Ground-state Hyperfine Splitting Research Articles

Towards measuring the ground state hyperfine splitting of antihydrogen – a progress report

We report the successful commissioning and testing of a dedicated field-ioniser chamber for measuring principal quantum number distributions in antihydrogen as part of the ASACUSA hyperfine spectroscopy apparatus. The new chamber is combined with a beam normalisation detector that consists of plastic scintillators and a retractable passivated implanted planar silicon (PIPS) detector.

Annihilation detector for an in-beam spectroscopy apparatus to measure the ground state hyperfine splitting of antihydrogen

The matter-antimatter asymmetry observed in the universe today still lacks a quantitative explanation. One possible mechanism that could contribute to the observed imbalance is a violation of the combined Charge-, Parity- and Time symmetries (CPT). A test of CPT symmetry using anti-atoms is being carried out by the ASACUSA-CUSP collaboration at the CERN Antiproton Decelerator using a low temperature beam of antihydrogen—the most simple atomic system built only of antiparticles. While hydrogen is the most abundant element in the universe, antihydrogen is produced in very small quantities in a laboratory framework. A detector for in-beam measurements of the ground state hyperfine structure of antihydrogen has to be able to detect very low signal rates within high background. To fulfil this challenging task, a two layer barrel hodoscope detector was developed. It is built of plastic scintillators with double sided readout via Silicon Photomultipliers (SiPMs). The SiPM readout is done using novel, compact and cost efficient electronics that incorporate power supply, amplifier and discriminator on a single board. This contribution will evaluate the performance of the new hodoscope detector.

Frequency metrology using highly charged ions

Due to the scaling laws of relativistic fine structure splitting, many forbidden optical transitions appear within the ground state configurations of highly charged ions (HCI). In some hydrogen-like ions, even the hyperfine splitting of the 1s ground state gives rise to optical transitions. Given the very low polarizability of HCI, such laser-accessible transitions are extremely impervious to external perturbations and systematics that limit optical clock performance and arise from AC and DC Stark effects, such as black-body radiation and light shifts. Moreover, AC and DC Zeeman splitting are symmetric due to the much larger relativistic spin-orbit coupling and corresponding fine-structure splitting. Appropriate choice of states or magnetic sub-states with suitable total angular momentum and magnetic quantum numbers can lead to a cancellation of residual quadrupolar shifts. All these properties are very advantageous for the proposed use of HCI forbidden lines as optical frequency standards. Extremely magnified relativistic, quantum electrodynamic, and nuclear size contributions to the binding energies of the optically active electrons make HCI ideal tools for fundamental research, as in proposed studies of a possible time variation of the fine structure constant. Beyond this, HCI that cannot be photoionized by vacuum-ultraviolet photons could also provide frequency standards for future lasers operating in that range.

Steps towards the hyperfine splitting measurement of the muonic hydrogen ground state: pulsed muon beam and detection system characterization

The high precision measurement of the hyperfine splitting of the muonic-hydrogen atom ground state with pulsed and intense muon beam requires careful technological choices both in the construction of a gas target and of the detectors. In June 2014, the pressurized gas target of the FAMU experiment was exposed to the low energy pulsed muon beam at the RIKEN RAL muon facility. The objectives of the test were the characterization of the target, the hodoscope and the X-ray detectors. The apparatus consisted of a beam hodoscope and X-rays detectors made with high purity Germanium and Lanthanum Bromide crystals. In this paper the experimental setup is described and the results of the detector characterization are presented.

Measurement of positronium thermalization in isobutane gas for precision measurement of ground-state hyperfine splitting

The thermalization parameter of positronium in pure isobutane gas was measured in order to take into account the thermalization effect on precision measurements of the ground-state hyperfine splitting (HFS) of positronium. The momentum-transfer cross section was measured to be for positroniums with kinetic energy below 0.17 eV. Using this value, our new HFS experiment revealed that the positronium thermalization effect on HFS was as large as . In this article, we show the details of Ps thermalization measurement, which have not been published before, and also its effect on HFS.

