Ground-state Hyperfine Splitting Research Articles

Determination of the ground-state hyperfine splitting of trapped 171Yb+ ions

We present the determination of the ground-state hyperfine splitting (νHFS) in laser-cooled 171Yb+ ions using our microwave quantum frequency standard (QFS). Employing Ramsey spectroscopy in a closed-loop measurement configuration, we have achieved a νHFS value of 12 642 812 118 469.0(8) mHz with a fractional uncertainty of 6.6×10−14. This result aligns with previously reported values and represents the highest accuracy reported to date for such measurements conducted in a single-shot closed-loop configuration, without averaging over multiple dates. The development of this accurate 171Yb+ microwave QFS holds promise as a transportable time-frequency reference for satellite navigation systems.

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.

Diffusion of muonic hydrogen in hydrogen gas and the measurement of the 1$s$ hyperfine splitting of muonic hydrogen

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (\muμp) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the \muμp atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state by an inelastic collision with a H_22 molecule. The resulting increase of kinetic energy after this cycle modifies the \muμp atom diffusion in the hydrogen gas and the arrival time of the \muμp atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the \muμp diffusion in the H_22 gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H_22 molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment.

Precise measurement of the hyperfine splitting in muonium with a high intensity pulsed muon beam at J-PARC

At J-PARC, the MuSEUM (Muonium Spectroscopy Experiment Using Microwave) collaboration aims to precisely measure the ground-state hyperfine splitting of muonium atoms arising from the muon and electron spins. The pulsed muon beam is stopped in a krypton gas cell to form muonium atoms. The transitions of spin states are induced with a microwave cavity, which are then measured by positron counters. After the previously performed successful measurements with a nearly-zero magnetic field, we are currently planning a measurement with the 2.9T magnetic field by measuring two Zeeman-split sub-levels, so that increased statistics will allow us to more precisely determine the transition frequency down to ∼1ppb. Moreover, a new microwave cavity with a unique geometry is being designed to perform the measurement at an even stronger field of 2.9T in the future.

Pseudopotential analysis on hyperfine splitting frequency shift of alkali-metal atoms in noble gases, revisited.

Theoretical pseudopotentials and dispersion potentials are used to study ground-state hyperfine splitting frequencies of alkali-metal atoms (Li, Na, K, Rb, and Cs) in noble gases (He, Ne, Ar, Kr, and Xe) in all combinations. With a single fitting parameter, calculations based on first-order perturbation theory qualitatively present each temperature dependence of the measured frequency shift. With this parameter and excitation energies of alkali-metal and noble-gas atoms, the hyperfine splitting frequency of alkali-metal atoms is suitable for investigating the properties of noble-gas atoms, such as the s-wave scattering length of electrons, the electric-dipole polarizability, and the van der Waals radius. This study suggests the possibility of improving excitation energies and van der Waals potentials of colliding pairs.

Enhanced intensity difference squeezing with a low gain off-resonant Four-Wave Mixing in potassium vapor

Although potassium stands out among alkalies by its smallest ground state hyperfine splitting, smaller than Doppler broadening, investigations of its four-wave mixing (FWM) quantum properties, like squeezing and entanglement, were neglected. Here we present measurements of quantum correlations in potassium vapor using far-detuned double Λ scheme for FWM. We obtained the relative intensity difference squeezing (IDS) of -6.1 dB, with the squeezing bandwidth between 0.9 to 4.5 MHz on the noise spectra. The squeezing maximum in potassium compares well with the best results obtained in Rb and Cs, and has larger value than previously reported IDS in potassium. This result agrees qualitatively well with the squeezing calculated using analytical expressions from the model of operators when with chosen parameters FWM generates both squeezing and probe at their maximums. The ultimate squeezing level in potassium, predicted by the model, when conjugate absorption in the cell and optical losses behind the cell are neglected, is −10.29 dB. This is among the largest predicting squeezing obtained by FWM in alkalies.

