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Significant progress has been made in recent years demonstrating an all-optical high sensitivity Radio Frequency (RF) sensor exploiting the Electromagnetically Induced Transparency (EIT) effect in an atomic vapor. In order to exploit the potential of these Rydberg RF receivers in practical telecommunications applications, it is necessary to operate these devices outside of a sophisticated optics laboratory and to use rugged components in a noisy environment. We present a simple analytic model for the operation of a sensitive Rydberg RF receiver to predict the optical modulation in response to an RF signal. We show that the optical modulation depth can be maximized using an optimum coupling intensity. The optical modulation depth drops off rapidly as the RF source is detuned away from resonance. By detuning the coupling frequency to compensate for the RF detuning we demonstrate that the useful RF bandwidth of the receiver can be significantly extended. We measure this variation in optical response using a Rubidium vapor at a 15GHz RF carrier frequency. Using readily available optical components we obtain good agreement with our model. This convenient analytic approach will simplify the design and operation of Rydberg RF receivers as sensitive components in future 5G mobile communications, particularly for the power-limited uplink from mobile device to base-station.

Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms and thus it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in both the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function (RDF) of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center and thus they can be unambiguously identified as Rydberg orbitals. We found that due to two-dimensional ductility of planar superatoms’ transition orbitals, superatoms have the superiority in RSE regulation. Our findings provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

We investigate the long-range, two-body interactions between rubidium and potassium atoms in highly excited ($n=70$) Rydberg states. After establishing properly symmetrized asymptotic basis states, we diagonalize an interaction Hamiltonian consisting of the standard Coulombic potential expansion and atomic fine structure to calculate electronic potential energy curves. We find that when both atoms are excited to either the $70s$ state or the $70p$ state, both the $\Omega=0+$ symmetry interactions and the $\Omega=0-$ symmetry interactions demonstrate a deep potential well capable of supporting many bound levels; the size of the corresponding dimer states are on the order of 2.25 $\mu$m. We estabish $n$-scaling relations for the equilibrium separation $R_e$ and the dissociation energy $D_e$ and find these relations to be consistent with similar calculations involving the homonuclear interactions between rubidium and cesium. We discuss the specific effects of $\ell$-mixing and the exact composition of the calculated potential well \textit{via} the expansion coefficients of the asymptotic basis states. Finally, we apply a Landau-Zener treatment to show that the dimer states are stable with respect to predissociation., Comment: 8 pages, 4 figures, 4 tables

Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-NOT gate. The gates need only three steps for coupling one Rydberg state, depend on easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotation error in the weak interaction regime. Importantly, they can work with very weak interactions so that well-separated qubits can be entangled. The gates are sensitive to the irremovable fluctuation of Rydberg interactions, but can still have a fidelity over 98\% with realistic position fluctuation of qubits separated over 20~$\mu$m., Comment: 7 pages, 3 figures

An analysis is performed of data on the trans → cis-photoisomerization of azobenzene (trans-AB) in light of the Rydberg 3s orbital (R3s) of the azo-group induces the formation of electronically (e-) polarized tautomers (Z+) in addition to its electrically neutral tautomer (Z). The Z+ tautomers have a chromogenic center in the form of a phenylaminyl type cation (PhAT) with a Vis excitation band at λm = 445–450 nm. It is found that the isomerization of trans-AB under the action of Vis light and UV radiation proceeds through the photoexcited polarized e-tautomer Z+*, which undergoes adiabatic changes in its e-configurations under the influence of the R3s-orbital. The Z+* state (with one PhAT cation) then transitions to the Z++* state (with two PhAT cations), which participates in competitive transformations: isomerization in cis-AB and a return to Z+*, which relaxes in Z+. It is shown that a rotational isomerization pathway can form when there are no steric obstacles blocking rotation around the N–N bond. When there are such obstacles, isomerization proceeds through adiabatic displacement of the ph-rings in intermediate Z++*, first into its rectilinear conformation, and then toward one another through the stage of intermediate e-polarized excited state cis-AB*, which has a three-electron bond in addition to the σ-bond of the azo-group between adjacent sp2 orbitals.

Photodissociation dynamics of the jet-cooled vinoxy radical (CH2CHO) via the B2A″ state was studied in the near-ultraviolet (near-UV) region of 308-328 nm using high-n Rydberg H atom time-of-flight (HRTOF) and resonance-enhanced multiphoton ionization (REMPI) techniques. The vinoxy radical beam was produced by 193 nm photolysis of ethyl vinyl ether followed by supersonic expansion. The H + CH2CO product channel was observed directly in the H atom TOF spectra. The H atom photofragment yield (PFY) spectra were obtained by integrating the H atom TOF spectra and measuring the H atom REMPI signals, and showed several vibronic bands of the B2A″ state. The translational energy distributions of the H + CH2CO products, P(ET)'s, were obtained at several vibronic transitions. The P(ET) distributions were broad, peaking at a low energy of ∼3500 cm-1. The product translational energy release was moderate; the average translational energy release in the maximum available energy, ⟨fT⟩, was in the range of 0.24-0.27. The product angular distributions in this wavelength region were slightly anisotropic, with the β parameter in the range of 0.10-0.24. The near-UV photodissociation mechanism of the H + CH2CO product channel of the vinoxy radical is consistent with unimolecular dissociation on the electronic ground state (X2A″) following internal conversion from the B2A″ state to the A2A' state and then to the X2A″ state (although unimolecular dissociation from the first excited A2A' may also contribute).

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.

Exciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe2 and WSe2 gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s–3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe2 and WSe2. An exciton polaron is a quasiparticle composed of an exciton dressed with an electron-hole cloud, and this concept has been used to explain the ground excitonic states in charged monolayer transition metal dichalcogenides. Here the authors present experimental and theoretical evidence of exciton-polaron Rydberg states in monolayer MoSe2 and WSe2.