The FAMU experiment: muonic atoms to probe the proton structure

The goal of the FAMU experiment is the measurement of the proton Zemach radius using muonic hydrogen, a subject that has raised much interest in recent years due to its implications in the so-called proton radius puzzle. In order to extract the Zemach radius, the FAMU collaboration aims at measuring the hyperfine splitting of the µp ground state, since the effect of the proton finite size affects the HF transition energy. The proposed experimental method requires a detection system which is suited for time resolved X-ray spectroscopy: in this contribution the results of the first measurements performed at the RIKEN-RAL muon facility in order to verify the fitness of the detection system in the pulsed intense muon beam are presented. The characteristic X-rays from atomic transitions in muonic atoms formed in different targets have been detected using a HPGe detector and five scintillating counters based on LaBr3(Ce) crystals, whose output has been recorded for 5 ps using a 500 MHz digitizer to measure both the energy and the time spectrum of the detected events. With a detailed pulse analysis considering pile-up events, both the expected characteristic X-rays and lifetimes of various elements were measured, paving the way for future measurements to be carried out in early 2016.

New Precision Measurement for Proton Zemach Radius with Laser Spectroscopy

In this proceeding, a new proposal aiming to improve the precision of the proton Zemach radius will be presented. A circularly polarized laser will be shed on a sample of muonic hydrogen in its ground state. By observing the maximum muon decay asymmetry during scanning laser wave length, the ground-state hyperfine splitting energy can be identified, which is directly related to Zemach radius.citedupays The precision of Zemach radius by this measurement is estimated to be three times better compared to PSI experiment. This result will contribute to the solution of proton size puzzle.

Efficient parametric non-degenerate four-wave mixing in hot potassium vapor

We have observed high gains of the probe and the conjugate beams in non-degenerate four-wave mixing in hot potassium vapor, using a double-Λ configuration at the D1 line of the 39 K isotope. Gains of up to 82 for the conjugate beam and 63 for the probe beam have been achieved. Higher gains were obtained than with other alkali atoms under comparable experimental conditions due to lower ground state hyperfine splitting in the potassium atom. Experimental parameters for maximal gain have been determined. Notable gains are achieved at low pump intensities (~10 W cm−2) that are attainable even by conventional laser diodes. Due to their high gains, the probe and the conjugate beams may be suitable for utilization in quantum correlation and relative intensity squeezing experiments.

The ASACUSA CUSP: an antihydrogen experiment

In order to test CPT symmetry between antihydrogen and its counterpart hydrogen, the ASACUSA collaboration plans to perform high precision microwave spectroscopy of ground-state hyperfine splitting of antihydrogen atom in-flight. We have developed an apparatus (“cusp trap”) which consists of a superconducting anti-Helmholtz coil and multiple ring electrodes. For the preparation of slow antiprotons and positrons, Penning- Malmberg type traps were utilized. The spectrometer line was positioned downstream of the cusp trap. At the end of the beamline, an antihydrogen beam detector was located, which comprises an inorganic Bismuth Germanium Oxide (BGO) single-crystal scintillator housed in a vacuum duct and surrounding plastic scintillators. A significant fraction of antihydrogen atoms flowing out the cusp trap were detected.

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

A microwave frequency standard based on laser-cooled (113)Cd(+) ions has been developed in recent years, and the short-term frequency instability is measured to be 6.1×10(-13)/√τ. By comparing the Cd(+) clock to a superior frequency reference, the ground-state hyperfine splitting of (113)Cd(+) is measured precisely to be 15199862855.0192(10) Hz with a fractional precision of 6.6×10(-14). This result is consistent with previous results, and the measurement precision is improved by nearly one order more than the best result reported before.

Towards a precise measurement of the antihydrogen ground state hyperfine splitting in a beam: the case of in-flight radiative decays

The ASACUSA antihydrogen setup at the CERN Antiproton Decelerator (AD) consists of an antihydrogen source (cusp magnet coupled to a positron source and an antiproton catching magnet) followed by a spectrometer beamline. After production in the cusp, the antihydrogen atoms decay while they escape the trap leading to changes in their effective magnetic moment which in turn affect their trajectories in the beamline. Those sequential decays in the presence of a varying magnetic field strength from their production point in the cusp to their detection at the end of the spectrometer line can in principle greatly affect the prospects for a precision measurement of the antihydrogen hyperfine splitting given the so-far relatively low number of available anti-atoms. The impact of the antihydrogen decay in this context has for the first time been simulated. The implementation of atomic radiative decay has been done in Geant4 to extend the particle tracking capabilities originally embedded in Geant4 to excited atoms, and to allow studies of the effect of dynamic atomic properties on trajectories. This new tool thus allows the study of particle–matter interaction via the Geant4 toolkit while properly taking into account the atomic nature of the object under study. The implementation as well as impacts on the experimental sensitivity for antihydrogen spectroscopy are discussed in this paper.