Upgrade of ASACUSA’s antihydrogen detector

The goal of the ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) CUSP experiment at CERN’s Antiproton Decelerator is to measure the ground state hyperfine splitting of antihydrogen in order to test whether CPT invariance is broken.The ASACUSA hodoscope is a detector consisting of two layers of 32 plastic scintillator bars individually read out by two serially connected silicon photomultipliers (SiPMs) on each end. Two additional layers for position resolution along the beam axis were scintillator fibres, which will now be replaced by scintillating tiles placed onto the existing bars and also read out by SiPMs. If the antiproton of antihydrogen annihilates in the centre of the hodoscope, particles (mostly pions) are produced and travel through the various layers of the detector and produce signals.The hodoscope was successfully used during the last data taking period at CERN. The necessary time resolution to discriminate between particles travelling through the detector from outside and particles produced in the centre of the detector was achieved by the use of waveform digitisers and software constant fraction discrimination. The disadvantage of this readout scheme was the slow readout speed, which was improved by two orders of magnitude. This was done by omitting the digitisers and replacing them with TDCs reading out the digital time-over-threshold (ToT) signal using leading edge discrimination.

The Proton Structure in and out of Muonic Hydrogen

Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities), and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen (μH). Updated theory predictions for the Lamb shift and HFS in μH are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in μH and its impact on our understanding of the nucleon spin structure. To narrow down this search, we present a novel theory prediction obtained by scaling the measured HFS in hydrogen while leveraging radiative corrections. We also summarize recent developments in the spectroscopy of simple atomic and molecular systems and emphasize how they allow for precise determinations of fundamental constants, bound-state QED tests, and New Physics searches.

Laser excitation of the 1s-hyperfine transition in muonic hydrogen

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (\muμp) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2\times10^{-4}2×10−4 relative accuracy. In the proposed experiment, the \muμp atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, then is quenched back to the singlet state by an inelastic collision with a H_22 molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a \muμp atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by the laser bandwidth and collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where \muμp is formed and the laser spectroscopy will occur.

Wide range linear magnetometer based on a sub-microsized K vapor cell.

39K atoms have the smallest ground state (2S1/2) hyperfine splitting of all the most naturally abundant alkali isotopes and, consequently, the smallest characteristic magnetic field value B0=A2S1/2/μB≈170G, where A2S1/2 is the ground state's magnetic dipole interaction constant. In the hyperfine Paschen-Back regime (B≫B0, where B is the magnitude of the external magnetic field applied on the atoms), only eight Zeeman transitions are visible in the absorption spectrum of the D1 line of 39K, while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of 39K, this behavior is reached already at relatively low magnetic field B>B0. For each circular polarization (σ-,σ+), four spectrally resolved atomic transitions having sub-Doppler widths are recorded using a sub-microsized vapor cell of thickness L=120-390nm. We present a method that allows to measure the magnetic field in the range of 0.1-10kG with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with large gradients (up to 3 G/µm). The theoretical model describes well the experimental results.

Ground-state hyperfine structure of light muon-electron ions

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.

Nonlinear collision shifts of the 0-0 hyperfine transition due to van der Waals molecule formation.

We consider the origin of nonlinear collision shifts for the 0-0 hyperfine transition in alkali/noble-gas systems due to van der Waals molecule formation. Developing a semi-empirical model, we describe the shift as arising from three fundamental interactions: (1) a fractional change in the alkali's valence electron density at the alkali nucleus, η, which affects the hyperfine contact term; (2) a mixing of p-wavefunction character into the alkali ground state (characterized by the probability for p-state character appearing in the perturbed wavefunction ξ1 2), which gives rise to an electric quadrupole term in the ground-state hyperfine splitting; and (3) an interaction of the alkali's valence electron with the magnetic field produced by molecular rotation, characterized by a magnetic field strength BvdW. In addition to these molecular parameters, the model also depends on the formation rate of van der Waals molecules, kfP2, and the breakup rate of the molecules, kbP, where P is the noble-gas pressure. Fitting the model to the 85Rb/Xe and 87Rb/Xe experimental data of McGuyer and co-workers (and taking previously measured values for kf and BvdW), we find that η = 9 × 10-3, ξ1 2 = 5 × 10-3, and kb = 2.9×107s-1/Torr.

Precision determination of the ground-state hyperfine splitting of trapped 113Cd+ ions.

We measured the ground-state hyperfine splitting of trapped 113Cd+ ions to be 15199862855.02799(27) Hz with a fractional uncertainty of 1.8×10-14. The ions were trapped and laser-cooled in a linear quadrupole Paul trap. The fractional frequency stability was measured to be 4.2×10-13/τ, obtained from Ramsey fringes of high signal-to-noise ratios and taken over a measurement time of nearly 5 h, which is close to the short-term stability limit estimated from the Dick effect. Our result is consistent with previously reported values, but the measurement precision is four times better than the best result obtained to date.

