Hyperfine Research Articles

Modulation transfer spectroscopy of the D1 transition of potassium: theory and experiment

We report on a study of modulation transfer spectroscopy of the 4S1/2→4P1/2 (D1) transition of naturally abundant potassium in a room-temperature vapour cell. This transition is critical for laser cooling and optical pumping of potassium and our study is therefore motivated by the need for robust laser frequency stabilisation. Despite the absence of a closed transition, the small ground-state hyperfine splitting in potassium results in strong crossover features in the D1 modulation transfer spectrum. To emphasise this we compare the D1 and D2 spectra of potassium with those of rubidium. Further, we compare our experimental results with a detailed theoretical simulation, examining different pump–probe polarisation configurations to identify the optimal signals for laser frequency stabilisation. We find good agreement between the experiment and the theory, especially for the lin∥lin polarisation configuration.

A perturbed energy level of the holmium atom

This study focuses on two lines of atomic holmium for which standard hyperfine structure analysis could not be performed. The lines were studied by laser-induced fluorescence spectroscopy using a Ti-sapphire laser. Usually, the hyperfine structure of spectral lines is described by the well-known Casimir formula. However, this was not possible in the analysis of these two lines. The common feature of these two lines is that their upper energy levels are identical. In this study, hyperfine structure analyses were performed by considering a perturbation in the hyperfine splitting of the upper energy level of both lines. Shifts were introduced for the hyperfine sub-levels with F = 4 to 7 of the perturbed level, with the help of which the positions of all components of both laser lines could be satisfactorily explained. The same behaviour was found for three other spectral lines present in the Fourier transform spectrum, which are connected to the same perturbed upper energy level. The perturbation must be caused by a hitherto unknown energy level of odd parity with small J -value. The energy, J - quantum number and hyperfine constant A of this level were estimated.

Analyzing the photoassociation spectrum of ultracold 85Rb 133Cs molecule in (3)3Σ+ state.

We establish a theoretical model to analyze the photoassociative spectroscopy of 85Rb 133Cs molecules in the (3)3Σ+ state. The vibrational energy, spin-spin coupling constant, and hyperfine interaction constant of the (3)3Σ+ state are determined based on nine observed vibrational levels. Consequently, the Rydberg-Klein-Rees potential energy curve of the (3)3Σ+ state is obtained and compared with the ab initial potential energy curve. Our model can be adopted to analyze the photoassociative spectroscopy of other heteronuclear alkali-metal diatomic molecules in the (3)3Σ+ state.

Dynamics of electron-hole pairs in interface exciplex OLEDs investigated by magnetic field effects

Interface exciplex organic light-emitting diodes (OLEDs) have attracted intense attention due to the advantages including well-confined recombination regions, barrier-free charge transport and thermally activated delayed fluorescence (TADF) characteristics. To investigate the spin evolutions and dynamics of electron-hole (e-h) pairs, such as polaron pairs (PPs) and charge transfer (CT) excitons, in interface exciplex OLEDs is crucial for a better understanding on their energy gain and loss mechanisms. In this work, microscopic dynamics of e-h pairs in interface exciplex OLEDs were investigated by magneto-electroluminescence (MEL) and magneto-conductivity (MC) responses. The interface exciplex OLEDs were fabricated using 4,4,4-tris(N-3-methylphenyl-N-phenylamino) triphenylamine (m-MTDATA) as the donor and 2,4,6-tris(biphenyl-3-yl)-1,3,5-triazine (T2T) as the acceptor. Hyperfine interaction (HFI)- and different g-factors between electrons and holes (Δg mechanism)-dominated spin flip processes, and recombination and dissociation processes such as triplet-triplet annihilation (TTA) and triplet-charge annihilation (TQA) were identified, and their changes with temperature and current were explored. Our results may provide valuable insights into the evolution of carriers and facilitate the development of interface exciplex-based OLEDs.