Even-parity Rydberg and autoionizing Rydberg spectrum of antimony have been calculated by relativistic multichannel theory, in which the ionic core dipole polarization effect due to the Rydberg ele...

Two-photon absorption (2PA) spectra of liquid cyclohexane and hexanes are reported for the energy range 6.4-8.5 eV (177-145 nm), providing detailed information about their electronic structures in bulk liquid. Using a broadband pump-probe fashion, we measured the continuous 2PA spectra by simultaneous absorption of a 266 nm (4.6 eV) pump photon and one UV-vis probe photon from the white-light continuum (1.8-3.9 eV). Theoretical one-photon absorption (1PA) and 2PA cross sections of isolated gas phase molecules are computed by the equation of motion coupled-cluster method with single and double substitutions (EOM-CCSD) to substantiate the assignment of the experimental spectra, and the natural transition orbital (NTO) analysis provides visualization of the participating orbitals in a transition. Our analysis suggests that upon solvation transitions at the lowest excitation energy involving promotion of electron to the 3s Rydberg orbitals are blue-shifted (∼0.55 eV for cyclohexane and ∼0.18 eV for hexanes) to a greater extent as compared to those involving other Rydberg orbitals, which is similar to the behavior observed for water and alcohols. All other transitions experience negligible (cyclohexane) or minor red-shift by ∼0.15-0.2 eV (hexane) upon solvation. In both alkanes, the spectra are entirely dominated by Rydberg transitions: the most intense bands in 1PA and 2PA spectra are due to the excitation of electrons to the Rydberg "p" and "d" type orbitals, respectively, although one transition terminating in the 3s Rydberg has significant 2PA strength. This work demonstrates that the gas phase electronic transition properties in alkanes are not significantly altered upon solvation. In addition, electronic structure calculations using an isolated-molecule framework appear to provide a reasonable starting point for a semiquantitative picture for spectral assignment and also to analyze the solvatochromic shifts for liquid phase absorption spectra.

Purpose: This work aims at investigating the zinc atoms in the triplet preionization – Rydberg states. The energy levels of atoms having two electrons outside the closed shell were studied mainly by the optical spectroscopy methods. However, just using the microwave spectroscopy to measure the frequency of transitions between the two Rydberg states allows to increase the accuracy of measurements in two or more orders of magnitude. Disign/methodology/approach:A line of three dye lasers is used to excite the zinc atoms into the triplet Rydberg states with a predetermined set of quantum numbers. The radiation of the first two of them is transformed into the second harmonic in nonlinear crystals. Dye lasers are excited by the radiation of the second harmonic of one YAG: ND3+ laser. All three radiations are reduced to the zone of interaction with the laser and the microwave radiation, which is located between the plates of the ionization cell, where the pulsed electric field is created. The excited Rydberg atoms are recorded with the field ionization procedure. The beam of neutral atoms is created by an effusion cell under the vacuum conditions, the residual pressure does not exceed 10-5 mm Hg. A pulsed electric field of some certain intensity results inionization of atoms excited by microwave radiation and in acceleration of electrons, which have appeared in the direction of the secondary electron multiplier, though being insufficient for ionization of atoms excited only by the laser radiation and which are initial for interaction with microwaves. By scanning the microwave radiation frequency with the given step and measuring the signal intensity of the secondary electron multiplier, the excitation spectrum of the atoms under study can be obtained. Findings: Using the created laser-microwave spectrometer, the frequencies of the F→D, F→F and F→G transitions between the triplet Rydberg states of zinc atoms were measured. From the analysis made of the transition frequencies, the quantum defect decomposition constants were obtained by the Ritz formula for the D, F, and G states of zinc atoms. Conclusions: The frequencies of the F→D, F→F and F→G transitions between the triplet Rydberg states of zinc atoms were measured that allowed obtaining the quantum defect decomposition constants according to the Ritz formula for the D, F and G states of zinc atoms, that in turn had allowed to calculate the energy of these terms and the transition frequencies at least in two orders of magnitude more accurately as against the similar measurements made by the optical spectroscopy. Key words: zinc atom, triplet states of atoms, Rydberg states, laser excitation, microwave radiation

We report in this paper energy positions of Rydberg series from metastable state of Ca3+ ion.. Calculations are performed up to n = 20 using the Screening Constant by Unit Nuclear Charge (SCUNC). The present results compared wellwith the experimental data of Ghassan A Alna’washi which are the only available values.The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

We propose a method to continuously frequency shift a target laser that is frequency stabilized by a reference laser, which is several hundreds of nanometers detuned. We demonstrate the technique using the $\mathrm {5S_{1/2}} \rightarrow \mathrm {5P_{3/2}} \rightarrow \mathrm {29D_{5/2}}$ Rydberg transition in 87Rb vapor and lock the 482 nm target laser to the 780 nm reference laser using the cascaded electromagnetically induced transparency signal. The stabilized frequency of the target laser can be shifted by about 1.6 GHz by phase modulating the reference laser using a waveguide-type electro-optical modulator. This simple method for stable frequency shifting can be used in atomic or molecular physics experiments that require a laser frequency scanning range on the order of several GHz.

To our knowledge, this is the first study to report the quantum defects of F31 and F33 highly-excited states of neutral mercury. The frequencies of 36 measured two-photon Rydberg–Rydberg 6snfFJ1,3→...

With the redefinition of the International System of Units (SI) that occurred in November 2018, there has been much attention on the development of atom-based sensors for metrology applications that are directly linked to the SI. In particular, great progress has been made in using Rydberg atom-based techniques for electric field (E-field) metrology. These Rydberg atombased E-field sensors have made it possible to develop atom-based receivers, which potentially have many benefits over conventional technologies in detecting and receiving modulated signals.

