Rydberg Resonances Research Articles

Stark Effects of Rydberg Excitons in a Monolayer WSe2 P-N Junction.

The enhanced Coulomb interaction in two-dimensional semiconductors leads to tightly bound electron-hole pairs known as excitons. The large binding energy of excitons enables the formation of Rydberg excitons with high principal quantum numbers (n), analogous to Rydberg atoms. Rydberg excitons possess strong interactions among themselves as well as sensitive responses to external stimuli. Here, we probe Rydberg exciton resonances through photocurrent spectroscopy in a monolayer WSe2 p-n junction formed by a split-gate geometry. We show that an external in-plane electric field not only induces a large Stark shift of Rydberg excitons up to quantum principal number 3 but also mixes different orbitals and brightens otherwise dark states such as 3p and 3d. Our study provides an exciting platform for engineering Rydberg excitons for new quantum states and quantum sensing.

Resonant Auger decay of dissociating CH3I near the I 4d threshold.

Resonant Auger processes provide a unique perspective on electronic interactions and excited vibrational and electronic states of molecular ions. Here, new data are presented on the resonant Auger decay of excited CH3I in the region just below the I 4d-1 ionization threshold. The resonances include the Rydberg series converging to the five spin-orbit and ligand-field split CH3I (I 4d-1) thresholds, as well as resonances corresponding to excitation from the I 4d5/2,3/2 orbitals into the σ* lowest unoccupied molecular orbital. This study focuses on participator decay that populates the lowest lying states of CH3I+, in particular, the X̃2E3/2 and 2E1/2 states, and on spectator decay that populates the lowest-lying (CH3I2+)σ* states of CH3I+. The CH3I (I 4d-1)σ* resonances are broad, and dissociation to CH3 + I competes with the autoionization of the core-excited states. Auger decay as the molecule dissociates produces a photoelectron spectrum with a long progression (up to v3+ ∼ 25) in the C-I stretching mode of the X̃2E3/2 and 2E1/2 states, providing insights into the shape of the dissociative core-excited surface. The observed spectator decay processes indicate that CH3I+ is formed on the repulsive wall of the lower-lying (CH3I2+)σ* potentials, and the photon-energy dependence of the processes provides insights into the relative slopes of the (4d-1)σ* and (CH3I2+)σ* potential surfaces. Data are also presented for the spectator decay of higher lying CH3I (I 4d-1)nl Rydberg resonances. Photoelectron angular distributions for the resonant Auger processes provide additional information that helps distinguish these processes from the direct ionization signal.

Satellite radio detection via dual-microwave Rydberg spectroscopy

Rydberg electric field sensors exploit the large number of Rydberg resonances to provide sensitivity over a broad range of the electromagnetic spectrum. However, due to the difficulty of accessing resonant Rydberg states at ultra-high frequency (UHF) and below, ubiquitous bands in the world's current wireless communications infrastructure, they currently fall, short in sensitivity in this range. We present a resonant Rydberg electric field sensor operating in the UHF band using a dual-optical dual-microwave spectroscopy scheme. Adding an additional microwave photon allows us to access transitions between Rydberg states with higher angular momentum (L=3→4), which have lower resonant frequencies than transitions typically used in Rydberg sensors. We discuss the applicability of this type of sensor across the UHF band and below and measure the resonant sensitivity of our system at 2.3 GHz to be 70(5) μV m−1 Hz−1∕2, 57 times better than the measured sensitivity with a far off-resonant probing scheme at this frequency. We also show the effectiveness of this sensing scheme by measuring Sirius XM satellite radio (2.320–2.345 GHz) received outside the laboratory and rebroadcast onto the atoms.

Screening Constant per Unit Nuclear Charge Studies of Rydberg Resonances Due to the 4p → nd and ns Transitions in Se+ Ions

Calculations of high-lying energy resonances of 12 Rydberg series due to the 4p → nd and 4p → ns transitions from the 4s24p3 3S°3/2 ground-state and the 4s24p3 2P°3/2,1/2 and 4s24p3 2D°5/2,3/2 metastable states of the Se+ ion are reported. The calculations believed to be the first theoretical ones are performed using the Screening Constant per Unit Nuclear Charge (SCUNC) method up to n = 40. Analysis of the present results is achieved in the framework of the standard quantum-defect theory and of the SCUNC-procedure by calculating the effective nuclear charge. For many resonances, the SCUNC-method reproduces the ALS measurements excellently [Esteves et al., Phys. Rev. A, 84 013406 (2011)] up to n = 25. However, for some resonances belonging to the 4s24p2 (1D2)nd (2D) and 4s24p2 (1D2)ns (2D) and to the 4s24p2 (1D2)nd (2S) and 4s24p2 (1D2)nd (2P1/2) Rydberg series, the ALS data overlap at high n values. In addition, negative quantum-defect values were determined where positive values are allowable. In the present work, positive quantum defect values almost constants are obtained along all the series investigated up to n = 40, and the narrow resonances are clearly separated. Overall, the present theoretical study provides confidence in the ALS data on Se+ ions for astrophysical interest as far as the understanding of the chemical evolution of Se in the universe is concerned.