Fine- and hyperfine structure semi-empirical studies of atomic cobalt. Even-parity configurations system

We present the results of multiconfiguration semi–empirical calculations of the fine structure (fs) and the hyperfine structure (hfs) for the even-parity level system of atomic cobalt (Co I), using all available experimental data. These results were obtained using our proprietary software package designed for complex atom structure analysis. Through the iterative fine-structure calculation procedure, predictions of energy levels along with their Landé gJ factors and wave functions were obtained for each electronic state. Good agreement was achieved between the theoretical hyperfine structures and the experimental constants, which confirmed the validity of the propositions in the spectroscopic descriptions of observed Co I levels. For some levels no experimental hfs constants were known; in such cases these values are predicted.

Precision Measurement of Vibrational Quanta in Tritium Hydride.

Saturated absorption measurements of transitions in the (2-0) band of radioactive tritium hydride are performed with the ultrasensitive noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy intracavity absorption technique in the range 1460-1510nm. The hyperfine structure of rovibrational transitions of tritium hydride, in contrast to that of hydrogen deuteride, exhibits a single isolated hyperfine component, allowing for the accurate determination of hyperfineless rovibrational transition frequencies, resulting in R(0)=203 396 426 692(22) kHz and R(1)=205 380 033 644(21) kHz. This corresponds to an accuracy 3 orders of magnitude better than previous measurements in tritiated hydrogen molecules. Observation of an isolated component in P(1) with reversed signal amplitude contradicts models for line shapes in hydrogen deuteride based on crossover resonances.

Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle.

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2 V cm^{-1}, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 ^{2}S_{1/2}(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)-1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.203001; A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.230801] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)NATUAS0028-083610.1038/229110a0], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)_{stat}(1.8)_{syst} kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)-2P_{1/2}(1) interval [N. Bezginov et al., Science 365, 1007 (2019)SCIEAS0036-807510.1126/science.aau7807], we determine the Rydberg frequency to be cR_{∞}=3 289 841 960 204(15)_{stat}(7)_{syst}(13)_{2S-2P} kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.

Fast fitting of spectral lines with Gaussian and hyperfine structure models

The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task. We present a new computer program Spectrum Iterative Fitter (SPIF) for the fitting of spectra with Gaussians or with hyperfine line profiles. The aim is to show the computational efficiency of the program and to use it to examine the general accuracy of approximating spectra with simple models. We describe the implementation of the program. To characterise its performance, we examined spectra with isolated Gaussian components or a hyperfine structure, also using synthetic observations from numerical simulations of interstellar clouds. We examined the search for the globally optimal fit and the accuracy to which single-velocity-component and multi-component fits recover true values for parameters such as line areas, velocity dispersion, and optical depth. The program is shown to be fast, with fits of single Gaussian components reaching on graphics processing units speeds approaching one million spectra per second. This also makes it feasible to use Monte Carlo simulations or Markov chain Monte Carlo calculations for the error estimation. However, in the case of hyperfine structure lines, degeneracies affect the parameter estimation and can complicate the derivation of the error estimates. The use of many random initial values makes the fits more robust, both for locating the global $ minimum and for the selection of the optimal number of velocity components.

µSR studies for radical reactions of unsaturated organophosphorus compounds

In this paper, the µSR studies of some unsaturated organophosphorus compounds containing heavier congeners of cyclobutane-1,3-diyl and anthracene are reviewed by discussing the usefulness of µSR for main group chemistry. The regioselective addition of muonium (Mu = [µ+e–]) to one of the skeletal phosphorus atoms in an electron-donating air-stable crystalline 1,3-diphosphacyclobutane-2,4-diyl leading to the paramagnetic 4-membered P-heterocycle was characterized by the Δ1 (ΔM = ± 1) resonance signal observed by muon (avoided) level-crossing resonance (µLCR). Meanwhile, a crystalline 1,3-diphosphacyclobutane-2,4-diyl bearing an electron-deficient nitrogen heterocyclic unit was analyzed by transverse-field muon spin rotation (TF-µSR) to characterize predominant muoniation at the skeletal radical carbon centre. A 9-phosphaanthracene bearing the trifluoromethyl (CF3) stabilizing groups at the peri positions was also investigated from the views of radical reactivity, and the regioselective addition of muonium to the skeletal sp2-type phosphorus atom was characterized by the muon hyperfine coupling (hfc) constant observed by TF-µSR and the Δ0 (ΔM = 0) signal of µLCR. The light mass of muon (Mass = 0.1134 amu) causes the larger zero-point energy and promotes the high-energy molecular structure in which the fused aromatic rings are almost flat, although the CF3 groups would prefer the non-planar saddle-like 9-phosphaanthracene skeleton.