We present the derivation of simple analytical expressions for calculating the widths of Rydberg states with small orbital angular momenta in Zn+, Cd+, Hg+ ions of group IIb of the periodic system of elements induced by blackbody radiation (BBR) at ambient temperatures from 100 to 3000 K. The probabilities of radiative transitions from excited nS, nP, nD and nF states to all dipole-accessible states of ions are calculated. The wave functions of the quantum defect (QD) method for the initial and final states of the Rydberg electron are used to calculate the amplitudes of transitions between bound states. The dependences of the probabilities of induced decays and excitations on the BBR temperature, the principal and orbital quantum numbers of the Rydberg ion are determined. Analytical expressions are derived for numerical estimates of the contributions of the probabilities of thermally induced decays and excitations to the width of the Rydberg energy level. The numerical values of the coefficients of interpolation polynomials representing asymptotic expansions in powers of the principal quantum number n for the relative probabilities of decays and excitations of Rydberg states with large values of n and small orbital angular momenta l = 0, 1, 2, 3 are calculated.

The near-edge X-ray absorption fine structure (NEXAFS) spectra of indole, 2,3-dihydro-7-azaindole, and 3-formylindole in the gas phase have been measured at the carbon and nitrogen K-edges. The spectral features have been interpreted based on density functional theory (DFT) calculations within the transition potential (TP) scheme, which is accurate enough for a general description of the measured C 1s NEXAFS spectra as well as for the assignment of the most relevant features. For the nitrogen K-edge, the agreement between experimental data and theoretical spectra calculated with TP-DFT was not quite satisfactory. This discrepancy was mainly attributed to the many-body effects associated with the excitation of the core electron, which are better described using the time-dependent density functional theory (TDDFT) with the range separated hybrid functional CAM-B3LYP. An assignment of the measured N 1s NEXAFS spectral features has been proposed together with a complete description of the observed resonances. Intense transitions from core levels to unoccupied antibonding π* states as well as several transitions with mixed-valence/Rydberg or pure Rydberg character have been observed in the C and N K-edge spectra of all investigated indoles.

The functional dependence of the values ​​of the terms and ionization potentials of atoms and/or dimers on the information-energy codes of photons interacting with matter is revealed on the basis of absorption spectra, which characterize the physicochemical properties of matter and represent information of a related type determined by self-consistent codes of the source and receiver of information. The tangential function for the systematization of electronic terms in the informational model of quantization (IMQ) has shown the periodic nature of the functions with self-consistency of the photon codes with the codes of atoms in the Periodic Table of Elements. A hypothesis has been proposed about the “subjective” interaction of a photon with matter; an approximation of the ionization potentials of atoms was carried out on the basis of a unified criterion. Extrapolation of the terms and ionization potentials of dimers showed that all the terms observed in absorption fit into series similar to Rydberg terms, and taking the multiplicity into account, certain of their sums form series with different regression coefficients characterizing the intemers (possible valences of dimers). The information component of the interaction of light and matter has revealed real prospects for the development of a new theory of quantum optics and the systematization of large spectroscopy databases.

Entangled photon pairs are a fundamental component for testing the foundations of quantum mechanics, and for modern quantum technologies such as teleportation and secured communication. Current state-of-the-art sources are based on nonlinear processes that are limited in their efficiency and wavelength tunability. This motivates the exploration of physical mechanisms for entangled photon generation, with a special interest in mechanisms that can be heralded, preferably at telecommunications wavelengths. Here we present a mechanism for the generation of heralded entangled photons from Rydberg atom cavity quantum electrodynamics (cavity QED). We propose a scheme to demonstrate the mechanism and quantify its expected performance. The heralding of the process enables non-destructive detection of the photon pairs. The entangled photons are produced by exciting a rubidium atom to a Rydberg state, from where the atom decays via two-photon emission (TPE). A Rydberg blockade helps to excite a single Rydberg excitation while the input light field is more efficiently collectively absorbed by all the atoms. The TPE rate is significantly enhanced by a designed photonic cavity, whose many resonances also translate into high-dimensional entanglement. The resulting high-dimensionally entangled photons are entangled in more than one degree of freedom: in all of their spectral components, in addition to the polarization—forming a hyper-entangled state, which is particularly interesting in high information capacity quantum communication. We characterize the photon comb states by analyzing the Hong-Ou-Mandel interference and propose proof-of-concept experiments.

Condensation of hydrogen Rydberg atoms (highly electronically excited) into the lowest energy state of condensed hydrogen i.e. the ultra-dense hydrogen phase, H(0), has gained increased attention not only from the fundamental aspects but also from the applied point of view. The physical properties of ultra-dense hydrogen H(0) were recently reviewed (Physica Scripta 2019 https://doi.org/10.1088/1402-4896/ab1276 ), summarizing the results reported in 50 publications during the last ten years. The main application of H(0) so far is as the fuel and working medium in nuclear particle generators and nuclear fusion reactors which are under commercial development. The first fusion process showing sustained operation above break-even was published in 2015 (AIP Advances) and used ultra-dense deuterium D(0) as fuel. The first generator giving a high-intensity muon flux intended for muon-catalyzed fusion reactors was patented in 2017, using H(0) as the working medium. Here, we first focus on the different nuclear processes using hydrogen isotopes for energy generation, and then on the detailed processes of formation of H(0). The production of H(0) employs heterogeneous catalysts which are active in hydrogen transfer reactions. Iron oxide-based, alkali promoted catalysts function well, but also platinum group metals and carbon surfaces are active in this process. The clusters of highly excited Rydberg hydrogen atoms H(l) are formed upon interaction with alkali Rydberg matter. The final conversion step from ordinary hydrogen Rydberg matter H(l) to H(0) is spontaneous and does not require a solid surface. It is concluded that the exact choice of catalyst is not very important. It is also concluded that the crucial feature of the catalyst is to provide excited alkali atoms at a sufficiently high surface density and in this way enabling formation and desorption of H(0) clusters. Finally, the relation to industrial catalytic processes which use H(0) formation catalysts is described and some important consequences like the muon and neutron radiation from H(0) are discussed.

