High Rydberg States Research Articles

High-Resolution Continuous-Wave Laser Spectroscopy of Long-Lived Rydberg States in NO.

High-resolution continuous-wave (cw) laser spectroscopy of nitric oxide (NO) molecules has been performed to study and characterize the energy-level structure of and effects of electric fields on the high Rydberg states. The experiments were carried out with molecules flowing through a room temperature gas cell. Rydberg-state photoexcitation was implemented using the resonance enhanced three-color three-photon excitation scheme. Excited molecules were detected by high-sensitivity optogalvanic methods. Detailed measurements were made of Rydberg states with principal quantum numbers n = 22 and 32 in the series converging to the lowest rotational and vibrational state of the NO+ cation. The experimental data were compared with the results of numerical calculations which provided insight into the orbital angular momentum character of the intermediate H 2Σ+ state, improved determinations of the nf and ng quantum defects, a bound on the magnitude of the nh quantum defect, and information on the decay rates of the nf and ng Rydberg states. These measurements represent a step-change in laser spectroscopic studies of high Rydberg states in small atmospheric molecules. They open opportunities for more detailed studies of slow decay processes of Rydberg NO molecules confined in electrostatic traps, the synthesis of ultralong range Rydberg bimolecules, and the development of optical methods for trace gas detection.

Ion-core switching in Rydberg series of XeKr

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

Electrostatic Trapping of N_{2} Molecules in High Rydberg States.

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

Excitation and ionization of OCS molecules in strong UV and NIR laser fields

Abstract Rydberg state excitation (RSE) is a highly non-linear physical phenomenon that is induced by the ionization of atoms or molecules in strong femtosecond laser fields. Here we observe that both parent and fragments (S, C, OC) of the tri-atomic molecule carbonyl sulfide (OCS) can survive strong 800 nm or 400 nm laser fields in high Rydberg states. The dependence of parent and fragment RSE yields on laser intensity and ellipticity is investigated in both laser fields, and the results are compared with those for strong-field ionization. Distinctly different tendencies for laser intensity and ellipticity are observed for fragment RSE compared with the corresponding ions. The mechanisms of RSE and strong-field ionization of OCS molecules in different laser fields are discussed based on the experimental results. Our study sheds some light on the strong-field excitation and ionization of molecules irradiated by femtosecond NIR and UV laser fields.

Microwave coupled Zeeman splitting spectroscopy of a cesium nPJ Rydberg atom.

We perform measurements of microwave spectra of cesium Rydberg 51S1/2 → 51PJ transitions with the linewidth approaching the Fourier limit. A two-photon scheme excites the ground-state atoms to the Rydberg 51S1/2 state, and a weak microwave photon couples the Rydberg transition of 51S1/2 → 51PJ. The hyperfine structure of 51P1/2 can be clearly resolved with a narrow linewidth microwave spectra by using the method of ion detection. Furthermore, we investigate the Zeeman effect of the 51P1/2,3/2 state. The theoretical calculations reproduce the measurement well. Our experimental measurements provide a reliable technical solution for the investigation of high angular momentum Rydberg states, which is conducive to further realizing the coherent manipulation of Rydberg energy levels and improving the sensitivity of electromagnetic field measurement.

Oscillator Strengths and Cross Sections of the Valence-Shell Excitations of HBr Studied by Fast Electron Impact.

The oscillator strengths and cross sections of the valence-shell excitations of HBr were determined by fast electron scattering with an incident electron energy of 1500 eV and an energy resolution of 80 meV. The momentum transfer dependence behaviors of the generalized oscillator strengths have been used to elucidate the transition characteristics. The present results show that the strong spin-orbital interaction results in the observation of some triplet states in the (Λ, S) coupling and the constant generalized oscillator strength ratios for the pair states with the same electronic configuration and quantum number Ω, and the quantitative spin-orbit coupling coefficients of b3Π1(v = 0) and C1Π(v = 0) are determined. The optical oscillator strengths of the valence-shell excitations were obtained by extrapolating the generalized oscillator strengths to the limit of zero squared momentum transfer. The present optical oscillator strengths give an independent cross-check of the previous experimental and theoretical results, and the comparison shows that the line-saturation effect is more severe for the high Rydberg states with large intensities and narrow natural widths. The integral cross sections of the valence-shell excitations of HBr were obtained from the excitation threshold to 5000 eV by the BE-scaling method. The present oscillator strengths and cross sections supplement the fundamental molecular database of HBr and can be used for modeling in the semiconductor industry, astrophysics, and atmospheric chemistry.

