Continuous Stern-Gerlach Effect Research Articles

Quantum logic inspired techniques for spacetime-symmetry tests with (anti-)protons

Cosmological observations as well as theoretical approaches to physics beyond the standard model provide strong motivations for experimental tests of fundamental symmetries, such as CPT invariance. In this context, the availability of cold baryonic antimatter at CERN has opened an avenue for ultrahigh-precision comparisons of protons and antiprotons in Penning traps. This work discusses an experimental method inspired by quantum logic techniques that will improve particle localization and readout speed in such experiments. The method allows for sympathetic cooling of the (anti-)proton to its quantum-mechanical ground state as well as the readout of its spin alignment, replacing the commonly used continuous Stern–Gerlach effect. Both of these features are achieved through coupling to a laser-cooled ‘logic’ ion co-trapped in a double-well potential. This technique will boost the measurement sampling rate and will thus provide results with lower statistical uncertainty, contributing to stringent searches for time dependent variations in the data. Such measurements ultimately yield extremely high sensitivities to CPT violating coefficients acting on baryons in the standard-model extension, will allow the exploration of previously unmeasured types of symmetry violations, and will enable antimatter-based axion-like dark matter searches with improved mass resolution.

Application of the Continuous Stern-Gerlach Effect for Laser Spectroscopy of the ^{40}Ar^{13+} Fine Structure in a Penning Trap.

We report on the successful demonstration of a novel scheme for detecting optical transitions in highly charged ions. We applied it to determine the frequency of the dipole-forbidden 2p ^{2}P_{1/2}-^{2}P_{3/2} transition in the fine structure of ^{40}Ar^{13+} using a single ion stored in the harmonic potential of a Penning trap. Our measurement scheme does not require detection of fluorescence, instead it makes use of the continuous Stern-Gerlach effect. Our value of 679.216464(4)_{stat}(5)_{syst} THz is in reasonable agreement with the current best literature values and improves its uncertainty by a factor of 24.

The ALPHATRAP experiment

The ALPHATRAP experiment at the Max-Planck Institute for Nuclear Physics in Heidelberg aims at probing the validity of quantum electrodynamics in extremely strong electromagnetic fields. To this end, ALPHATRAP will determine the value of the magnetic moment, or the g-factor, of the electron bound in highly charged ions. Quantum electrodynamics predicts this value with extraordinary precision. As the bound electron in highly charged ions is exposed to the strongest fields available for high-precision spectroscopy in the laboratory, reaching up to 1016 V/cm in hydrogenlike lead 208Pb81+, a comparison of the theoretical prediction with a measured value can yield the most stringent test of the Standard Model in strong fields. The targeted precision of eleven digits or more can be achieved by storing single highly charged ions in a cryogenic Penning trap, where its eigenfrequencies can be determined with ultra-sensitive electronics to highest precision. Additionally, the spin state can be non-destructively determined using the continuous Stern–Gerlach effect, allowing spectroscopy of the Larmor precession. ALPHATRAP is constructed to enable the injection and the storage of externally produced ions. The coupling to the Heidelberg EBIT gives access to even the heaviest highly charged ions and thus extends the available field strength by more than two orders of magnitude compared to previous experiments. This article describes the technical architecture and the performance of ALPHATRAP and summarises the experimental measurement possibilities.

Measurement of Ultralow Heating Rates of a Single Antiproton in a Cryogenic Penning Trap.

We report on the first detailed study of motional heating in a cryogenic Penning trap using a single antiproton. Employing the continuous Stern-Gerlach effect we observe cyclotron quantum transition rates of 6(1) quanta/h and an electric-field noise spectral density below 7.5(3.4)×10^{-20} V^{2} m^{-2} Hz^{-1}, which corresponds to a scaled noise spectral density below 8.8(4.0)×10^{-12} V^{2} m^{-2}, results which are more than 2 orders of magnitude smaller than those reported by other ion-trap experiments.

Beyond antihydrogen: testing CPT with the molecular antihydrogen ion

Measurements of Zeeman, Zeeman-hyperfine and ro-vibrational transitions in $\bar {H}_{2}^{-}(\bar {p}e^{+}\bar {p})$ compared to $H_{2}^{+}$ have the potential for more precise tests of CPT than can be obtained from antiprotons and antihydrogen. In particular, measurements of ro-vibrational transitions have a potential sensitivity to a difference between antiproton and proton mass three orders of magnitude higher than antihydrogen/hydrogen. Methods are outlined for precision measurements on a single $\bar {H}_{2}^{-}$ or ${H}_{2}^{+}$ ion in a cryogenic Penning trap, with non-destructive state identification using the continuous Stern-Gerlach effect or changes in mass. $\bar {H}_{2}^{-}$ can be produced using the $\bar {H}^{+}+\bar {p} \rightarrow \bar {H}_{2}^{-} + e^{+}$ reaction.

Electron Magnetic Moment in Highly Charged Ions: The ARTEMIS Experiment

AbstractThe magnetic moment (g‐factor) of the electron is a fundamental quantity in physics that can be measured with high accuracy by spectroscopy in Penning traps. Its value has been predicted by theory, both for the case of the free (unbound) electron and for the electron bound in a highly charged ion. Precision measurements of the electron magnetic moment yield a stringent test of these predictions and can in turn be used for a determination of fundamental constants such as the fine structure constant or the atomic mass of the electron. For the bound‐electron magnetic‐moment measurement, two complementary approaches exist, one via the so‐called “continuous Stern–Gerlach effect”, applied to ions with zero‐spin nuclei, and one a spectroscopic approach, applied to ions with nonzero nuclear spin. Here, the latter approach is detailed, and an overview of the experiment and its status is given.