Coherent Carrier Spin Dynamics in FAPbBr3 Perovskite Crystals.

Coherent spin dynamics of electrons and holes are studied in hybrid organic-inorganic lead halide perovskite FAPbBr3 bulk single crystals using the time-resolved Kerr ellipticity technique at cryogenic temperatures. The Larmor spin precession of the carrier spins in a magnetic field is monitored to measure the Landé g-factors of electrons (+2.44) and holes (+0.41). These g-factors are highly isotropic. The measured spin dephasing times amount to a few nanoseconds, and the longitudinal hole spin relaxation time is 470 ns. The important role of the strong hyperfine interaction between carrier spins and nuclear spins is demonstrated via dynamic nuclear polarization. At low temperatures, electron and hole spin relaxation predominantly occurs via the hyperfine interaction, whose importance significantly decreases at temperatures above 12 K. We overview the spin dynamics in various lead halide perovskite crystals and polycrystalline films and conclude on their common features provided by charge carrier localization at cryogenic temperatures.

Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium.

We present a rigorous quantum scattering study of the effects of hyperfine and Zeeman interactions on cold Li-H2 collisions in the presence of an external magnetic field using a recent abinitio potential energy surface. We find that the low-field-seeking states of H2 predominantly undergo elastic collisions: the ratio of elastic-to-inelastic cross sections exceeds 100 for collision energies below 100 mK. Furthermore, we demonstrate that most inelastic collisions conserve the space-fixed projection of the nuclear spin. We show that the anisotropic hyperfine interaction between the nuclear spin of H2 and the electron spin of Li can have a significant effect on inelastic scattering in the ultracold regime, as it mediates two processes: the electron spin relaxation in lithium and the nuclear spin-electron spin exchange. Given the predominance of elastic collisions and the propensity of inelastic collisions to retain H2 in its low-field-seeking states, our results open up the possibility of sympathetic cooling of molecular hydrogen by atomic lithium, paving the way for future exploration of ultracold collisions and high-precision spectroscopy of H2 molecules.

Prospective Optical Lattice Clocks in Neutral Atoms with Hyperfine Structure

Optical lattice clocks combine the accuracy and stability required for next-generation frequency standards. At the heart of these clocks are carefully engineered optical lattices tuned to a wavelength where the differential AC Stark shift between ground and excited states vanishes—the so called ‘magic’ wavelength. To date, only alkaline-earth-like atoms utilizing clock transitions with total electronic angular momentum J=0 have successfully realized these magic wavelength optical lattices at the level necessary for state-of-the-art clock operation. In this article, we discuss two additional types of clock transitions utilizing states with J≠0, leveraging hyperfine structure to satisfy the necessary requirements for controlling lattice-induced light shifts. We propose realizing (i) clock transitions between same-parity clock states with total angular momentum F=0 and (ii) M1/E2 clock transitions between a state with F=0 and a second state with J=1/2, mF=0. We present atomic species which fulfill these requirements before giving a detailed discussion of both manganese and copper, demonstrating how these transitions provide the necessary suppression of fine structure-induced vector and tensor lattice light shifts for clock operations. Such realization of alternative optical lattice clocks promises to provide a rich variety of new atomic species for neutral atom clock operation, with applications from many-body physics to searches for new physics.

Measurement of steep dispersion associated with magnetically assisted gain in Zeeman degenerate two-level system of cold atoms

We report on the measurements of magnetically assisted dispersion and gain in a Zeeman degenerate two-level system associated with the closed D 2 hyperfine transition Fg=3→Fe=2 cold cesium atoms. We use a Mach–Zehnder interferometer to measure the dispersive properties of this system in the presence of a magnetic field, transversal to the quantization direction, when the atomic system is excited by a coupling and probe beams with orthogonal polarizations. We have measured the spectrum of the refraction index for different magnitudes of the external magnetic field and different coupling beam intensities. A previously published theoretical model, using a simpler atomic transition Fg=1→Fe=0 , accounts reasonably for the experimentally observed gain and dispersive lineshapes.