Precise determination of adiabatic ionisation energies of large polyatomic molecules: p-diaminobenzene

We present a procedure, based on established principles, to accurately determine the ionisation energies of medium-sized to large polyatomic molecules in supersonic beams. The method combines single-photon excitation from the electronic ground state using tunable vacuum-ultraviolet laser radiation, the delayed pulsed-field ionisation of high Rydberg states with sequences of pulsed electric fields, and the modelling of the lineshapes from calculations of the field-ionisation dynamics of high Rydberg states and of the rotational contours of the photoelectron bands. The method is illustrated by a measurement of the adiabatic ionisation energy of p-diaminobenzene (p-DB), for which we obtain the value of 54,617.47(15) cm , which represents a more than 20-fold accuracy improvement over previous determinations.

Imaging-Assisted Single-Photon Doppler-Free Laser Spectroscopy and the Ionization Energy of Metastable Triplet Helium.

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules and are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation that exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities, and thus their Doppler shifts. With the example of spectra of (1s)(np) ^{3}P_{0-2}←(1s)(2s) ^{3}S_{1} transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1MHz in the UV. Using a retroreflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental [G. Clausen etal., Phys. Rev. Lett. 127, 093001 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.093001] and high-level theoretical [V. Patkós etal., Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] values of this quantity.

Very-high- and ultrahigh-frequency electric-field detection using high angular momentum Rydberg states

We demonstrate resonant detection of rf electric fields from 240 to 900 MHz (very high frequency to ultrahigh frequency) using electromagnetically induced transparency to measure orbital angular momentum $L=3\ensuremath{\rightarrow}{L}^{\ensuremath{'}}=4$ Rydberg transitions. These Rydberg states are accessible with three-photon infrared optical excitation. By resonantly detecting rf in the electrically small regime, these states enable a new class of atomic receivers. We find good agreement between measured spectra and predictions of quantum defect theory for principal quantum numbers $n=45$ to 70. Using a superhetrodyne detection setup, we measure the noise floor at $n=50$ to be $13\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{V}/(\mathrm{m}\sqrt{\mathrm{Hz}})$. Additionally, we utilize data and a numerical model incorporating a five-level master equation solution to estimate the fundamental sensitivity limits of our system.

Sensitivity extension of atom-based amplitude-modulation microwave electrometry via high Rydberg states

The Rydberg atom-based microwave electric field sensor has high sensitivity for weak RF-field detection. Selection of Rydberg states with larger electric dipole moment is beneficial to enhance the sensitivity, and we choose Rydberg states with its principal quantum number up to n ∼ 80. We study the probe laser transmission response to a microwave field for these chosen high Rydberg states at room temperature. It agrees well with theoretical simulation based on an optical Bloch equation with considered microwave-atom interaction and Doppler broadening effect. In our experiment, the microwave sensing sensitivity based on 85 Rb transition | 78 S 1 / 2 ⟩ → | 78 P 3 / 2 ⟩ arrives at 5.102(49) nV cm − 1 Hz − 1 / 2 at 1 kHz.

Imaging the photodissociation dynamics of internally excited ethyl radicals from high Rydberg states.

The site-specific hydrogen-atom elimination mechanism previously reported for photoexcited ethyl radicals (CH3CH2) [D. V. Chicharro et al., Chem. Sci., 2019, 10, 6494] is interrogated in the photodissociation of the ethyl isotopologues CD3CD2, CH3CD2 and CD3CH2 through the velocity map imaging (VMI) detection of the produced hydrogen- and deuterium-atoms. The radicals, generated in situ from photolysis of a precursor using the same laser pulse employed in their excitation to Rydberg states, decompose along the Cα-H/D and Cβ-H/D reaction coordinates through coexisting statistical and site-specific mechanisms. The experiments are carried out at two excitation wavelengths, 201 and 193 nm. The comparison between both sets of results provides accurate information regarding the primary role in the site-specific mechanism of the radical internal reservoir. Importantly, at 193 nm excitation, higher energy dissociation channels (not observed at 201 nm) producing low-recoil H/D-atoms become accessible. High-level ab initio calculations of potential energy curves and the corresponding non-adiabatic interactions allow us to rationalize the experimental results in terms of competitive non-adiabatic decomposition paths. Finally, the adiabatic behavior of the conical intersections in the face of several vibrational modes - the so-called vibrational promoting modes - is discussed.

Pulsed-ramped-field-ionisation zero-kinetic-energy photoelectron spectroscopy of the metastable rare-gas atoms Ar, Kr and Xe.