We have used 308 nm photolysis of acetaldehyde to measure a photoionization spectrum of the formyl (HCO) radical between 8 and 11.5 eV using an 11 meV FWHM photoionization energy resolution. We have confirmed that the formyl radical is the carrier of the spectrum by generating an identical spectrum of the HCO product in the Cl + H2CO reaction. The spectrum of HCO and its deuterated isotopologue (DCO) have several resolved autoionizing resonances above the Franck-Condon envelope, which we assign to autoionization after initial excitation into neutral 3sσ and 3p Rydberg states converging to the first triplet excited state of HCO+(a 3A'). The quantum defects for these states are δ3sσ = 1.06 ± 0.02 and δ3p = 0.821 ± 0.019. We report absolute photoionization cross-section measurements of σHCOPI(9.907 eV) = 4.5 ± 0.9 Mb, σHCOPI(10.007 eV) = 4.8 ± 1.0 Mb, σHCOPI(10.107 eV) = 6.0 ± 1.2 Mb, σHCOPI(10.107 eV) = 5.7 ± 1.2 Mb, and σHCOPI(10.304 eV) = 10.6 ± 2.2 Mb relative to the photoionization cross section of the methyl radical. The absolute cross-section measurements are a factor of ∼1.5 larger than those determined in past studies, although the presence of strong autoionizing features supports a dependence on photoionization energy resolution. We propose that the semiempirical model of Xu and Pratt for estimation of free radical photoionization cross sections is more accurate when applied with a reference species containing the same atoms as the free radical rather than isoelectronic species with different atoms.

The Hawking temperature and Entropy of Reissner-Nordstrom (RN) black hole can be derived from energy quantization of the test particle moving around different circular orbits which is analog to the Bohr’s atomic model. Energy transitions (recall the Rydberg formula) can lead to radiations that can be experimentally detected in the future. Following gravitoelectromagnetism (GEM) it is possible to split the upper bound of energy without the quantization effects on energy level splitting in atoms and molecules due to the hypothetical nature of the gravitipole. Here we have mentioned the entropy and other thermodynamic properties of RN black holes within string theory going well beyond the thermodynamic limit.

According to the existing paradigm, helium atoms and helium-like ions (hereafter, heliumic systems) in a relatively weak external static electric field do not exhibit the linear Stark effect—in distinction to hydrogen atoms and hydrogen-like ions. In the present paper we consider the classical dynamics of a muonic-electronic heliumic system in Rydberg states–starting from the concept from our previous paper. We show that there are two states of the system where the averaged electric dipole moment is non-zero. Consequently, in these states the heliumic system should exhibit the linear Stark effect even in a vanishingly small electric field, which is a counter-intuitive result. We also demonstrate the possibility of controlling the overall precession of the electronic orbit by an external electric field. In particular, we show the existence of a critical value of the external electric field that would “kill” the precession and make the electronic orbit stationary. This is another counter-intuitive result. We calculate analytically the value of the critical field and show that it is typically smaller or even much smaller than 1 V/cm.

We have theoretically investigated the modulation structures of the excited-state population of an argon atom exposed to a linearly polarized 800-nm laser pulse in the tunneling region. The numerical result identifies a nearly opposite phase modulation structure between the low-lying n = 4–7 states and over all higher $$n>7$$ states. This phase-dependent alternating population phenomenon is found to be related to the periodic channel-closing effect that results from ac-Stark-shifted multiphoton resonances. Moreover, the angular momentum states attributed to different parities have a similar alternating effect, which confirms a multiphoton process in the tunneling region. We introduce a mechanism of two-photon $$\Lambda $$ -type Raman transitions involving Rydberg and continuum states with a simultaneous redistribution of states to account successfully for this observed out-of-phase angular momentum state population.

The measurements of Montenbrook et al. to determine the water surface level of the Walchensee alpine lake in Bavaria (Germany) are a vivid example of the manifestation of the peculiarities of the relationship between the GPS satellite system as a source and remote sensing of the Earth’s surface. The experiments were conducted in 2007 in the framework the GORS (GPS Occultation, Reflectometry and Scatterometry) program. The authors described the observed features in detail but did not provide their physical justification. In this study, it is shown that the observed effects are caused by the resonant interaction of electromagnetic waves with a medium containing Rydberg molecular complexes. They are the main reason for the delay of satellite constellation signals at altitudes of 60 to 110 km.

In this paper, we proposed a model based on Rydberg atoms for controlling the optical bistability (OB) and optical multistability (OM) in a ring cavity. The atoms interact with an elliptical polarized probe light and a strong coupling light in the presence of external magnetic field. We realized that the threshold of OB can be controlled by elliptical polarized parameter when the first excited states of the atoms interact with Rydberg state. Also, we found that by adjusting the elliptical parameter of probe light, the switching from OB to OM is possible when we consider the strong coupling between Rydberg level and first excited state of the atomic system. We find that when the probe light becomes linearly the OB and OM disappear due to Rydberg electromagnetically induced transparency. However, by adjusting the polarized parameter of the probe light the threshold of OB can be controlled due to Rydberg electromagnetically absorption. Our proposed model can be used as an all-optical device for switching between OB and OM with potential applications in optical communication.

