Rydberg Electronic States Research Articles

Rydberg-State Double-Well Potentials of Van der Waals Molecules

Recent progress in studies of Rydberg double-well electronic energy states of MeNg (Me = 12-group atom, Ng = noble gas atom) van der Waals (vdW) molecules is presented and analysed. The presentation covers approaches in experimental studies as well as ab initio-calculations of potential energy curves (PECs). The analysis is shown in a broader context of Rydberg states of hetero- and homo-diatomic molecules with PECs possessing complex ‘exotic’ structure. Laser induced fluorescence (LIF) excitation spectra and dispersed emission spectra employed in the spectroscopical characterization of Rydberg states are presented on the background of the diverse spectroscopic methods for their investigations such as laser vaporization–optical resonance (LV-OR), pump-and-probe methods, and polarization labelling spectroscopy. Important and current state-of-the-art applications of Rydberg states with irregular potentials in photoassociation (PA), vibrational and rotational cooling, molecular clocks, frequency standards, and molecular wave-packet interferometry are highlighted.

Controlled‐NOT Gate Based on the Rydberg States of Surface Electrons

AbstractDue to the long coherence time and efficient manipulation, the surface electron (SE) provides a perfect 2D platform for quantum computation and quantum simulation. In this work, a theoretical scheme to realize the controlled‐NOT gate is proposed, where the two‐qubit system is encoded on the four‐level Rydberg structure of SE. The state transfer is achieved by a three‐level structure with an intermediate level. By simultaneously driving the SE with two external electromagnetic fields, the dark state in the electromagnetically induced transparency effect is exploited to suppress the population of the most dissipative state and increase the robustness against dissipation. The fidelity of the scheme is 0.9989 with experimentally achievable parameters.

Do we need delocalised wavefunctions for the excited state dynamics of 1,1-difluoroethylene?

In this work, we set up a model Hamiltonian to study the excited state quantum dynamics of 1,1-difluoroethylene, a molecule that has equivalent atoms exchanged by a torsional symmetry operation leading to equivalent minima on the potential energy surface. In systems with many degrees of freedom where the minimum energy geometry is not unique, the ground state wavefunction will be delocalised among multiple minima. In this small test system, we probe the excited state dynamics considering localised (in a single minimum) and delocalised (spread over among multiple minima) wavefunctions and check whether this choice would influence the final outcome of the quantum dynamics calculations. Our molecular Hamiltonian comprises seven electronic states, including valence and Rydberg states, computed with the MS-CASPT2 method and projected onto the vibrational coordinates of the twelve normal modes of 1,1-difluoroethylene in its vibrational ground state. This Hamiltonian has been symmetrised along the torsional degree of freedom to make both minima completely equivalent and the model is supported by the excellent agreement with the experimental absorption spectrum. Quantum dynamics results show that the different initial conditions studied do not appreciably affect the excited state populations or the absorption spectrum when the dynamics is simulated assuming a delta pulse excitation.

Low energy inelastic electron scattering from carbon monoxide: II. Excitation of the b3Σ+, j3Σ+, B1Σ+, C1Σ+ and E1Π Rydberg electronic states

In this second part of a two part paper (first part: Zawadzki et al (2020 J. Phys. B: At. Mol. Opt. Phys. 53 165201)) we present differential scattering cross sections for excitation of several Rydberg electronic states of carbon monoxide by electron impact. The first part concerned the low-lying valence states of CO. In the present study cross sections are obtained experimentally using low-energy electron energy-loss spectroscopy and theoretically using the R-matrix method. Incident electron energies range from near-threshold of 12.5 eV to 20 eV while the scattering angles range from 20° to 120°. The R-matrix calculations use three distinct close-coupling models and their results are compared to available experimental and theoretical cross sections. The overall comparison leads to significantly improved description of the excitation cross sections for this target.

Stereodynamic Control of Collision-Induced Nonadiabatic Dynamics of NO (A2Σ+) with H2, N2, and CO: Intermolecular Interactions Drive Collision Outcomes.