The photoionisation of the metastable rare-gas atoms Rg = Ar, Kr and Xe is investigated at the Rg+ […](ns)2(np)5 2P3/2 ← Rg[…](ns)2(np)5((n + 1)s) 13P2 photoionisation threshold (n = 3, 4 and 5 for Ar, Kr and Xe) using the technique of pulsed-ramped-field-ionisation zero-kinetic-energy (PRFI-ZEKE) photoelectron spectroscopy. This technique, which monitors the field ionisation of high Rydberg states induced by a slowly growing electric-field ramp after a prepulse of opposite polarity, was recently introduced to record photoelectron spectra with high resolution and high sensitivity [Harper, Chen, Boyé-Péronne and Gans, Phys. Chem. Chem. Phys., 2022, 117, 9353]. A tunable UV laser system with a bandwidth of 30 MHz is used here to establish the factors determining the resolution and overall accuracy of this new method. In particular, the effects of stray electric fields, and of the magnitude of the prepulse and the field ramp on PRFI-ZEKE photoelectron spectra are studied by combining experiments with numerical simulations of the field-ionisation of high Rydberg states and of the electron flight times from the ionisation spot to the detector. A spectral resolution of 0.05 cm-1 is demonstrated in the photoelectron spectrum of metastable Ar.

Adiabatic theory for high Rydberg molecules

AbstractMolecules in high Rydberg states, or high Rydberg molecules, are special types of excited species. Classically, at least one of the valence electrons of such molecules is excited to a high‐energy near‐threshold orbit with a negative eccentricity. Therefore, the electron spends most of its orbiting time on roaming slowly far away from the parent ionic core. With this classical picture in mind, we develop a general adiabatic theory termed the inverse Born‐Oppenheimer approximation, in contrast to the conventional Born‐Oppenheimer adiabatic theory for molecules in ground or lower excited states, to describe high Rydberg molecules. A thorough theoretical formulation starting from the non‐relativistic molecular Hamiltonian and Schrödinger equation is presented with emphasis on the mathematical rigorousness of this theory. Quantitative calculations of the transition rate constants for many radiative and nonradiative processes involved in high Rydberg molecules are shown explicitly.

Oscillator strengths and cross sections of high Rydberg states in ammonia studied by fast electron scattering

We report the experimental generalized oscillator strengths (GOSs) for transitions from the ground state to the Rydberg states , , , and an ‘undefined’ state in ammonia. The experiment was performed using an angle-resolved electron energy loss spectrometer operated at an incident energy of 1500 eV and an energy resolution of about 80 meV. The experimental observation confirms the recent theoretically predicted appreciable vibrational effects on the GOS for the transition (2021 J. Phys. B: At. Mol. Opt. Phys. 54 135202). The measured GOS data are fitted with the Lassettre formula to determine the corresponding optical oscillator strengths for dipole-allowed transitions. Furthermore, the fitted curves enable the integrations of GOSs over the momentum transfer squares to obtain the Born excitation cross sections. The integral cross sections are scaled to an accurate scale by using the BE-scaling method. The data in this work can supplement the molecular database and deepen our understanding of the scattering mechanism.

Optical-optical double resonance spectroscopy of Rb 5D3/2,5/2 in magnetic fields

We have investigated the optical-optical double resonance (OODR) spectroscopy of 87Rb for transition 5S1/2 → 5P3/2 → 5D3/2,5/2 in magnetic fields. Unlike the electromagnetically induced transparency (EIT) spectroscopy of the transition to high Rydberg states (Opt Express, 25(2017)33575), the spectral observation to this low excited state remains much discrepancy compared to the theory simulation as the strong coupling between 5P3/2 and 5D3/2,5/2 leads to a state-dependent spectral broadening due to double resonance optical pumping (DROP) effect. Instead, the OODR method employs a weak optical coupling between these two states, serving as probe, where the spectral broadening can be ignored. We experimentally record the Zeeman-splitting spectrum of 87Rb to 5D3/2 and 5D5/2 in magnetic fields by OODR and the observed spectra are well in accordance with the theoretical calculation. It shows OODR is more suitable to investigate the high resolution spectroscopy of the excited state when the relaxation in DROP can't be neglected.

Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H[formula omitted

Precision measurements of transitions between singlet (S=0) Rydberg states of H2 belonging to series converging on the X+2Σg+(v+=0,N+=0) state of H2+ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number ℓ and leads to quadratic Stark shifts of low-ℓ states and to linear Stark shifts of the nearly degenerate manifold of high-ℓ states. Transitions to the Stark manifold were observed for the principal numbers 50 and 70, at fields below 50 mV/cm, with linewidths below 500 kHz. The energy-level structure was calculated using a matrix-diagonalisation approach, in which the zero-field positions of the ℓ≤3 Rydberg states were obtained either from multichannel-quantum-defect-theory calculations or experiment, and those of the ℓ≥4 Rydberg states from a long-range core-polarisation model. This approach offers the advantage of including rovibronic channel interactions through the MQDT treatment while retaining the advantages of a spherical basis for the determination of the off-diagonal elements of the Stark operator. Comparison of experimental and calculated transition frequencies enabled the quantitative description of the Stark manifolds, with residuals typically below 50 kHz. We demonstrate how the procedure leads to quantum defects and binding energies of high Rydberg states with unprecedented accuracy, opening up new prospects for the determination of ionisation energies in molecules.