Laser-Frequency Stabilization Based on Steady-State Spectral-Hole Burning inEu3+∶Y2SiO5

We present and analyze a method of laser-frequency stabilization via steady-state patterns of spectral holes in Eu(3+)∶Y(2)SiO(5). Three regions of spectral holes are created, spaced in frequency by the ground-state hyperfine splittings of (151)Eu(3+). The absorption pattern is shown not to degrade after days of laser-frequency stabilization. An optical frequency comparison of a laser locked to such a steady-state spectral-hole pattern with an independent cavity-stabilized laser and a Yb optical lattice clock demonstrates a spectral-hole fractional frequency instability of 1.0×10(-15)τ(-1/2) that averages to 8.5(-1.8)(+4.8)×10(-17) at τ=73 s. Residual amplitude modulation at the frequency of the rf drive applied to the fiber-coupled electro-optic modulator is reduced to less than 1×10(-6) fractional amplitude modulation at τ>1 s by an active servo. The contribution of residual amplitude modulation to the laser-frequency instability is further reduced by digital division of the transmission and incident photodetector signals to less than 1×10(-16) at τ>1 s.

Positronium energy levels at order mα7: Vacuum polarization corrections in the two-photon-annihilation channel

We have calculated all contributions to the energy levels of parapositronium at order mα7 coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting.

An independent quark model study of weak leptonic decays of pseudoscalar mesons

An independent quark model with a relativistic power-law potential is used to study the weak leptonic decays of light and heavy pseudoscalar mesons. The partial decay width and the decay constant for the weak leptonic decay are derived from the quark–antiquark momentum distribution amplitude which is obtained from the bound quark eigenfunction with the assumption of a strong correlation existing between quark–antiquark momenta inside the decaying meson in its rest frame. The model parameters are first determined from the application of the model to study the ground state hyperfine splitting of ρ, K, D, Ds, B, Bs and Bc mesons. The same model with no adjustable parameters is then used to evaluate the decay constants fM and the decay widths of pseudoscalar mesons. The model predictions agree quite well with the available experimental data as well as with those of several other models. The decay constant for pion and kaon are obtained as fπ = 132 MeV and fk = 161 MeV which closely agree with experimental values. But in case of heavier mesons for which experimental data are not yet available, the present model gives its predictions as fBC > fBS > fB, fDS > fD, fD > fB and fπ > fB which are in conformity with most of other model predictions. The model predictions of the corresponding decay widths and the branching ratios for the [Formula: see text] and [Formula: see text] decay modes are in close agreement with the available experimental data.

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications.

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based. We further use these transitions to demonstrate strong population pumping by resonant excitation of the bound exciton transitions, suggesting several possible approaches to a solid-state atomic clock using bismuth in silicon, or eventually in enriched 28Si.

An atomic hydrogen beam to test ASACUSA’s apparatus for antihydrogen spectroscopy

The ASACUSA collaboration aims to measure the ground state hyperfine splitting (GS-HFS) of antihydrogen, the antimatter pendant to atomic hydrogen. Comparisons of the corresponding transitions in those two systems will provide sensitive tests of the CPT symmetry, the combination of the three discrete symmetries charge conjugation, parity, and time reversal. For offline tests of the GS-HFS spectroscopy apparatus we constructed a source of cold polarised atomic hydrogen. In these proceedings we report the successful observation of the hyperfine structure transitions of atomic hydrogen with our apparatus in the earth's magnetic field.