Total and state-specific electron-ion recombination rates and photoionization of Ca XV for high temperature plasma

The inverse processes of photoionization and electron-ion recombination of (Ca XV + hν↔ Ca XVI + e), are studied using the unified method of Nahar and Pradhan for a large number of bound states, 582 in total with n≤10 and l≤9, for their characteristic features particularly in the high energy region that can impact plasmas at high temperature. The unified method which implements close-coupling (CC) approximation and the R-matrix method includes both the radiative recombination (RR) and dielectronic recombination (DR) for the total recombination and yields self-consistent sets of results for both the inverse processes. The present study, carried out in large scale computations, employs a large CC wavefunction expansion of 29 LS states belonging to n=2,3 complexes of the core ion Ca XVI, and appeared to be the first detailed study for the electron-ion recombination of the ion. The present results include (i) state-specific photoionization cross sections (σPI(nLS)) leaving the core ion in the ground state, (ii) state-specific recombination rate coefficients (αRC(nLS,T)) that include both the RR and DR, (iii) total recombination rate coefficients (αRC) with temperature that include contributions of infinite number of recombined states, and (iv) a spectrum of total electron-ion recombination cross sections and rates with respect to photoelectron energy. The study finds that the core ion excitations from the ground to high n=3 states have introduced Rydberg resonances which are stronger and Seaton resonances which are more enhanced in the high energy region of σPI compared to those introduced by excitations to the n=2 states. Such features have contributed to the shape of the temperature dependent state-specific αRC(nLS,T), and have resulted in three DR bumps/ shoulders in the high temperature region of the total αRC(T) where the third DR bump at temperature of ∼ 4 MK has raised αRC(T) at high T above all previous rates. The results are expected to be accurate within 10%–15% and provide more complete and precise spectral modelings for the high temperature plasmas where the highly charged Ca XV is more abundant.

Observation of the Rydberg Resonance in Surface Electrons on Superfluid Helium Confined in a 4-$$\mu$$m Deep Channel

We report the first observation of the microwave-induced intersubband (Rydberg) resonance in the surface-bound electrons on superfluid helium confined in a single 4-$\mu$m deep channel. The resonance signal from a few thousand of surface electrons comprising the Wigner Solid (WS) is detected by observing WS melting due to the microwave absorption. The observed transition frequency for the two lowest Rydberg states, in the range of 0.4-0.5 THz, is determined by the image charges induced by the surface electrons in conducting electrodes of the microchannel and the potentials due to applied voltages, and is in a good agreement with our calculations. The observed large broadening of the resonance on the order of 10 GHz, which is due to inhomegeneous distribution of the pressing electric field in the microchannel, is also in a reasonable agreement with our finite-element modeling calculations. This study of the confined electrons is motivated by their potential use for charge and spin qubits.

Continuous radio-frequency electric-field detection through adjacent Rydberg resonance tuning

We demonstrate the use of multiple atomic-level Rydberg-atom schemes for continuous frequency detection of radio-frequency (RF) fields. Resonant detection of RF fields by electromagnetically induced transparency and Autler-Townes (AT) splitting in Rydberg atoms is typically limited to frequencies within the narrow bandwidth of a Rydberg transition. By applying a second field resonant with an adjacent Rydberg transition, far-detuned fields can be detected through a two-photon resonance AT splitting. This two-photon AT splitting method is several orders of magnitude more sensitive than off-resonant detection using the Stark shift. We present the results of various experimental configurations and a theoretical analysis to illustrate the effectiveness of this multiple level scheme. These results show that this approach allows for the detection of frequencies in a continuous band between resonances with adjacent Rydberg states.