Intermolecular interactions, stereodynamics, and coupled potential energy surfaces (PESs) all play a significant role in determining the outcomes of molecular collisions. A detailed knowledge of such processes is often essential for a proper interpretation of spectroscopic observations. For example, nitric oxide (NO), an important radical in combustion and atmospheric chemistry, is commonly quantified using laser-induced fluorescence on the A2Σ+ ← X2Π transition band. However, the electronic quenching of NO (A2Σ+) with other molecular species provides alternative nonradiative pathways that compete with fluorescence. While the cross sections and rate constants of NO (A2Σ+) electronic quenching have been experimentally measured for a number of important molecular collision partners, the underlying photochemical mechanisms responsible for the electronic quenching are not well understood. In this paper, we describe the development of high-quality PESs that provide new physical insights into the intermolecular interactions and conical intersections that facilitate the branching between the electronic quenching and scattering of NO (A2Σ+) with H2, N2, and CO. The PESs are calculated at the EOM-EA-CCSD/d-aug-cc-pVTZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory, an approach that ensures a balanced treatment of the valence and Rydberg electronic states and an accurate description of the open-shell character of NO. Our PESs show that H2 is incapable of electronically quenching NO (A2Σ+) at low collision energies; instead, the two molecules will likely undergo scattering. The PESs of NO (A2Σ+) with N2 and CO are highly anisotropic and demonstrate evidence of electron transfer from NO (A2Σ+) into the lowest unoccupied molecular orbital of the collision partner, that is, the harpoon mechanism. In the case of ON + CO, the PES becomes strongly attractive at longer intermolecular distances and funnels population to a conical intersection between NO (A2Σ+) + CO and NO (X2Π) + CO. In contrast, for ON + N2, the conical intersection is preceded by an ∼0.40 eV barrier. Overall, our work shines new light into the impact of coupled PESs on the nonadiabatic dynamics of open-shell systems.

The density matrix via few dominant observables: The quantum interference in the isotope effect for atto-pumped N2.

Atto- and sub-femto-photochemistry enables preparation of molecules in a coherent superposition of several electronic states. Recently [Ajay et al., Proc. Natl. Acad. Sci. U. S. A. 115, 5890-5895 (2018)], we examined an effect of the nuclear mass during the non-adiabatic transfer between strongly coupled Rydberg and valence electronic states in N2 excited by an ultrafast pulse. Here, we develop and analyze an algebraic description for the density matrix and its logarithm, the surprisal, in such a superposition of states with a focus on the essentially quantum effect of mass. This allows for the identification of a few observables that accurately characterize the density matrix of the system with several coupled electron-nuclear states. We compact the time evolution in terms of time-dependent coefficients of these observables. Using the few observables, we derive an analytical expression for the time-dependent surprisal. This provides a mass-dependent phase factor only in the observables off-diagonal in the electronic index. The isotope effect is shown to be explicitly driven by the shift in the equilibrium position of the valence state potential. It is analytically given as a time-dependent phase factor describing the interference in the overlap of the two wave packets on the coupled electronic states. This phase factorizes as a product of classical and quantal contributions.

A combined experimental and theoretical study of the lowest-lying valence, Rydberg and ionic electronic states of 2,4,6-trichloroanisole

We investigate for the first time the gas-phase lowest-lying valence, Rydberg and ionic electronic states of 2,4,6-trichloroanisole (TCA) using synchrotron radiation for photoabsorption and photoelectron spectroscopy. The high-resolution vacuum ultraviolet photoabsorption spectrum, in the 4.0–10.8 eV energy-range, has been measured with absolute photoabsorption cross-sections and, thanks to novel ab initio calculations of the vertical energies and oscillator strengths, an assignment of the electronic transitions is comprehensively reported. The assignment of weak vibrational features in the absorption bands of TCA reveal that the ring and C–Cl stretching modes are mainly active. In the photoelectron spectrum the lowest 18 ionic bands, between 8 and 30 eV, have been observed and assigned using the first set of calculated valence and outer valence vertical ionisation energies. Finally, the measured absolute photoabsorption cross sections have also been used to estimate the photolysis lifetime of TCA in the upper stratosphere (20–50 km).

A revisited study of the low-lying electronic states of HF molecule

Hydrogen fluoride (HF) has served as a benchmark molecule for ab initio methods. Consequently, it has been extensively investigated in the past few decades. The energy ordering of the low-lying triplet electronic states has proven controversial in previous computational studies. In this work, the Gaussian basis of F and H atoms are calibrated by adding diffuse functions to the aug-cc-pV5Z valence basis sets. The electronic structure of HF molecule is studied by the multireference configuration interaction method plus Davidson correction method (MRCI+Q). The potential energy curves (PECs) of 19 electronic states are computed, and the spectroscopic constants of the bound states are determined. The low-lying triplet Rydberg electronic states 23Σ+ (3Σ+R1), 23Π (3ΠR1) and 13Δ (3ΔR1) are characterized and compared with the previous computational results. The transition dipole moments (TDMs) and Franck-Condon factors (FCFs) between the electronic states are subsequently calculated. Finally, the spontaneous radiative lifetimes of four spin-allowed transitions are obtained. The results of this paper will improve the understanding on the electronic excited states of HF molecule, especially the electronic structure and spectra characteristics of the triplet excited states.