High accuracy measurement of the ground-state hyperfine splitting in a 113Cd+ microwave clock: erratum.

We present an erratum to our Letter [Opt. Lett.40, 4249 (2015)OPLEDP0146-959210.1364/OL.40.004249]. This erratum corrects the nuclear Lande factor gI in Eq. (2). After correcting the error, the final ground-state hyperfine splitting frequency of the 113Cd+ ion is determined to be 15199862855.0287(10) Hz.

Measurement of the principal quantum number distribution in a beam of antihydrogen atoms

The ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration plans to measure the ground-state hyperfine splitting of antihydrogen in a beam at the CERN Antiproton Decelerator with initial relative precision of 10^{-6} or better, to test the fundamental CPT (combination of charge conjugation, parity transformation and time reversal) symmetry between matter and antimatter. This challenging goal requires a polarised antihydrogen beam with a sufficient number of antihydrogen atoms in the ground state. The first measurement of the quantum state distribution of antihydrogen atoms in a low magnetic field environment of a few mT is described. Furthermore, the data-driven machine learning analysis to identify antihydrogen events is discussed.Graphic

The FAMU experiment: muonic hydrogen high precision spectroscopy studies

The FAMU experiment aims to measure for the first time the hyperfine splitting of the muonic hydrogen ground state. From this measurement the proton Zemach radius can be derived and this will shed light on the determination of the proton charge radius. In this paper, we describe the scientific goal, the method and the detailed preparatory work. This includes the outcome of preliminary measurements, subsequent refined simulations and the evaluation of the expected results. The experimental setup being built for the measurement of the hyperfine splitting to be performed at the RAL laboratory muon facility is also described.

Spectroscopy properties of a single praseodymium ion in a crystal

Addressing and coherent control of single atoms in solids, with both optical and nuclear spin degrees of freedom is of particularly interest for applications ranging from nanoscale sensing to quantum computing. Here, we performed the spectroscopy study of single praseodymium ions in an yttrium aluminum garnet crystal at cryogenic temperature. The single nuclear spin of individual praseodymium ions is detected through a background-free optical upconversion readout technique. Single ions show stable photoluminescence with spectrally resolved hyperfine splitting of the praseodymium ground state. Based on this measurement, optical Rabi and optically detected nuclear magnetic resonance measurements are performed to study their spin coherence properties. We find short the spin coherence times of praseodymium nuclear spins which we attribute to spin phonon coupling.

First measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen

We report the first measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen between 100 and 300 K. Data were obtained from the X-ray spectra of delayed events in a gaseous target, made of a H2/O2 mixture, exposed to a muon beam. This work sets constraints on theoretical models of muon transfer and is of fundamental importance for the measurement of the hyperfine splitting of muonic hydrogen ground state as proposed by the FAMU collaboration.

Many-electron effects in the hyperfine splitting of lithiumlike ions

The rigorous QED evaluation of the one- and two-photon exchange corrections to the ground-state hyperfine splitting in Li-like ions is presented for the wide range of nuclear charge number $Z= 7 - 82$. The calculations are carried out in the framework of the extended Furry picture, i.e., with inclusion of the effective local screening potential in the zeroth-order approximation. The interelectronic-interaction contributions of the third and higher orders are taken into account in the framework of the Breit approximation employing the recursive perturbation theory. In comparison to the previous theoretical calculations, the accuracy of the interelectronic-interaction contributions to the ground-state hyperfine splitting in Li-like ions is substantially improved.

G−2 of charged leptons, α(MZ2) , and the hyperfine splitting of muonium

Following updates in the compilation of $e^+e^-\rightarrow{\rm hadrons}$ data, this work presents re-evaluations of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the electron ($a_e$), muon ($a_\mu$) and tau lepton ($a_\tau$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\alpha(M_Z^2)$. Combining the results for the hadronic vacuum polarisation contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of $a_\mu$ and its Standard Model prediction amounts to $\Delta a_{\mu} = (28.02 \pm 7.37) \times 10^{-10}$, corresponding to a muon $g-2$ discrepancy of $3.8\sigma$.