Biradical pincers involving two phenylene, biphenylene or terphenylene arms: Evidence for approach of two terminal nitroxides

Four new pincer-type bisnitroxides, o-C6H4{CH2O-(p-C6H4)n-N(O•)-But}2 (abbreviated as pBi and pTer for n = 2 and 3, respectively; pPh for n = 1 (known)), and o-C6H4{CH2O-(p-C6H4)n-1-(m-C6H4)–N(O•)-But}2 (mBi and mTer for n = 2 and 3, respectively) were prepared, where o-xylylenedioxy was chosen as a hinge and phenylene, biphenylene, and terphenylene were selected as an arm. The crystallographic analysis clarified the intramolecular proximity of the two radical groups was observed for mBi, whereas pBi and mTer possess an open V-shape. In toluene solution ESR, five hyperfine splitting lines were recorded for every compound at room temperature or higher. The antiferromagnetic exchange interaction is estimated as 2J/kB = −0.05 to −0.0002 K from ESR simulation. The orders of the exchange interactions are as follows: Ph > Bi > Ter regarding the arm lengths and m > p regarding the positional isomers. The temperature at which alternating linewidths appeared was found to be a convenient temperature scale in this study.

The Polarization of the Solar Ba ii D1 Line with Partial Frequency Redistribution and Its Magnetic Sensitivity

We investigate the main physical mechanisms that shape the intensity and polarization of the Ba ii D1 line at 4934 Å via radiative transfer numerical experiments. We focus especially on the scattering linear polarization arising from the spectral structure of the anisotropic radiation in the wavelength interval spanned by the line’s hyperfine structure (HFS) components in the odd isotopes of barium. After verifying that the presence of the low-energy metastable levels only impacts the amplitude, but not the shape, of the D1 linear polarization, we relied on a two-term atomic model that neglects such metastable levels but includes HFS. The D1 fractional linear polarization shows a very small variation with the choice of atmospheric model, enhancing its suitability for solar magnetic field diagnostics. Tangled magnetic fields with strengths of tens of gauss reduce the linear polarization, and saturation is reached at roughly 300 G. Deterministic inclined magnetic fields produce a U/I profile and, if they have a significant longitudinal component, a V/I profile, whose modeling requires accounting for HFS and the Paschen–Back effect. Because of the overlap between HFS components, the magnetograph formula cannot be applied to infer the longitudinal magnetic field. Accurately modeling the D1 intensity and polarization requires an atomic system that includes the metastable levels and the HFS, the detailed spectral structure of the radiation field, the incomplete Paschen–Back regime for magnetic fields, and an accurate treatment of collisions.

Precision spectroscopy of iodine absorption lines near the 1S0-3P2 transition of Yb atoms at 507 nm

We performed Doppler-free spectroscopy on the P(40)52-0 and P(52)53-0 lines of molecular iodine (127I2) near the 1S0-3P2 metastable transition of Yb at 507 nm. The frequency instability of an external-cavity diode laser locked to the observed hyperfine transitions of the 127I2 lines reached a level below 1.0 × 10−12, at the average time τ of the measurement of >10 s. The absolute frequency of the laser locked to the hyperfine transitions was measured with an uncertainty of 8 kHz (fractionally 1.4 × 10−11) using an optical frequency comb. The hyperfine transition intervals were fitted to a four-term Hamiltonian to validate the measurements and calculate the hyperfine constants of the iodine lines. The observed 30 hyperfine transitions of the P(40)52-0 and P(52)53-0 lines of 127I2 can be used as optical frequency references to investigate the 1S0-3P2 transition of Yb atoms.