Semiclassical theory of laser-assisted dissociative recombination

We study the process of laser-assisted dissociative recombination of an electron with a molecular cation using a semiclassical approach. In the region outside a reaction sphere the electron motion in the combined laser and Coulomb fields is treated classically. Within the sphere the laser-field effects are neglected, and the recombination probability is obtained from quantum-mechanical cross sections calculated for the laser-free process. Specific calculations are performed for dissociative recombination of ${\mathrm{H}}_{2}^{+}$ in the field of the intensity 2.09 GW/${\mathrm{cm}}^{2}$ and the wavelength $22.8\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$. In the energy region above 1 meV the cross section is significantly enhanced compared with the field-free case due to the Coulomb focusing effect. The influence of the indirect process due to electron capture into Rydberg states is also investigated. Although the Rydberg resonances are washed out due to the field effects, they influence significantly the magnitude of the dissociative recombination cross section.

Two-photon above-threshold ionization of helium

Multiphoton ionization provides a clear window into the nature of electron correlations in the helium atom. In the present study, the final state energy range extends up to the region near the $N=2$ and $N=3$ ionization thresholds, where two-photon ionization proceeds via continuum intermediate states above the lowest threshold. Our calculations are performed using multichannel quantum defect theory (MQDT) and the streamlined R-matrix method. The sum and integration over all intermediate states in the two-photon ionization amplitude is evaluated using the inhomogeneous R-matrix method developed by Robicheaux and Gao. The seamless connection of that method with MQDT allows us to present high resolution spectra of the final state Rydberg resonances. Our analysis classifies the resonances above the $N=2$ threshold in terms of their group theory quantum numbers. Their dominant decay channels are found to obey the previously conjectured propensity rule far more weakly for these even parity states than was observed for the odd-parity states relevant to single photon ionization.

High-resolution X-ray absorption spectroscopy of alkanethiolate self-assembled monolayers on Au(111) and Ag(111)

High-resolution C K-edge near-edge X-ray absorption fine structure (NEXAFS) spectra of non-substituted alkanethiolate self-assembled monolayers (SAMs) on Au(111) and Ag(111) were studied, with a particular emphasis on their fine structure and temperature dependence. Depending on the orientation of the light polarization with respect to the surface normal, the spectra were either dominated by the 'C−H' band, comprised of several σ*C−H / Rydberg resonances or exhibited several usually "hidden" features, including a sharp pre-edge resonance at ∼286.8 eV, related to the terminal methyl group of the SAM forming molecules and accompanied by a vibronic feature. The spectra exhibit pronounced reversible temperature dependence at going from cryogenic (60−70 K) to room temperature, including a shift of the 'C−H' band to lower energy by 250−300 meV, broadening and decrease in intensity of nearly all resonances, and disappearance of several "fine structure" features. This behavior was attributed to the nuclear motion effects, with the major impact of progressing orientational and conformational disorder in the SAMs, and correlated with the length of the of molecular backbone and specific character of the SAM-ambient interface.

Mapping Resonance Structures in Transient Core-Ionized Atoms

The nature of transient electronic states created by photoabsorption critically determines the dynamics of the subsequently evolving system. Here, we investigate K-shell photoionized atomic neon by absorbing a second photon within the Auger-decay lifetime of 2.4 fs using the European XFEL, a unique high-repetition-rate, wavelength-tunable x-ray free-electron laser. By high-resolution electron spectroscopy, we map out the transient Rydberg resonances unraveling the details of the subsequent decay of the hollow atom. So far, ultra-short-lived electronic transients, which are often inaccessible by experiments, were mainly inferred from theory but are now addressed by nonlinear x-ray absorption. The successful characterization of these resonances with femtosecond lifetimes provides the basis for a novel class of site-specific, nonlinear, and time-resolved studies with strong impact for a wide range of topics in physics and chemistry. (Less)

Photoionization features of the ground and excited levels of Cl II and benchmarking with experiment

This report presents i) various characteristic features in photoionization cross sections (σPI) of Cl II + hν → Cl III + e for many fine structure levels of Cl II, 392 in total with n ≤ 10 and l ≤ 9, ii) comparison of features with those observed in an experiment carried out at the Advanced Light Source at Lawrence Berkeley National Lab, and iii) partial photoionization cross sections of the ground level for ionization leaving the core ion in to various excited levels for applications in plasma modeling. The features correspond to resonant structures, the shape of the background, and their interference effect in σPI of this near neutral ion Cl II with 16 electrons. σPI for the 5 levels of the ground configuration 3s23p4(3P0,1,2, 1D2, 1S0) of Cl II show regions of narrow Rydberg resonances at and near threshold energies, and resonant structures at higher energies in contrast to typical smooth decrease in the background. Various other features in σPI of levels of excited equivalent electron states and broad Seaton resonances in single valence electron excited levels are illustrated with examples. Comparison of calculated σPI of the 15 lowest levels with the combined features of the measured photoionization spectrum shows excellent agreement by reproducing and thus identifying them to the levels that they belong to. The calculations were carried out in relativistic Breit-Pauli R-matrix (BPRM) method using a close coupling wave function expansion of 45 levels up to 4s of the core ion Cl III. These levels were optimized using a set of 12 configurations going up to orbital 5s, 3s23p3, 3s3p4, 3p5, 3s23p23d, 3s23p24s, 3s23p24p, 3s23p24d, 3s23p24f, 3s23p25s, 3s3p33d, 3s23p3d2, 3p43d producing 283 levels of Cl III. The autoionizing resonances are delineated with a fine energy mesh to observe the fine structure effects. The present results will provide high precision parameters for various applications involving this less studied ion.