Rydberg States of H3 and HeH as Potential Coolants for Primordial Star Formation.

Current theory and measurements establish the age of the universe as ca. 13.8 billion years. For the first several hundred million years of its existence, it was a dark, opaque void. After that, the hydrogen atoms comprising most of the "ordinary" matter began to condense and ionize, eventually forming the first stars that would illuminate the sky. Details of how these "primordial" stars formed have been widely debated, but remain elusive. A central issue in this process is the mechanism by which the primordial gas (mainly hydrogen and helium atoms) collected via the action of dark matter cooled and further accreted to fusion densities. Current models invoke collisional excitation of H2 molecular rotations and subsequent radiative rotational transitions allowed by the weak molecular quadrupole moment. In this work, we review the salient considerations and present some new ideas, based on recent spectroscopic observations of neutral H3 Rydberg electronic state emission in the mid-infrared region.

Relaxation of the Excited Rydberg States of Surface Electrons on Liquid Helium.

We report the first direct observation of the decay of the excited-state population in electrons trapped on the surface of liquid helium. The relaxation dynamics, which are governed by inelastic scattering processes in the system, are probed by the real-time response of the electrons to a pulsed microwave excitation. Comparison with theoretical calculations allows us to establish the dominant mechanisms of inelastic scattering for different temperatures. The longest measured relaxation time is around 1 μs at the lowest temperature of 135mK, which is determined by the inelastic scattering due to the spontaneous two-ripplon emission process. Furthermore, the image-charge response shortly after applying microwave radiation reveals interesting population dynamics due to the multisubband structure of the system.

Observation of gerade Rydberg state of Cd2 van der Waals complex cooled in free-jet expansion beam and excited using optical-optical double resonance method

We report on the observation of a gerade Rydberg electronic energy state of Cd2 van der Waals (vdW) complex vibrationally cooled in a free-jet expansion beam. Cd2 in the beam were excited from the X10g+(51S0) ground via the b30u+(53P1) intermediate to the final gerade state using optical–optical double resonance (OODR) method. A pronounced vibrational progression with partly resolved isotopologue components was recorded and analyzed. The analysis of isotopic separation indicated the excitation to high vibrational levels (υ′≈50). A comparison with the result of ab initio calculations reveals, that Cd2 was most probably excited to the 31g -state correlating with the 63S1 atomic asymptote.

Cosmology, astrobiology and the RNA world: just add quintessential water

AbstractLaboratory generation of water nanoclusters from amorphous ice and strong terahertz (THz) radiation from water nanoclusters ejected from water vapour into a vacuum suggest the possibility of water nanoclusters ejected into interstellar space from abundant amorphous ice-coated cosmic dust produced by supernovae explosions. Water nanoclusters (section ‘Water nanoclusters’) offer a hypothetical scenario connecting major mysteries of our Universe: dark matter (section ‘Baryonic dark matter’), dark energy (section ‘Dark energy’), cosmology (section ‘Cosmology’), astrobiology (section ‘Astrobiology’) and the RNA world (section ‘The RNA world’) as the origin of life on Earth and habitable exoplanets. Despite their expected low density in space compared to hydrogen, their quantum-entangled diffuse Rydberg electronic states make cosmic water nanoclusters a candidate for baryonic dark matter that can also absorb, via the microscopic dynamical Casimir effect, the virtual photons of zero-point-energy vacuum fluctuations above the nanocluster cut-off vibrational frequencies, leaving only vacuum fluctuations below these frequencies to be gravitationally active, thus leading to a possible common origin of dark matter and dark energy. This picture includes novel explanations of the small cosmological constant, the coincidence of energy and matter densities, possible contributions of the red-shifted THz radiation from cosmic water nanoclusters at redshift z ≅ 10 to the cosmic microwave background (CMB) spectrum, the Hubble constant crisis, the role of water as a known coolant for rapid early star formation and ultimately, how life may have originated from RNA protocells on Earth and exoplanets and moons in the habitable zones of developed solar systems. Together, they lead to a cyclic universe cosmology – based on the proposed equivalence of cosmic water nanoclusters to a quintessence scalar field – instead of a multiverse based on cosmic inflation theory. Recent CMB birefringence measurements may support quintessence. Finally, from the quantum chemistry of water nanoclusters interacting with prebiotic organic molecules, amino acids and RNA protocells on early Earth and habitable exoplanets, this scenario is consistent with the anthropic principle that our Universe must have those properties which allow life, as we know it – based on water, to develop at the present stage of its history.

