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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

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.

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.

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

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

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 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.

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.

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.

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.

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 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.

Quantum gates and entanglement based on dipole-dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable fidelity and the robustness to the technical issues and detrimental innate factors., Comment: 57 pages, 10 figures

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.

The spectral characteristics of the resonance effect of the electromagnetic-induced transparency (EIT) of rubidium atomic vapors induced by intense radiation with a wavelength in the region from 479 to 486 nm in the presence of microwave radiation at a frequency of 1 to 300 GHz, which splits the energy of transition of the atom from the resonant 5P3/2 states into the Rydberg nD5/2 state, are determined. The magnitude of the splitting of the EIT peak is proportional to the electric field intensity of the microwave radiation. Simple approximation expressions are obtained for the numerical calculation of the transition amplitude between Rydberg nD5/2 and (n + 1)P3/2 states with large principal quantum numbers n. A setup has been developed for measuring the electric field intensity of microwave radiation based on measuring the frequency of splitting of the resonance of an electron microscope in the absorption spectrum of probe radiation.

Highly sensitive phase- and frequency-resolved detection of microwave electric fields is of central importance in a wide range of fields, including cosmology1,2, meteorology3, communication4 and microwave quantum technology5. Atom-based electrometers6,7 promise traceable standards for microwave electrometry, but their best sensitivity is currently limited to a few μV cm−1 Hz−1/2 (refs. 8,9) and they only yield information about the field amplitude and polarization10. Here, we demonstrate a conceptually new microwave electric field sensor—the Rydberg-atom superheterodyne receiver (superhet). The sensitivity of this technique scales favourably, achieving even 55 nV cm−1 Hz−1/2 with a modest set-up. The minimum detectable field of 780 pV cm−1 is three orders of magnitude smaller than what can be reached by existing atomic electrometers. The Rydberg-atom superhet allows SI-traceable measurements, reaching uncertainty levels of 10−8 V cm−1 when measuring a sub-μV cm−1 field, which has been inaccessible so far with atomic sensors. Our method also enables phase and frequency detection. In sensing Doppler frequencies, sub-μHz precision is reached for fields of a few hundred nV cm−1. This work is a first step towards realizing electromagnetic-wave quantum sensors with quantum projection noise-limited sensitivity. Such a device will impact diverse areas like radio astronomy, radar technology and metrology. The Rydberg-atom superhet, based on microwave-dressed Rydberg atoms and a tailored electromagnetically induced transparency spectrum, allows SI-traceable measurements of microwave electric fields with unprecedented sensitivity.

Trapped neutral atoms have become a prominent platform for quantum science, where entanglement fidelity records have been set using highly-excited Rydberg states. However, controlled two-qubit entanglement generation has so far been limited to alkali species, leaving the exploitation of more complex electronic structures as an open frontier that could lead to improved fidelities and fundamentally different applications such as quantum-enhanced optical clocks. Here we demonstrate a novel approach utilizing the two-valence electron structure of individual alkaline-earth Rydberg atoms. We find fidelities for Rydberg state detection, single-atom Rabi operations, and two-atom entanglement surpassing previously published values. Our results pave the way for novel applications, including programmable quantum metrology and hybrid atom-ion systems, and set the stage for alkaline-earth based quantum computing architectures., ISM and JPC contributed equally to this work

Resonant mechanisms of electron–ion recombination accompanied by the formation of Rydberg atoms in a plasma containing atomic and molecular ions are investigated. An analytical approach is developed for the description of three-particle electron capture into a Rydberg state as a result of resonant energy transfer from a free electron to the electronic shell of a quasimolecular ion formed during the collision of an atomic ion with a buffer gas atom. An efficient method is proposed to calculate dissociative recombination rates under thermal excitation of all rotational–vibrational (rovibrational) levels of the molecular ion. The dependence of the cross sections and the rate constants of the processes on the principal quantum number is established, and the relative role of these processes is determined in a wide range of temperatures of the electron, Te, and gas, T, components of the plasma. Conditions are found under which integral contributions of the continuous spectrum of the molecule and of the whole rovibrational quasicontinuum to the total rate of resonant electron capture are dominant. A specific analysis is carried out by an example of Ne + Xe+ + e and Ar + Xe+ + e heteronuclear systems with significantly different dissociation energies (D0 = 33 and 171 meV) of the ground electronic term of the RgXe+ (Rg = Ne and Ar) ion. It is shown that the capture rate constants essentially depend on the binding energy |en| of the resulting Xe(n) atom, the temperatures T and Te, and the relationship between D0 and the thermal energy kBT.