Band-edge excitons of few-layer nickel phosphorous trisulfide (NiPS3) are characterized via micro-thermal-modulated reflectance (μTR) measurements from 10 to 300 K. Prominent μTR features of the A exciton series and B are simultaneously detected near the band edge of NiPS3. The A exciton series contains two sharp A1 and A2 levels and one threshold-energy-related transition (direct gap, E∞), which are simultaneously detected at the lower energy side of NiPS3. In addition, one broadened B feature is present at the higher energy side of few-layer NiPS3. The A series excitons may correlate with majorly d-to-d transition in the Rydberg series with threshold energy of E∞ ≅ 1.511 eV at 10 K. The binding energy of A1 is about 36 meV, and the transition energy is A1 ≅ 1.366 eV at 300 K. The transition energy of B measured by μTR is about 1.894 eV at 10 K. The excitonic series A may directly transit from the top of valence band to the conduction band of NiPS3, while the B feature might originate from the spin-split-off valence band to the conduction band edge. The direct optical gap of NiPS3 is ~1.402 eV at 300 K, which is confirmed by μTR and transmittance experiments.

We have observed the ultrafast conformational dynamics of electronically excited N-methyl piperidine (NMP) using time-resolved Rydberg fingerprint spectroscopy. Optical excitation at various wavelengths ranging from 212 nm to 229 nm leads to the 3s or 3p Rydberg states and induces coherent oscillatory motions with periods of about 700 fs. These coherent motions survive the internal conversion from 3p to 3s but then dephase on a time scale of a few oscillations. Intramolecular vibrational energy redistribution on a picosecond time scale leads to an equilibrium between two conformeric structures that are separated in binding energy by 0.09 eV. Model calculations using the DFT-SIC method are in excellent agreement with the experiments and identify the conformers as the chair and twist structures of NMP. The analysis of the equilibrium parameters at long time delays as a function of excitation wavelength allows for the extraction of thermodynamic parameters for the conformeric transformation. We derive an enthalpy of the chair to the twist reaction in the 3s excited state of 62 meV with an entropy of 19.70 Jmol-1K-1. An activation energy of 276 meV is also obtained with a kinetic model.

A cold Rydberg gas, with its atoms prepared initially all in the excited state |n0> , with n0 »1, contains an excessive amount of energy, and presumably is to relax by the Penning-type molecular auto-ionization (MAI), in which a portion of excess energy of one atom is given to another near-by atom and ionizing it. Its complementary process, the resonant energy transfer (RET), is discussed, in which the excess energy of one atom is used on another to form a hyper-excited atomic state |na> with na»n0. This process is always present, provided certain resonance energy conditions are satisfied. In this report, the n0 and density dependences of the RET rates are studied in detail, employing a simple model: 1) at low densities, the RET is mediated by the dipole-dipole coupling Vdd and its rates are generally much smaller than that of MAI, especially for small n0. But 2) as the density increases, our model shows that the rates become of comparable magnitude or even larger than the MAI rates. The Vdd is no longer adequate. We, then construct a semi-empirical potential to describe the RET process. 3) At high densities, we show that the atomic orbital of |na> overlaps with that of neighboring atoms, and the electron-electron potential becomes prominent, resulting in much higher rates.

The optical formation of coherent superposition states, a wavepacket, can allow the study of zeroth-order states, the evolution of which exhibit structural and electronic changes as a function of time: this leads to the notion of a molecular movie. Intramolecular vibrational energy redistribution, due to anharmonic coupling between modes, is the molecular movie considered here. There is no guarantee, however, that the formed superposition will behave semi-classically (e.g. Gaussian wavepacket dynamics) or even as an intuitively useful zeroth-order state. Here we present time-resolved photoelectron spectroscopy (TRPES) studies of an electronically excited triatomic molecule wherein the vibrational dynamics must be treated quantum mechanically and the simple picture of population flow between coupled normal modes fails. Specifically, we report on vibronic wavepacket dynamics in the zeroth-order 3pσ2Σu Rydberg state of NO2. This wavepacket exemplifies two general features of excited state dynamics in polyatomic molecules: anharmonic multimodal vibrational coupling (forming polyads); nonadiabatic coupling between nuclear and electronic coordinates, leading to predissociation. The latter suggests that the polyad vibrational states in the zeroth-order 3p Rydberg manifold are quasi-bound and best understood to be scattering resonances. We observed a rapid dephasing of an initially prepared 'bright' valence state into the relatively long-lived 3p Rydberg state whose multimodal vibrational dynamics and decay we monitor as a function of time. Our quantum simulations, based on an effective spectroscopic Hamiltonian, describe the essential features of the multimodal Fermi resonance-driven vibrational dynamics in the 3p state. We also present evidence of polyad-specificity in the state-dependent predissociation rates, leading to free atomic and molecular fragments. We emphasize that a quantum molecular movie is required to visualize wavepacket dynamics in the 3pσ2Σu Rydberg state of NO2.

We report in this paper energy positions of the 2P°_2s22p2(1D)nd 2P, 2P°_2s22p2(1D)nd 2S, 2P°_2s22p2(1D)ns 2D, 2P°_2s22p2(1S)nd 2D, and 2P°_2s22p3(3P)np 2D Rydberg series in the photoionization spectra originating from 2P° metastable state of O+ ions. Calculations are performed up to n = 30 using the Modified Orbital Atomic Theory (MAOT). The present results are compared to the experimental data of Aguilar which are the only available values. The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

Multiple Rydberg series converging to the O2+c4Σ-u state, accessed by 20-25 eV extreme ultraviolet (XUV) light, serve as important model systems for the competition between nuclear dissociation and electronic autoionization. The dynamics of the lowest member of these series, the 3sσg state around 21 eV, has been challenging to study owing to its ultra-short lifetime (

We report a comprehensive study on the electronic excited states of tetrafluoro-1,4-benzoquinone, through high-resolution vacuum ultraviolet photoabsorption spectroscopy and time-dependent density functional theory calculations performed within the nuclear ensemble approach. Absolute cross section values were experimentally determined in the 3.8-10.8 eV energy range. The present experimental results represent the highest resolution data yet reported for this molecule and reveal previously unresolved spectral structures. The interpretation of the results was made in close comparison with the available data forpara-benzoquinone [Joneset al.,J. Chem. Phys., 2017,146, 184303]. While the dominant absorption features for both molecules arise from analogous π* ← π transitions, some remarkable differences have been identified. The perfluoro effect manifests in different ways: shifts in band positions and cross sections, appearance of features associated with excitations to σ CF* orbitals, and spectrum broadening by quenching of either vibrational or Rydberg progressions. The level of agreement between experiment and theory is very satisfactory, yet that required the inclusion of nuclear quantum effects in the calculations. We have also discussed the role of temperature on the absorption spectrum, as well as the involvement of core-excited resonances in promoting dissociative electron attachment reactions in the 3-5 eV range.