Long-range Rydberg molecule Rb2 : Two-electron R -matrix calculations at intermediate internuclear distances

The adiabatic potential energy curves of Rb$_2$ in the long-range Rydberg electronic states are calculated using the two-electron \textit{R}-matrix method [M. Tarana, R. \v{C}ur\'{i}k, Phys. Rev. A \textbf{93}, 012515 (2016)] for the intermediate internuclear separations between 35 a.u. and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where the Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.

Bound→free and bound→bound multichannel emission spectra from selectively excited Rydberg states in the ZnAr and CdAr van der Waals complexes

Multichannel dispersed emission spectra originated upon a selective excitation of Rydberg electronic energy states in the ZnAr and CdAr van der Waals (vdW) complexes are simulated and analysed as a proof-of-concept of the future experimental approach. Simulations of the emission spectra are based on ab-initio calculated interatomic potentials and transition dipole moments (TDMs), that for ZnAr were newly calculated. Experimental set-up that is under construction along with the experimental procedure are discussed.

Rydberg spectrum of a single trapped Ca+ ion: A Floquet analysis

We compute the Rydberg spectrum of a single Ca$^+$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in Ca$^+$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for e$^-$+Ca$^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of Ca$^+(23P)$ and Ca$^+(52F)$ Rydberg lines.

Shuttling of Rydberg Ions for Fast Entangling Operations.

We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using the high electric polarizability of the Rydberg electronic states in combination with mutual Coulomb coupling of ions that establishes common modes of motion. After laser initialization of ions to a superposition of ground and Rydberg states, the entanglement operation is driven purely by applying a voltage pulse that shuttles the ion crystal back and forth. This operation can achieve entanglement on a sub-μs timescale, more than 2 orders of magnitude faster than typical gate operations driven by continuous-wave lasers. Our analysis shows that the fidelity achieved with this protocol can exceed 99.9% with experimentally achievable parameters.

Image-Charge Detection of the Rydberg States of Surface Electrons on Liquid Helium.

We propose and experimentally demonstrate a new spectroscopic method, image-charge detection, for the Rydberg states of surface electrons on liquid helium. The excitation of the Rydberg states of the electrons induces an image current in the circuit to which the electrons are capacitively coupled. In contrast to the conventional microwave absorption measurement, this method makes it possible to resolve the transitions to high-lying Rydberg states of the surface electrons. We also show that this method can potentially be used to detect quantum states of a single electron, which would pave a way to utilize the quantum states of the surface electrons on liquid helium for quantum computing.

Spectroscopy of CdKr van der Waals complex using OODR process: New determination of the [formula omitted] Rydberg state potential

Comprehensive spectroscopic study of CdKr van der Waals complex in its Rydberg electronic energy state E3Σ1+(5s6s3S1), using OODR process from the ground X1Σ0+(5s21S0) state via the intermediate A30+(5s5p3P1) or B31(5s5p3P1) states, is presented. Detection of the E3Σ1+,υ′←A30+,υ″ and E3Σ1+,υ′←B31,υ″ transition frequencies with higher accuracy and spectrally narrower laser extends previous analyses and simulations of laser induced fluorescence (LIF) excitation spectra. Potential energy curve of the E3Σ1+state exhibits double-well structure with inner (deeper) E3Σ1in+ and outer (shallower)E3Σ1out+ wells. More reliable characterization of both wells using inversed perturbation approach (IPA) methodology is achieved.

Compensation of the trap-induced quadrupole interaction in trapped Rydberg ions

The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.

Coupling between Rydberg States and Landau Levels of Electrons Trapped on Liquid Helium.

We investigate the coupling between Rydberg states of electrons trapped on a liquid helium surface and Landau levels induced by a perpendicular magnetic field. We show that this realizes a prototype quantum system equivalent to an atom in a cavity, where their coupling strength can be tuned by a parallel magnetic field. We determine experimentally the renormalization of the atomic transition energies induced by the coupling to the cavity, which can be seen as an analog of the Lamb shift. When the coupling is sufficiently strong, the transition between the ground and first excited Rydberg states splits into two resonances corresponding to dressed states with vacuum and one photon in the cavity. Our results are in quantitative agreement with the energy shifts predicted by the effective atom in a cavity model where all parameters are known with high accuracy.