen, carbon, and oxygen are the main contributors to the origin of life on Earth. The spectrum of nitrogen ion (N V) has been studied using Quantum defect theory (QDT) and Numerical Coulombic approximation (NCA). N V has two electrons in the core, with the nucleus, and one electron outside the core. It makes it hydrogen or lithium-like. In the first part, the energies of the ns, np, nd, and nf up to n < 30 were calculated with the help of QDT. In the second part, the wavelengths were calculated using the energies and line strength parameters using NCA. Very little experimental data on lifetime and transition probability are available; however, Biemont et al. have calculated the lifetime of the 48 levels of N V using coulomb approximation. In this study, we calculated the lifetime of 196 multiplets of N V. The results are compared with the available experimental and theoretical lifetimes; an excellent agreement was found between known lifetimes and calculated in this work. The lifetimes of 100 multiplets are presented for the first time. The lifetimes of each of the Rydberg series of N V were fitted, and a third-degree polynomial represents the lifetimes of each series.