Higher order corrections to the hyperfine splitting of positronium

The positronium ground state hyperfine splitting (hfs) has long been of interest as a high-precision test of our understanding of binding in QED. The positronium hfs is particularly sensitive to recoil effects (because the ratio of masses is one) and to virtual electron-positron annihilation, but positronium is insensitive to strong and weak interaction effects. Consequently, the comparison between theory and experiment for the positronium hfs, and more generally the positronium spectrum, tests different aspects of the theory compared to comparisons in other exotic atoms. For the past fifteen years there has been a persistent discrepancy between predicted and measured values of the positronium hfs of about four standard deviations (although a new experimental result is consistent with present theory). Recent experimental work is leading to new high-precision measurements, and the calculation of order- α 3 corrections has begun. The status of the positronium hfs problem and a discussion of recent progress is the topic of this contribution.

Study on the relationship between coherent population beating signal and the coherence of ground-state hyperfine sublevels

Coherent population beating (CPB) phenomenon occurs in a typical three-level system. When the frequency difference between two coherent pumping laser fields has a certain detuning from the ground-state hyperfine splitting, the excited state population will experience a transient oscillation before reaching equilibrium, and the oscillation frequency is equal to the detuning. The CPB phenomenon enables us to directly obtain the beat frequency between the measured radio frequency (RF) signal and the atomic transition frequency. Then we can get the standard frequency by compensating the beat frequency to the RF. We propose a scheme to implement atomic clock based on the CPB phenomenon in 2009, and the scheme has been implemented. When this effect is used to achieve an atomic clock, the frequency stability is directly related to the amplitude and SNR (signal to noise ratio) of the CPB signal. Influence of the ground-state hyperfine sublevels' coherence on CPB signal is theoretically simulated and experimentally investigated in this paper. A formula of the CPB signal is derived by using the semi-classical model of the interaction of atoms with light, and the theoretical simulation is done using the formula obtained. In the experiment two coherent pumping laser fields are used to interact with 87Rb atoms. A CPB process includes the coherence build-up and the CPB stimulation. The coherence of the ground-state hyperfine sublevels is achieved by controlling the pumping time of the coherent laser fields that are resonant to the ground-state hyperfine sublevels. With this method, the relationship between CPB signal and coherence of the ground-state hyperfine sublevels can be observed. Result shows that the amplitude of CPB signal is proportional to the ground-state hyperfine sublevels' coherence. The hign quality CPB signal can be achieved when the CPB stimulation is started with a pure coherent population trapping (CPT) state. In the CPB process, the coherence build-up rate is approximately equal to the coherence decay rate. So a 50% duty cycle square wave can be used to modulate the RF, and the period of the square wave had better be twice of the decay time of the ground-state hyperfine sublevels' coherence. To improve the SNR of CPB signal and the stability of atomic frequency standard, the ground-state hyperfine sublevels' coherence must be built up, improved, and maintained before the CPB stimulation. The feasibility of applying CPB phenomenon to the weak magnetic field measurement and other applications is also discussed in this paper.

Positronium energy levels at ordermα7: Light-by-light scattering in the two-photon-annihilation channel

Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energies at the level of $O({\ensuremath{\alpha}}^{3})$ corrections to the lowest-order result. We have obtained results for one set of such corrections involving light-by-light scattering of the photons produced in a two-photon virtual annihilation process. Our result is an energy shift $1.58377\phantom{\rule{0.16em}{0ex}}(8)m{\ensuremath{\alpha}}^{7}/{\ensuremath{\pi}}^{3}$ for the $n=1$ singlet state, correcting the ground-state hyperfine splitting by $\ensuremath{-}6.95$ kHz. We also obtained a new and more precise result for the light-by-light scattering correction to the real decay of parapositronium into two photons.

Microwave-Optical Double-Resonance Spectroscopy Experiment of 199Hg+ Ground State Hyperfine Splitting in a Linear Ion Trap

We report a spectroscopy experiment of the 199Hg+ ground state hyperfine splitting in a linear ion trap. The ions are optically pumped by a discharge lamp and cooled by helium buffer gas. The ground state hyperfine splitting is measured to be 40507347996.8(0.1) Hz by the microwave-optical double-resonance method. A narrow line width as 30 mHz is also observed. This progress builds the foundation for the realization of trapped 199Hg+ ion frequency standards.