Molecular Rydberg States Research Articles

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.

Formation of molecular Rydberg states in an intense laser field

Formation of molecular Rydberg states in an intense laser field

Dressed Ion-Pair States of an Ultralong-Range Rydberg Molecule

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than R_{∞}/2.

Electron correlation effects in attosecond photoionization of CO2

A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multi-electron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance.

Preparation of high orbital angular momentum Rydberg states by optical-millimeter-wave STIRAP.

Rydberg states of molecules are intrinsically challenging to study due to the presence of fast non-radiative decay pathways, such as predissociation. However, selectively exciting Rydberg states with values of the orbital angular momentum (ℓ) ℓ ≳ 3 is a productive strategy to minimize this rapid decay and to populate molecular Rydberg states with lifetimes that approach those of atoms. In this proof-of-principle demonstration, we transfer population to an nf Rydberg state of the calcium atom by stimulated Raman adiabatic passage, in which an optical and a millimeter-wave field couple the initial and final states via an intermediate nd Rydberg state. Numerical simulations reproduce the observed time and frequency dependences of the population transfer and suggest the utility of this scheme to populate high-ℓ Rydberg states of molecules.

Symmetry of molecular Rydberg states revealed by XUV transient absorption spectroscopy

Transient absorption spectroscopy is utilized extensively for measurements of bound- and quasibound-state dynamics of atoms and molecules. The extension of this technique into the extreme ultraviolet (XUV) region with attosecond pulses has the potential to attain unprecedented time resolution. Here we apply this technique to aligned-in-space molecules. The XUV pulses are much shorter than the time during which the molecules remain aligned, typically <100 fs. However, transient absorption is not an instantaneous probe, because long-lived coherences re-emit for picoseconds to nanoseconds. Due to dephasing of the rotational wavepacket, it is not clear if these coherences will be evident in the absorption spectrum, and whether the properties of the initial excitations will be preserved. We studied Rydberg states of N{}_{2} and O{}_{2} from 12 to 23 eV. We were able to determine the polarization direction of the electronic transitions, and hence identify the symmetry of the final states.

Optimisation of the dipole-Coulomb approximation for high-l Rydberg states of polar molecules

ABSTRACTThe present work deals with the question of the origin choice to get the maximal accuracy of the dipole-Coulomb approximation in the theory of molecular Rydberg states with high orbital momentum l. Concerning birefringence in polar molecules, the question of adequate origin choice has first been raised in the classical work by Buckingham & Longuet-Higgins in 1968, where it has been taken into account that the dipole moment of a polar molecular core (cation) depends on the origin choice. This dependence also leads to inseparability of dipole and quadrupole corrections to the Rydberg electron spectra in polar molecules. In the present work a new option for the problem is proposed as applied to the dipole-Coulomb approximation. Considering a simplified model of a molecular core as a system of N effective fixed point charges, we show both analytically and numerically that the optimal choice of origin, at least for a linear core, is the geometric centre of the core. On the other hand, results of the present work as well as previous publications show that the problem raised by Buckingham and Longuet-Higgins does not have a universal solution.Abbreviations: RS: Rydberg state; RSs: Rydberg states; ZEKE: zero electron kinetic energy; MATI: mass-analysed threshold ionisation; QDT: quantum defect theory; DCA: dipole-Couloumb approximation; CD: centre of dipole; CC: centre of charge; GC: geometric centre; DCAGC: dipole-Couloumb approximation with origin in the geometric centre; DCACD: dipole-Couloumb approximation with origin in the centre of dipole

Charge dynamics of a molecular ion immersed in a Rydberg-dressed atomic lattice gas

Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the vibrational motion of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. Aspects of the transport such as its direction can be controlled by the excitation laser. This leads to new directions in the investigation of hybrid atom-ion systems that can be experimentally explored using optically trapped strontium atoms.

Oscillatory Photoelectron Signal of N-Methylmorpholine as a Test Case for the Algebraic-Diagrammatic Construction Method of Second Order.

Motivated by recent progress in the application of time-resolved photoelectron spectroscopy (TRPES) to molecular Rydberg states, we report herein a detailed assessment of the performance of the second-order algebraic diagrammatic construction (ADC(2)) method in the simulation of their TRPES spectra. As the test case, we employ the tertiary aliphatic amine N-methylmorpholine (NMM), which is notable for the fact that the signal of its 3s state exhibits long-lived oscillations along the electron binding energy axis. The relaxation process of photoexcited NMM is simulated via the Born-Oppenheimer molecular dynamics method, and the resulting TRPES spectrum is generated on the basis of ionization energies and approximate Dyson orbital norms calculated with the continuum orbital technique. On the whole, the simulated TRPES spectrum achieves satisfactory agreement with experiment, which suggests that the ADC(2) method provides a realistic description of the potential energy surfaces of the relevant excited and ionized states. In particular, the simulations reproduce the fine oscillatory structure of the signal of the 3s state, and provide evidence to the effect that it results from a coherent vibrational wavepacket evolving along the deformation modes of the six-membered ring. However, it is found that ADC(2) underestimates electron binding energies by up to a few tenths of an electronvolt. The case of NMM demonstrates the usefulness of ADC(2) as a tool to aid the interpretation of the TRPES spectra of large organic molecules.