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

The state-resolved photodissociation of the CO(1Σ+) + S(1S0) photoproduct channel, formed by vacuum ultraviolet photoexcitation of OCS to a progression of the symmetric stretching vibration (ν1′) in the E and F states, has been investigated by using the time-sliced velocity map ion imaging technique. The total kinetic energy release spectra and the vibrational state specific anisotropy parameters (β) were obtained based on the raw images of S(1S0) photoproducts detected in the wavelength ranges of 134.40–140.98 nm, respectively. Except for vibrational band origins, the CO(1Σ+) photoproducts are found to have more significant populations at highly vibrationally excited states as the symmetric stretching vibrational excitation of the E and F states increases. Furthermore, the vibrational-state specific β values for the CO(1Σ+) + S(1S0) channel via the E and F states both show a sudden change from negative to positive in the vicinity of moderately vibronic levels of the E and F states. This anomalous phenomenon suggests that multiple excited states with different symmetries are involved in the photoexcitation process at relatively short photolysis wavelengths due to the strong vibronic couplings existing in the higher vibronic levels of the E and F states, and the formation of CO(1Σ+) + S(1S0) photoproducts may proceed by different nonadiabatic interactions from the prepared excited states to the lower dissociative state 1Σ+, with strong dependence of the initially symmetric stretching excitation in the Rydberg-type transitions.

In many areas of physics and chemistry, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic equations for describing natural phenomena. The Rydberg constant appears in the formula for calculating the wavelengths in the line spectrum emitted from the hydrogen atom. However, this Rydberg wavelength formula is a nonrelativistic formula derived at the level of classical quantum theory. In this paper, the Rydberg formula is rewritten as a wavelength formula taking into account the theory of relativity. When this is done, we come to an unexpected conclusion. What we try to determine by measuring spectra wavelengths is not actually the value of the Rydberg constant R∞ but the value Rn,m of Formula (18). R∞ came into common use in the world of nonrelativistic classical quantum theory. If the theory of relativity is taken into account, R∞ can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.

The excited-state decay dynamics of 2-ethylpyrrole following UV excitation in the wavelength range of 254.8-218.0 nm is investigated in detail using the femtosecond time-resolved photoelectron imaging method. The time-resolved photoelectron spectra and photoelectron angular distributions at all pump wavelengths are carefully analysed and the following picture is derived: at the longest pump wavelengths (254.8, 248.3 and 246.1 nm), 2-ethylpyrrole is excited to the S1(1πσ*) state having a lifetime of about 50 fs. At 248.3, 246.1 and 237.4 nm, another excited state of Rydberg character is excited. The lifetime of this state is ∼570 fs at 237.4 nm and becomes slightly longer at other two pump wavelengths. At the shortest pump wavelengths (230.8 and 218.0 nm), 2-ethylpyrrole is excited to a state which is tentatively assigned to the 11ππ* state, having a lifetime of 75 ± 15 and 48 ± 10 fs for the longer and shorter pump wavelengths, respectively. Internal conversion to the S1(1πσ*) state might be one of the decay mechanisms of the 11ππ* state.

Coincidence ion pair production (cipp) spectra of F2 were recorded on the DELICIOUS III coincidence spectrometer in the one-photon excitation region of 125 975–126 210 cm−1. The F+ + F− signal shows a rotational band head structure, corresponding to F2 Rydberg states crossing over to the ion pair production surface. Spectral simulation and quantum defect analysis allowed the characterization of five new molecular Rydberg states (F2**): one Π and four Σ states. The lowest-energy Rydberg state spectrum observed (T0 = 125 999 cm−1) lacked some of the predicted rotational structure, which allowed an accurate determination of the ion pair production threshold of 15.62294 ± 0.00043 eV. Using the well-known atomic fluorine ionization energy and electron affinity, this number leads to a ground state F–F dissociation energy of 1.60129 ± 0.00044 eV. Photoelectron photoion coincidence (PEPICO) experiments were also carried out on F2 and the dissociative photoionization threshold to F+ + F was determined as 19.0242 ± 0.0006 eV. Using the atomic fluorine ionization energy, this can be converted to an F2 dissociation energy of 1.60132 ± 0.00062 eV, further confirming the cipp-derived value above. Because the two experiments were independently energy-calibrated, they can be averaged to 1.60130 ± 0.00036 eV and this value can be used to derive the fluorine atom's 0 K heat of formation as 77.251 ± 0.017 kJ mol−1. This latter is in excellent agreement with the latest Active Thermochemical Table (ATcT) value but improves its accuracy by almost a factor of three.