The reaction of chlorine atom Cl(2P) (Cl(2P3/2) and Cl∗(2P1/2)) with D2 was investigated at collision energy from 4.5 kcal/mol to 6.5 kcal/mol with a high-resolution crossed molecular beam apparatus using the technique of D-atom Rydberg tagging detection. The contribution from the spin-orbit excited reaction Cl∗(2P1/2)+D2, which is prohibited by Born-Oppenheimer (BO) approximation, was observed. Collision-energy dependence of differential cross sections (DCSs) near the backward scattering direction was measured. The BO-forbidden reaction Cl∗+D2 was found to be dominant at lower collision energy. As collision energy increases, reactivity of BO-allowed reaction Cl+D2 increases much faster than that of BO-forbidden reaction and becomes dominant at higher collision energy. Our experiment indicates that the additional energy of spin-orbit excitation in Cl∗ facilitates BO-forbidden reaction to pass through the barrier at lower collision energy, while BO approximation is still valid at collision energy near and above the reaction barrier. This tendency of reactivity of Cl/Cl∗+D2 is similar to the isotopic reaction of Cl/Cl∗+H2.

Quantum beats in fluorescence decay from Zeeman-split magnetic sublevels have been measured for helium Rydberg states excited by synchrotron radiation. The Zeeman quantum beats observed in this prototypical case were fitted with an equation from a theoretical formulation. It is proposed that Zeeman quantum beat measurement can be a useful way to simply evaluate the polarization characteristics of extreme ultraviolet light.

We report on the results of studying the radio emission of the Rydberg states of atoms and molecules in the Earth’s upper atmosphere at ionospheric altitudes when the ionosphere is modified by high-power HF radio waves radiated by the Sura heating facility. Radio emission from the upper atmosphere, caused by the emission of highly excited Rydberg atoms and molecules with the principal quantum number n = 163–169 and n = 225 (decimeter wavelength range) and two spectral features that coincide with the frequencies of transitions between Rydberg states m = 169 → n = 168 with the transition frequency νn = 1375.35 MHz and m = 166 → n = 165 with νn = 1451.5 MHz were detected. Characteristic altitudes of the Rydberg radiation generation region were 150–250 km. The radio emission intensity corresponds to 10–45 K, which is comparable with the intensity of the radio emission generated during solar flares.

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting Square Gradient Minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant $\Delta$SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the Maximum Overlap Method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that $\Delta$SCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1-5 atoms when they are detected by the selective field ionization method. We investigated the spectra of the three-photon laser excitation $ 5S_{1/2} \to 5P_{3/2} \to 6S_{1/2} \to nP_{3/2} $ of cold Rb Rydberg atoms in a magneto-optical trap. We have found that for mesoscopic ensembles this method allows only a partial dipole blockage to be observed. This is most likely related to the presence of parasitic electric fields reducing the interaction energy of Rydberg atoms, the decrease in the probability of detecting high states, and the strong angular dependence of the interaction energy of Rydberg atoms in a single interaction volume., Comment: 16 pages, 7 figures

The response of a molecule to photoexcitation is governed by the coupling of its electronic states. However, if the energetic spacing between the electronically excited states at the Franck-Condon window becomes sufficiently small, it is infeasible to selectively excite and monitor individual states with conventional time-resolved spectroscopy, preventing insight into the energy transfer and relaxation dynamics of the molecule. Here, we demonstrate how the combination of time-resolved spectroscopy and extensive surface hopping dynamics simulations with a global fit approach on individually excited ensembles overcomes this limitation and resolves the dynamics in the n3p Rydberg states in acetone. Photoelectron transients of the three closely spaced states n3px, n3py, and n3pz are used to validate the theoretical results, which in turn allow retrieving a comprehensive kinetic model describing the mutual interactions of these states for the first time.

Photodissociation dynamics of H2O and D2O via the state by one-photon excitation have been investigated using the H/D atom Rydberg tagging time-of-flight technique. The TOF spectra of the H/D-atom product in both parallel and perpendicular polarizations have been measured. Product translational energy distributions and angular distributions have been derived from TOF spectra. By simulating these distributions, quantum state distributions of the OH/OD product as well as the state-resolved angular anisotropy parameters were determined. The most important pathway of H2O/D2O dissociation via the state leads to highly rotationally excited OH/OD(X, v = 0) products, while vibrationally excited OH/OD products with v ≥ 1 comprise only one third of the total OH/OD(X) population. The branching ratios of OH(A)/OH(X) and OD(A)/OD(X) have also been determined, 1.0/3.0 for H2O at 122.12 nm and 1.0/2.2 for D2O at 121.95 nm, which are reasonably consistent with the values predicted by the previous theory.

K. Suto has recently pointed out an interesting relativistic extension of Rydberg’s formula. Here we also discuss Rydberg’s formula, and offer additional evidence on how one can easily see that it is non-relativistic and therefore a good approximation, at best, when . We also extend the Suto formula to hold for any atom and examine the formula in detail.

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

The relationship E = −K holds between the energy E and kinetic energy K of the electron constituting a hydrogen atom. If the kinetic energy of the electron is determined based on that relationship, then the energy levels of the hydrogen atom are also determined. In classical quantum theory, there is a formula called the Rydberg formula for calculating the wavelength of a photon emitted by an electron. In this paper, in contrast, the formula for the wavelength of a photon is derived from the relativistic energy levels of a hydrogen atom derived by the author. The results show that, although the Rydberg constant is classically a physical constant, it cannot be regarded as a fundamental physical constant if the theory of relativity is taken into account.

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.