Microwave-assisted Rydberg electromagnetically induced transparency

We demonstrate electromagnetically induced transparency (EIT) in a four-level cascade-like system, where the two upper levels are Rydberg states coupled by a microwave field. A two-photon transition consisting of an off-resonant microwave field and an off-resonant optical field forms an effective coupling field to induce transparency of the probe light. We characterize the Rabi frequency of the effective coupling field, as well as the EIT microwave spectra. The results show that microwave-assisted EIT allows us to efficiently access Rydberg states with relatively high orbital angular momentum ℓ=3, which is promising for the study of exotic Rydberg molecular states.

Multiphoton Rydberg and valence dynamics of CH3Br probed by mass spectrometry and slice imaging.

The multiphoton dynamics of CH3Br were probed by Mass Resolved MultiPhoton Ionization (MR-MPI), Slice Imaging and Photoelectron Imaging in the two-photon excitation region of 66 000 to 80 000 cm-1. Slice images of the CH3+ and Br+ photoproducts of ten two-photon resonant transitions to np and nd Rydberg states of the parent molecule were recorded. CH3+ ions dominate the mass spectra. Kinetic energy release spectra (KERs) were derived from slice and photoelectron images and anisotropy parameters were extracted from the angular distributions of the ions to identify the processes and the dynamics involved. At all wavelengths we observe three-photon excitations, via the two-photon resonant transitions to molecular Rydberg states, forming metastable, superexcited (CH3Br#) states which dissociate to form CH3 Rydberg states (CH3**) along with Br/Br*. A correlation between the parent Rydberg states excited and CH3** formed is evident. For the three highest excitation energies used, the CH3Br# metastable states also generate high kinetic energy fragments of CH3(X) and Br/Br*. In addition for two out of these three wavelengths we also measure one-photon photolysis of CH3Br in the A band forming CH3(X) in various vibrational modes and bromine atoms in the ground (Br) and spin-orbit excited (Br*) states.

Rydberg optical Feshbach resonances in cold gases

We propose a novel scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering-state to an excited Rydberg-molecular state using laser light. For the s-wave scattering of two colliding ${^{87}}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimised. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homo-nuclear atomic pairs as well as to atomic mixtures with s-wave (or even p-wave) scattering.

A parallel algorithm for Hamiltonian matrix construction in electron–molecule collision calculations: MPI-SCATCI

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron – molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron–molecule collisions.

Imaging the breakdown of molecular-frame dynamics through rotational uncoupling

We demonstrate the breakdown of molecular-frame dynamics induced by the uncoupling of molecular rotation from electronic motion in molecular Rydberg states. We observe this non-Born-Oppenheimer regime in the time domain through photoelectron imaging of a coherent molecular Rydberg wave packet in $\textrm{N}_2$. The photoelectron angular distribution shows a radically different time evolution than that of a typical molecular-frame-fixed electron orbital, revealing the uncoupled motion of the electron as it precesses around the $averaged$ anisotropic potential of the rotating ion-core.

Oscillator strengths for the Rydberg states of NaHe

The oscillator strengths for Rydberg states of a NaHe molecule are calculated using a semianalytic procedure with the l-coupling effect taken into account (due to the dipole potential of a core). This effect gives rise to nonzero oscillator strengths for transitions forbidden in the atomic model of molecular Rydberg states. The difference between calculations in terms of the atomic model and calculations with consideration of the dipole moment of a core is shown for allowed transitions.

HLE16: A Local Kohn-Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies.

Local exchange-correlation functionals have low cost and convenient portability but are known to seriously underestimate semiconductor band gaps and the energies of molecular Rydberg states. Here we present a new local approximation to the exchange-correlation functional called HLE16 that gives good performance for semiconductor band gaps and molecular excitation energies and is competitive with hybrid functionals. By the simultaneous increase of the local exchange and decrease of the local correlation, electronic excitation energies were improved without excessively degrading the ground-state solid-state cohesive energies, molecular bond energies, or chemical reaction barrier heights, although the new functional is not recommended for optimizing lattice constants or molecular bond lengths. The new functional can be useful as-is for calculations on semiconductors or excited states where it is essential to control the cost, and it can also be useful in establishing a starting point for developing even better new functionals that perform well for excited states.