The energy dependence of the rates of the reactions between He+ and ammonia (NY3, Y = {H,D}), forming NY2+, Y and He as well as NY+, Y2 and He, and the corresponding product branching ratios have been measured at low collision energies Ecoll between 0 and kB·40 K using a recently developed merged-beam technique [Allmendinger et al., ChemPhysChem, 2016, 17, 3596]. To avoid heating of the ions by stray electric fields, the reactions are observed within the large orbit of a highly excited Rydberg electron. A beam of He Rydberg atoms was merged with a supersonic beam of ammonia using a curved surface-electrode Rydberg–Stark deflector, which is also used for adjusting the final velocity of the He Rydberg atoms, and thus the collision energy. A collision-energy resolution of about 200 mK was reached at the lowest Ecoll values. The reaction rate coefficients exhibit a sharp increase at collision energies below ∼kB·5 K and pronounced deviations from Langevin-capture behaviour. The experimental results are interpreted in terms of an adiabatic capture model describing the rotational-state-dependent orientation of the ammonia molecules by the electric field of the He+ atom. The model faithfully describes the experimental observations and enables the identification of three classes of |JKMp〉 rotational states of the ammonia molecules showing different low-energy capture behaviour: (A) high-field-seeking states with |KM| ≥ 1 correlating to the lower component of the umbrella-motion tunnelling doublet at low fields. These states undergo a negative linear Stark shift, which leads to strongly enhanced rate coefficients; (B) high-field-seeking states subject to a quadratic Stark shift at low fields and which exhibit only weak rate enhancements; and (C) low-field-seeking states with |KM| ≥ 1. These states exhibit a positive Stark shift at low fields, which completely suppresses the reactions at low collision energies. Marked differences in the low-energy reactivity of NH3 and ND3—the rate enhancements in ND3 are more pronounced than in NH3—are quantitatively explained by the model. They result from the reduced magnitudes of the tunnelling splitting and rotational intervals in ND3 and the different occupations of the rotational levels in the supersonic beam caused by the different nuclear-spin statistical weights. Thermal capture rate constants are derived from the model for the temperature range between 0 and 10 K relevant for astrochemistry. Comparison of the calculated thermal capture rate coefficients with the absolute reaction rates measured above 27 K by Marquette et al. (Chem. Phys. Lett., 1985, 122, 431) suggests that only 40% of the close collisions are reactive.

In the literature, there were studies of Rydberg states of hydrogenic atoms/ions in a high-frequency laser field. It was shown that the motion of the Rydberg electron is analogous to the motion of a satellite around an oblate planet (for a linearly polarized laser field) or around a (fictitious) prolate planet (for a circularly polarized laser field): it exhibits two kinds of precession – one of them is the precession within the orbital plane and another one is the precession of the orbital plane. In this study, we study a helium atom or a helium-like ion with one of the two electrons in a Rydberg state, the system being under a high-frequency laser field. For obtaining analytical results, we use the generalized method of the effective potentials. We find two primary effects of the high-frequency laser field on circular Rydberg states. The first effect is the precession of the orbital plane of the Rydberg electron. We calculate analytically the precession frequency and show that it differs from the case of a hydrogenic atom/ion. In the radiation spectrum, this precession would manifest as satellites separated from the spectral line at the Kepler frequency by multiples of the precession frequency. The second effect is a shift of the energy of the Rydberg electron, also calculated analytically. We find that the absolute value of the shift increases monotonically as the unperturbed binding energy of the Rydberg electron increases. We also find that the shift has a nonmonotonic dependence on the nuclear charge Z: as Z increases, the absolute value of the shift first increases, then reaches a maximum, and then decreases. The nonmonotonic dependence of the laser field-caused energy shift on the nuclear charge is a counterintuitive result.

A sensitive method to study a dilute ultracold plasma based on the autoionization resonances of Rydberg atoms is demonstrated. Ultracold 40Ca Rydberg atoms are prepared in a continuously operating magneto-optical trap. A method that allows the detection of the plasma with ion and electron densities below 109 m–3 is shown. Experimental studies of resonances at the two-photon $$4s3d{{\,}^{1}}{{D}_{2}}{-} 90{{\,}^{1}}{{D}_{2}}$$ Rydberg transition have been carried out using 672 and 798 nm resonant laser beams. The autoionization resonance is observed during fluorescence of single-charged 40Ca ions at a wavelength of 397 nm. The dependence of the amplitude of autoionization resonance on the density of ions in the continuously generated ultracold plasma is obtained.

14 pags., 10 figs., 2 tabs., The nonadiabatic photodissociation dynamics of the CH$_3$ (and CD$_3$) radical from the 3p$_z$ and 3s Rydberg states is investigated by applying a one-dimensional (1D) wave packet model that uses recently calculated ab initio 1D electronic potential-energy curves and nonadiabatic couplings. Calculated predissociation lifetimes are found to be too long as compared to the experimental ones. The 1D dynamical model, however, is able to predict qualitatively and explain the fragmentation mechanisms that produce the hydrogen-fragment translational energy distributions (TED) measured experimentally for the ground vibrational resonance of the 3p$_z$ and 3s Rydberg states (CH$_3$($v=0$, 3p$_z$) and CH$_3$($v=0$, 3s)). The CH$_3$($v=0$, 3p$_z$) TED found experimentally displays a rather large energy spreading, while the experimental CH$_3$($v=0$, 3s) TED is remarkably more localized in energy. The present model also predicts a widely spread CH$_3$($v=0$, 3p$_z$) TED, produced by a complex dissociation mechanism which involves predissociation to one dissociative valence state through a nonadiabatic coupling, as well as transfer of population to a second valence state through three conical intersections. Also in agreement with experiment, the model predicts a rather localized CH$_3$($v=0$, 3s) TED because the conical intersections no longer operate in this photodissociation process, and predissociation occurs only into a single valence state. Another complex dissociation mechanism is predicted by the model for initial CH$_3$($v>0$, 3s) and CD$_3$($v>0$, 3s) resonances. In this case the mechanism is gradually activated, as vibrational excitation increases, by the interplay between the two nonadiabatic couplings connecting the 3s and 3p$_{x,y}$ Rydberg states with the dissociative $^2$A$_1$ valence state, and produces complex TEDs with signals from several resonances of both 3s and 3p$_{x,y}$. Thus the present 1D quantum model reveals a rich photodissociation dynamics of methyl, where a variety of complex fragmentation mechanisms is favored by the presence of different nonadiabatic couplings between the electronic states involved., This work was funded by the Ministerio de Ciencia e Innovacion (MICINN, Spain), Grant No. PGC2018-096444-B-100. The Centro de Supercomputacion de Galicia (CESGA, Spain) is acknowledged for the use of its resources.