Theoretical and experimental studies on the captured electron population probability of hydrogen-like O and N ions in collision with Al surface

The study of the interaction between highly charged ions and solid surfaces not only has great significance for basic scientific research such as atomic physics, astrophysics, and high energy density physics but also has promising application prospects in biomedicine, nanotechnology, surface analysis, and microelectronics. In this paper, the intermediate Rydberg states formed during highly charged O<sup>7+</sup> and N<sup>6+</sup> ions incident on Al surface are studied theoretically by using the two-state vector model. Both the probability of electron capture into different Rydberg states (<i>n<sub>A</sub></i> = 2 − 7) and the most probable neutralization distances are given. The calculation shows that the larger principal quantum number <i>n<sub>A</sub></i> is relevant to smaller probability. Therefore, the X-rays emitted by O<sup>7+</sup> and N<sup>6+</sup> ions incident on the Al surface come mainly from the de-excitation of the smaller <i>n<sub>A</sub></i> to the ground state. In order to confirm the calculations, we measured the X-ray emission spectra of O<sup>7+</sup> and N<sup>6+</sup> ions in collisions with the Al surface in the energy range of 3-20 keV/q. The experiments were performed at an ECR ion source located in Institute of modern physics. We also calculated the transition energies (n<i>p</i>-1<i>s</i>) from different high Rydberg states to the ground state by using the FAC code. The center of the measured <i>K</i> X-ray peak is close to the calculated transition energy from the principal quantum number n=2 to n=1, it is consistent with our results obtained by the two-state vector model as well. In addition, we found the experimental <i>K</i> X-ray yield for O<sup>7+</sup> ions incidence at lower energy collisions is almost the same with N<sup>6+</sup> ions, but larger at higher energy collisions. When the ion incident kinetic energy is low, the X-ray emission is mainly owing to the decay of “above the surface”hollow atoms. Because of the small difference in the critical distances for the capture of electrons by O<sup>7+</sup> and N<sup>6+</sup> to form hollow atoms, the X-ray yields produced in both cases are almost the same at low energy collisions. In contrast, as increasing the incident energy, the ions have a long-range in the target, so the contribution from the decay of “above the surface” and “below the surface”hollow atoms need to be considered at the same time.

Advanced Laser-Photoionization Scheme of Separation of Heavy Isotopes in the Gases Separator Devices

An effective approach to determining the parameters of the optimal schemes of the method of laser selective photoionization of atoms (elements and isotopes) with finite ionization due to collisions, ionization by a pulsed electric field, ionization through high (Rydberg) states and narrow autoionization resonances for the separation of heavy isotopes has been proposed. in gas separator devices. On the basis of the theory of optimal control and previously developed quantum models for calculating the characteristics of elementary atomic processes, optimization models of isotope separation are numerically implemented in the scheme of selective laser photoionization with ionization due to collisions in gas mixtures, ionization by a pulsed electric field, autoionization, etc. etc. The data obtained quantitatively confirm the promise of the method of laser photoionization with finite ionization due to collisions, ionization by a pulsed electric field, ionization through high-lying (Rydberg) states and narrow autoionization resonances and give a set of parameters for the desired optimal schemes, in particular, the laser pulse optimal shape for rubidium and uranium isotopes.

Dielectronic recombination along high Rydberg states of Mg+ and Si11+ ions

In solving the multi-channel equation, I got the analytical expression of the multi-channel wave functions in terms of the solutions of the corresponding homogeneous equations. The homogeneous solutions are described in WKB Wenzel (1926 Z. Phys. 38 518) representation for both open and closed channels, and are calculated numerically using analogous means. By treating the open and closed channels equivalently in the calculation of the multi-channel wave functions, the generalized interaction matrix and generalized scattering matrix can be obtained for all the channels. With the obtained wave functions and generalized scattering matrix, the dielectronic recombination (DR) process can be calculated within the close-coupling framework by employing Bell and Seaton’s analytical deductions. In the method, high Rydberg states can easily be involved in numerical calculations. The method was applied to the calculations of DR of Mg+ and Si11+ ions along their high Rydberg states. The results are compared with those of the published experiments. Excellent agreements have been achieved, except at the extreme high Rydberg states for Si11+ ions, which is discussed in this paper.

Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2

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.