Collisional effects in modeling solar polarized lines

Context. Rigorous implementation of the effects of collisions in modeling the formation of the polarized solar lines is of utmost importance in order to realistically analyze the available, highly sensitive solar spectropolarimetric observations. Indeed, even when an observation seems to fit well with theory, one can misinterpret results if important effects due to collisions are not correctly implemented in the modeling process. Aims. We point out inconsistencies in the models adopted to implement the Paschen Back effect together with collisional effects on the solar linear polarization formed by scattering of anisotropic radiation. Because the significance of these inconsistencies increases as polarization becomes increasingly responsive to collisions, we investigate the range of hydrogen densities nH to which the polarization is sensitive. Methods. We used the density matrix formalism in the tensorial irreducible basis, which was developed within the theory of atom-radiation interaction and of atomic collisions. We solved the statistical equilibrium equations for multi-level atoms with hyperfine structure (HFS) in order to evaluate the collisional depolarization of levels of the D1-D2 lines of the K I atom. Results. We find that collisions play a prominent role, particularly at hydrogen densities of between 1013 and 1016 cm−3. Conclusions. So far, analyses of polarized lines formed in the presence of solar magnetic field have incorporated, if at all, collisional rates calculated assuming zero magnetic field. This could be a good approximation in the Hanle regime but not in the Paschen Back regime. For typical quiet Sun magnetic fields, the latter regime could be reached, and level-crossing takes place in several atomic systems. Therefore, one must be careful when using collisional rates calculated in the zero-field case to interpret linear polarization formed in magnetized media.

Hyperfine excitation of NH and ND by molecular hydrogen

The NH and ND radicals are of key importance in the comprehension of nitrogen chemistry and the enhancement of deuterated molecules in the interstellar medium. Observations by space telescopes yield spectra that can resolve the fine and hyperfine structure of these radicals, a consequence of the electronic and magnetic interactions of nitrogen, hydrogen, and deuterium nuclei. Accurate rate coefficients, induced by collisions with H2, are required to interpret spectra of these radicals. We report the first rate coefficients for fine and hyperfine transitions of NH and ND in collision with both ortho- and para-H2. Based on a recent four-dimensional potential energy surface, fine-structure resolved cross sections and rate coefficients are computed with the time-independent close-coupling method over a temperature range of 5–300 K. Our calculations include the first 25 energy levels of NH and ND. Hyperfine resolved cross sections and rate coefficients are determined using the infinite-order sudden (IOS) approximation between 5 and 200 K for NH and 100 K for ND. We consider the first 71 and 105 energy levels of NH and ND, respectively. General propensity rules are discussed. We found a significant isotopic substitution effect in the rate coefficients. In addition, the rate coefficients for collisions with H2 are larger than those with He by a factor of up to 5, leading to lower critical densities for collisional excitation with H2 than He. The impact of the new set of collisional data has been investigated in simple radiative transfer models of the NH emission seen toward the Orion Bar and the ejecta of the η Carinae binary star. We observed significant differences by a factor of 5 between the presently determined column densities for NH compared to those from the literature using He as a collider.

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.

Continuous cold rubidium atomic beam with enhanced flux and tunable velocity.

We present a cold atomic beam source based on a two-dimensional (2D)+ magneto-optical trap (MOT), capable of generating a continuous cold beam of 87Rb atoms with a flux up to 4.3 × 109 s-1, a mean velocity of 10.96(2.20) m/s, and a transverse temperature of 16.90(1.56) µK. Investigating the influence of high cooling laser intensity, we observe a significant population loss of atoms to hyperfine-level dark states. To account for this, we employ a multiple hyperfine level model to calculate the cooling efficiency associated with the population in dark states, subsequently modifying the scattering force. Simulations of beam flux at different cooling and repumping laser intensities using the modified scattering force are in agreement with experimental results. Optimizing repumping and cooling intensities enhances the flux by 50%. The influence of phase modulation on both the pushing and cooling lasers is experimentally studied, revealing that the mean velocity of cold atoms can be tuned from 9.5 m/s to 14.6 m/s with a phase-modulated pushing laser. The versatility of this continuous beam source, featuring high flux, controlled velocity, and narrow transverse temperature, renders it valuable for applications in atom interferometers and clocks, ultimately enhancing bandwidth, sensitivity, and signal contrast in these devices.