Interaction of charged impurities and Rydberg excitons in cuprous oxide

We investigate the influence of a static, uncorrelated distribution of charged impurities on the spectrum of bound excitons in the copper oxide Cu$_{\text{2}}$O. We show that the statistical distribution of Stark shifts and ionisation rates leads to the vanishing of Rydberg resonances into an apparent continuum. The appearance of additional absorption lines due to the broken rotational symmetry, together with spatially inhomogeneous Stark shifts, leads to a modification of the observed line shapes that agree qualitatively with the changes observed in the experiment.

Semiclassical theory of laser-assisted radiative recombination

We study the process of laser-assisted dissociative recombination of an electron with a molecular cation using a semiclassical approach. In the region outside a reaction sphere the electron motion in the combined laser and Coulomb fields is treated classically. Within the sphere the laser-field effects are neglected, and the recombination probability is obtained from quantum-mechanical cross sections calculated for the laser-free process. Specific calculations are performed for dissociative recombination of ${\mathrm{H}}_{2}^{+}$ in the field of the intensity 2.09 GW/${\mathrm{cm}}^{2}$ and the wavelength $22.8\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$. In the energy region above 1 meV the cross section is significantly enhanced compared with the field-free case due to the Coulomb focusing effect. The influence of the indirect process due to electron capture into Rydberg states is also investigated. Although the Rydberg resonances are washed out due to the field effects, they influence significantly the magnitude of the dissociative recombination cross section.

Influence of an electric field on Rydberg nD states of cold lithium atoms

Influence of a weak electric field on the coherent Rydberg resonances was studied on two-photon transitions 2S–nD by recording the resonance fluorescence of lithium atoms in a magneto-optical trap. It was observed that an isolated spectral line 2P–nD transferred to the spectral band width growing with a principal number n (or an electric field E). It was shown that the frequency tuning of a resonant radiation on the left (right) edge of the band allows to create a gas of Rydberg atoms with fixed and large dipole moments d ∝ ea 0 n 2 (e is the elementary charge, a 0 is the Bohr radius), oriented against (along) the electric field. The radiation frequency was tuned on the center of the band would produced atomic states with zero dipole moments, but with a big contribution of states with maximum angular momentum quantum number l ~ n.

Atomic measurements of high-intensity VHF-band radio-frequency fields with a Rydberg vapor-cell detector

We investigate and employ optical Rydberg resonances in an atomic vapor cell for measurements of high-intensity VHF-band radio frequency (rf) electric fields. An atomic vapor cell with integrated electrodes is used to generate high-intensity 50--500 MHz rf electric fields reaching $\ensuremath{\sim}5$ kV/m in a submillimeter gap. The fields are measured using Rydberg electromagnetically induced transparency as an optical readout of field-sensitive $30{D}_{J}$ and $35{D}_{J}$ Rydberg states of atoms within the gap. The rf electric field is determined by matching observed spectroscopic markers, including ac level shifts, even-harmonic rf sidebands, and rf-induced avoided crossings in the Rydberg manifold to calculated spectra derived from a nonperturbative Floquet theory. In our measurements, rf field frequencies and electric-field amplitudes are determined to an accuracy of $1.0%$ and $1.5%$, respectively. In the atom-field interaction, we observe a transition from a quantum regime, characterized by discrete even-harmonic Floquet states separated by an even multiple of the rf field frequency, into a semiclassical regime at very strong fields, in which the spectrum exhibits unresolved resonances whose strengths are smoothly modulated at a frequency of approximately five times the rf frequency. The underlying physics is explored.