The vacuum ultraviolet photodissociation of OCS via the F 31Π Rydberg states was investigated in the range of 134–140 nm by means of the time-sliced velocity map ion imaging technique. The images of S(1D2) products from the CO(X1Σ+)+S(1D2) dissociation channel were acquired at five photolysis wavelengths, corresponding to a series of symmetric stretching vibrational excitations in OCS(F 31Π, υ1=0–4). The total translational energy distributions, vibrational populations and angular distributions of CO(X1Σ+, υ) coproducts were derived. The analysis of experimental results suggests that the excited OCS molecules dissociate to CO(X1Σ+) and S(1D2) products via non-adiabatic couplings between the upper F 31Π states and the lower-lying states both in the C∞υ and Cs symmetry. Furthermore, strong wavelength dependent behavior has been observed: the greatly distinct vibrational populations and angular distributions of CO(X1Σ+, υ) products from the lower (υ1=0–2) and higher (υ1=3, 4) vibrational states of the excited OCS(F 31Π, υ1) demonstrate that very different mechanisms are involved in the dissociation processes. This study provides evidence for the possible contribution of vibronic coupling and the crucial role of vibronic coupling on the vacuum ultraviolet photodissociation dynamics.

The high-resolution absorption spectrum of 3-methoxyacrylonitrile (3MAN) was measured between 5.27 and 12.59 eV using a synchrotron-based Fourier-transform spectrometer. It was related to an absolute absorption cross-section scale. Complementary calculations at the DFT-MRCI/aug-cc-pVTZ level of theory document the vertical transition energies and oscillator strengths toward the first 19 states of both the E and Z geometrical isomers of 3MAN. Comparisons with the experimental absorption spectrum reveal the similarities and differences between 3MAN, a bifunctional molecule, with acrylonitrile and methylvinylether, where only one functional group is present. As in acrylonitrile, several broad valence transitions were observed up to the ionization limit. They are likely associated with the extended π-system induced by the nitrile group but might also involve σσ* transitions close to the ionization limit. As in methylvinylether, Rydberg series converging to the ionization limit are absent. This is attributed to a difference in neutral and cationic geometry due to a 60° rotation of the methyl group.

The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.

We present an overview of experimental and theoretical investigations exploring the dynamical evolution of Rydberg-to-valence character in the electronically excited states of small polyatomic mole...

A strong Coulomb interaction could lead to a strongly bound exciton with high-order excited states, similar to the Rydberg atom. The interaction of giant Rydberg excitons can be engineered for a correlated ordered exciton array with a Rydberg blockade, which is promising for realizing quantum simulation. Monolayer transition metal dichalcogenides, with their greatly enhanced Coulomb interaction, are an ideal platform to host the Rydberg excitons in two dimensions. Here, we employ helicity-resolved magneto-photocurrent spectroscopy to identify Rydberg exciton states up to 11s in monolayer WSe2. Notably, the radius of the Rydberg exciton at 11s can be as large as 214 nm, orders of magnitude larger than the 1s exciton. The giant valley-polarized Rydberg exciton not only provides an exciting platform to study the strong exciton-exciton interaction and nonlinear exciton response but also allows the investigation of the different interplay between the Coulomb interaction and Landau quantization, tunable from a low- to high-magnetic-field limit.

A brief overview of experimental and theoretical studies on the use of single neutral atoms captured in arrays of optical dipole traps as qubits of a quantum computer is presented. Methods for loading and registering atoms in traps, and performing two-qubit quantum logic gates via dipole-dipole interaction during short-term laser excitation of atoms into Rydberg states are discussed.

In our previous papers (Can. J. Phys. 91 (2013) 715; 92 (2014) 1405), we studied Rydberg states of systems consisting of a nucleus of charge Z, a muon, and an electron, both the muon and electron being in circular states. The studies of such quasimolecules μZe were motivated by numerous applications of muonic atoms and molecules, where one of the electrons is substituted by the heavier lepton μ–. We demonstrated that the muonic motion can represent a rapid subsystem, while the electronic motion can represent a slow subsystem. We showed that the spectral lines emitted by the muon in such systems experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogenic atom/ion. In the present paper, we also consider Rydberg states of quasimolecules μZe with Z > 1 (i.e., Rydberg states of muonic–electronic helium and helium-like ions). However, our current approach has important distinctions from our previous papers. The systems considered here are truly stable and the electron orbit is generally elliptical (although the relatively small influence of the electron on the muon is neglected). In our previous papers, the influence of the electron on the muon was taken into account; however, in the rotating frame used in our previous papers, the motion of the muon was only metastable (not truly stable), and furthermore, only circular orbits of the electron were considered in our previous paper. In the present paper, we show that the effective potential energy of the Rydberg electron is mathematically equivalent to the potential energy of a satellite moving around an oblate planet. Based on this, we demonstrate that the unperturbed orbital plane of the Rydberg electron undergoes simultaneously two different precessions: precession within the orbital plane and precession of the orbital plane around the axis of the muonic circular orbit. We provide analytical expressions for the frequencies of both precessions. The shape of the elliptical orbit of the Rydberg electron is not affected by the perturbation, which is the manifestation of the (approximate) conservation of the square of the angular momentum of the Rydberg electron. This means that the above physical systems have a higher than geometrical symmetry (also known as a hidden symmetry) which is a counterintuitive result of general physical interest. We note that the above problem of the motion of the Rydberg electron in muonic–electronic helium atoms or helium-like ions is mathematically equivalent to another problem from atomic physics: a hydrogen Rydberg atom in a linearly-polarized electric field of a high-frequency laser radiation.