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states.

The dependence of multipole moments and polarizabilities on external fields appears in many applications including biomolecular molecular mechanics, optical non-linearity, nanomaterial calculations, and the perturbation of spectroscopic signatures in atomic clocks. Over a wide range of distances, distributed multipole and polarizability potentials can be applied to obtain the variation of atom-centered atoms-in-molecules electric properties like bonding-quenched polarizability. For cylindrically symmetric charge distributions, we examine single-center and atom-centered effective polarization potentials in a non-relativistic approximation for Rydberg states. For ions, the multipole expansion is strongly origin-dependent, but we note that origin-independent invariants can be defined. The several families of invariants correspond to optimized representations differing by origin and number of terms. Among them, a representation at the center of dipole polarizability optimizes the accuracy of the potential with terms through 1/r4. We formulate the single-center expansion in terms of polarization-modified effective multipole moments, defining a form related to the source-multipole expansion of Brink and Satchler. Atom-centered potentials are an origin independent alternative but are limited both by the properties allowed at each center and by the neglected effects like bond polarizability and charge flow. To enable comparisons between single-center effective potentials in Cartesian or spherical form and two-center effective potentials with differing levels of mutual induction between atomic centers, we give analytical expressions for the bond-length and origin-dependence of multipole and polarizability terms projected in the multipole and polarizability expansion of Buckingham. The atom-centered potentials can then be used with experimental data and ab initio calculations to estimate atoms-in-molecules properties. Some results are given for BaF+ and HF showing the utility and limitations of the approach. More detailed results on X 1Σ+ CaF+ are published separately.

Long-range Rydberg molecules, Rydberg macrodimers and Rydberg aggregates in an ultracold Cs gas

We present an overview of our recent investigations of long-range interactions in an ultracold Cs Rydberg gas. These interactions are studied by high-resolution photoassociation spectroscopy, using excitation close to one-photon transitions into np3/2 Rydberg states with pulsed and continuous-wave ultraviolet laser radiation, and lead to the formation of long-range Cs2 molecules. We observe two types of molecular resonances. The first type originates from the correlated excitation of two atoms into Rydberg-atom-pair states interacting at long range via multipole-multipole interactions. The second type results from the interaction of one atom excited to a Rydberg state with one atom in the electronic ground state. Which type of resonances is observed in the experiments depends on the laser intensity and frequency and on the pulse sequences used to prepare the Rydberg states. We obtain insights into both types of molecular resonances by modelling the interaction potentials, using a multipole expansion of the long-range interaction for the first type of resonances and a Fermi-contact pseudo-potential for the second type of resonances. We analyse the relation of these long-range molecular resonances to molecular Rydberg states and ion-pair states, and discuss their decay channels into atomic and molecular ions. In experiments carried out with a two-colour two-photon excitation scheme, we observe a large enhancement of Rydberg-excitation probability, which we interpret as a saturable autocatalytic antiblockade phenomenon.

Transition from SAMO to Rydberg State Ionization in C60 in Femtosecond Laser Fields.

The transition between two distinct ionization mechanisms in femtosecond laser fields at 785 nm is observed for C60 molecules. The transition occurs in the investigated intensity range from 3 to 20 TW/cm2 and is visualized in electron kinetic energy spectra below the one-photon energy (1.5 eV) obtained via velocity map imaging. Assignment of several observed broad spectral peaks to ionization from superatom molecular orbitals (SAMOs) and Rydberg states is based on time-dependent density functional theory simulations. We find that ionization from SAMOs dominates the spectra for intensities below 5 TW/cm2. As the intensity increases, Rydberg state ionization exceeds the prominence of SAMOs. Using short laser pulses (20 fs) allowed uncovering of distinct six-lobe photoelectron angular distributions with kinetic energies just above the threshold (below 0.2 eV), which we interpret as over-the-barrier ionization of shallow f-Rydberg states in C60.

Super-atom molecular orbital excited states of fullerenes.

Super-atom molecular orbitals are orbitals that form diffuse hydrogenic excited electronic states of fullerenes with their electron density centred at the centre of the hollow carbon cage and a significant electron density inside the cage. This is a consequence of the high symmetry and hollow structure of the molecules and distinguishes them from typical low-lying molecular Rydberg states. This review summarizes the current experimental and theoretical studies related to these exotic excited electronic states with emphasis on femtosecond photoelectron spectroscopy experiments on gas-phase fullerenes.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.