Absolute single photoionization cross-sections of Br3+: experiment and theory

Absolute single photoionization cross section measurements for Br3+ ions are reported in the photon energy range 44.79–59.54 eV at a photon energy resolution of 21 ± 3 meV. Measurements were performed at the Advanced Light Source at Lawrence Berkeley National Laboratory using the merged-beams technique. Numerous resonance features in the experimental spectrum are assigned and their energies and quantum defect values are tabulated. The cross-section measurements are also compared with Breit–Pauli R-matrix calculations with suitable agreement over the photon energy range investigated. Analysis of the measured spectrum including Rydberg resonance series identifications produced a new emperical determination of the ionizational potential of Br3+ of 46.977 ± 0.050 eV, which is 805 meV lower than the most recently published value of 47.782 eV. This disparity between our determination and the earlier published value is similar to an 843 meV shift in the accepted ionization potential published for iso-electronic Se2+ as part of this same research program.

Characteristic features in photoionization of Fe XIX

Characteristic features of the resonances and background cross sections for photoionization (σPI) of oxygen-like iron ion, Fe XIX + hν → Fe XX + e, are demonstrated. The features are introduced by excitations of the core ion to states of n = 2,3,4 complexes in σPI of the ground, equivalent electron, and single valence electron excited states. Study from a large number of states is important to establish the general properties of photoionization for complex ions. This is the first detailed study of the ion with a complete set of σPI for 900 bound states with n ≤ 10 and l ≤ 9. The ion itself is of great interest for being detected in the x-ray to UV spectra of various astronomical objects. It is found that i) the ground and equivalent electron states have high peak narrow Rydberg resonances in the low energy region corresponding to n = 2 excitations only, ii) for other excited states the resonant features are stronger for core ion excitations to n = 3 complex compared to those for n = 2,4, iii) Seaton resonances due to photo-excitation of the core (PEC) are found most distinct in the energy region for dipole allowed excitation from n = 2 to n = 3 states, and iv) resonances with lower peaks in the energy region between n = 3 and n = 4 excitation indicate convergence. Computations were carried out in the R-matrix method using a large close coupling wavefunction expansion up to orbital 4f and 16 configurations. The present results should provide the data for precise modeling and applications.

Photoionization of Rb2+ ions in the valence energy region 37–44 eV

Absolute photoionization cross sections for the Rb2+ ion were recently measured at high resolution over the energy range 37.31–44.08 eV, with autoionizing Rydberg resonance series identified, using the photon-ion merged-beam setup at the Advanced Light Source (als) in Berkeley (Macaluso D A et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49, 235002; 2017 50, 119501). Detailed photon-energy scans taken at 13.5 ± 2.5 meV bandwidth illustrated multiple Rydberg resonance series associated with the ground and metastable states. Here we present theoretical cross section results obtained using the Dirac–Coulomb R-matrix approximation with a detailed analysis of the resonances. The calculations were performed for the , ground state and the corresponding metastable level. Results from the large-scale calculations are benchmarked against the als high-resolution measurements and reproduce the dominant resonance features in the spectra, providing confidence in the theoretical work for astrophysical applications.

L-shell spectroscopy of neon and fluorine like copper ions from laser produced plasma

Ne, F, and O-like Rydberg resonance lines along with some of the inner shell satellite lines of Copper plasma, in the wavelength range of 7.9–9.5 Å, are experimentally observed using a thallium acid phthalate crystal spectrometer. The plasma is produced by the irradiation of a Cu target with a 15 J, 500 ps Nd: Glass laser with a focusable intensity up to 5 × 1014 W/cm2. The observed lines result from the transitions among 2p-nd, 2p-ns, and 2s-nd (n = 4–6) levels. Transition wavelengths, transition probabilities, and oscillator strengths of these lines are calculated using the Multi-Configuration Dirac-Fock method. In this computation, the contribution of relativistic corrections such as two-body Breit corrections and QED corrections due to vacuum polarization and self-energy has also been considered. FLYCHK simulations are used to analyze the distribution of the various charge states of the Copper ions and to find the temperature and density of plasma. Moreover, the effect of self-absorption of the plasma (opacity), as well as of suprathermal electrons on charge state distribution of ions, is also studied. The synthetic spectrum provides a best-match with the experimental spectrum at a laser intensity of 1.3 × 1014 W/cm2 for Tc = 150 eV, Th = 1000 eV, f = 0.008, and density 4.5 × 1020 cm−3.The temperature and density ranges are also calculated using a radiative hydrodynamic code. The calculated temperature and density range are in agreement with the experimentally determined values. The effect of the change in laser intensity on the L-shell spectrum of Cu is studied which indicates the switching between lower (Cu XX) and higher charge states (Cu XXI and Cu XXII) at higher laser intensities.