Improving the accuracy of the muon mass and magnetic moment anomaly via the bound-muon g factor

A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude.

Single Microwave Photon Detection with a Trapped Electron

We investigate theoretically the use of an electron in a Penning trap as a detector of single microwave photons. At the University of Sussex we are developing a chip Penning trap technology, designed to be integrated within quantum circuits. Microwave photons are guided into the trap and interact with the electron’s quantum cyclotron motion. This is an electric dipole transition, where the near field of the microwave radiation induces quantum jumps of the cyclotron harmonic oscillator. The quantum jumps can be monitored using the continuous Stern-Gerlach effect, providing the quantum non demolition signal of the microwave quanta. We calculate the quantum efficiency of photon detection and discuss the main features and technical challenges for the trapped electron as a quantum microwave sensor.

BASE – The Baryon Antibaryon Symmetry Experiment

The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton g-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle*s motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penning-trap method we expect that in our measurements a fractional precision of δg/g 10−9 can be achieved. The successful application of this method to the antiproton will consist a factor 1000 improvement in the fractional precision of its magnetic moment. The BASE collaboration has constructed and commissioned a new experiment at the Antiproton Decelerator (AD) of CERN. This article describes and summarizes the physical and technical aspects of this new experiment.

Quantum annealing: The fastest route to quantum computation?

The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton $g$-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle's motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penning-trap method we expect that in our measurements a fractional precision of $\delta g/g$ 10$^{-9}$ can be achieved. The successful application of this method to the antiproton will represent a factor 1000 improvement in the fractional precision of its magnetic moment. The BASE collaboration has constructed and commissioned a new experiment at the Antiproton Decelerator (AD) of CERN. This article describes and summarizes the physical and technical aspects of this new experiment.

Demonstration of the double Penning Trap technique with a single proton

Spin flips of a single proton were driven in a Penning trap with a homogeneous magnetic field. For the spin-state analysis the proton was transported into a second Penning trap with a superimposed magnetic bottle, and the continuous Stern–Gerlach effect was applied. This first demonstration of the double Penning trap technique with a single proton suggests that the antiproton magnetic moment measurement can potentially be improved by three orders of magnitude or more.

Observation of Spin Flips with a Single Trapped Proton

Radio-frequency induced spin transitions of one individual proton are observed. The spin quantum jumps are detected via the continuous Stern-Gerlach effect, which is used in an experiment with a single proton stored in a cryogenic Penning trap. This is an important milestone towards a direct high-precision measurement of the magnetic moment of the proton and a new test of the matter-antimatter symmetry in the baryon sector.

Towards a direct measurement of the g-factor of a single isolated protonThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May–4 June, 2010.

Our Penning trap experiment aims at a direct high-precision measurement of the proton g-factor. We present the experimental setup and the measurement technique using the continuous Stern-Gerlach effect. Recent test measurements with a single proton stored in a Penning trap with a strong magnetic bottle and a new toroidal detection system are discussed. For a stringent test of the CPT symmetry the described technique can also be applied to the antiproton.

Developments for the direct determination of the g-factor of a single proton in a Penning trap

The measurement and comparison of the magnetic moment (or g-factor) of the proton and antiproton provide a stringent experimental test of the CPT-theorem in the baryonic sector (Quint et al., Nucl Instrum Methods Phys Res, B 214:207, 2004). We present an experimental setup for the first direct high-precision measurement of the g-factor of a single isolated proton in a double cylindrical Penning trap. The application of the continuous Stern-Gerlach effect to detect quantum jumps between the two spin states of the particle, together with a novel trap design specially developed for this purpose, offers the possibility of measuring the magnetic moment not only of a single proton but also of a single antiproton. It is aimed to achieve a relative uncertainty of 10 − 9 or better. Preliminary results including mass spectra of particle clouds as well as single proton preparation and detection are shown.

The anomalous magnetic moment of the electron

The value of the electron's magnetic moment is a fundamental quantity in physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to quantum electrodynamics (QED) as the relativistic quantum field theory of electrodynamics. In fact, the measured values both for free and for bound electrons are explained by corresponding QED calculations on the part per trillion and part per billion level of accuracy, respectively. This agreement is amongst the best known in physics today. In turn, it allows highly precise determinations of related fundamental constants like the fine structure constant α or the electron mass. The present article discusses the application of the continuous Stern–Gerlach effect to the precise measurement of magnetic moments, especially of the electron bound in highly charged ions and possible tests of calculations in the framework of QED of bound states. Also, a test of QED in a more general approach by the comparison of values for the fine structure constant derived from different measurements, will be discussed.

Calculation of electrostatic fields using quasi-Green's functions: application to the hybrid Penning trap

Penning traps offer unique possibilities for storing, manipulating and investigating charged particles with high sensitivity and accuracy. The widespread applications of Penning traps in physics and chemistry comprise e.g. mass spectrometry, laser spectroscopy, measurements of electronic and nuclear magnetic moments, chemical sample analysis and reaction studies. We have developed a method, based on the Green's function approach, which allows for the analytical calculation of the electrostatic properties of a Penning trap with arbitrary electrodes. The ansatz features an extension of Dirichlet's problem to nontrivial geometries and leads to an analytical solution of the Laplace equation. As an example we discuss the toroidal hybrid Penning trap designed for our planned measurements of the magnetic moment of the (anti)proton. As in the case of cylindrical Penning traps, it is possible to optimize the properties of the electric trapping fields, which is mandatory for high-precision experiments with single charged particles. Of particular interest are the anharmonicity compensation, orthogonality and optimum adjustment of frequency shifts by the continuous Stern–Gerlach effect in a quantum jump spectrometer. The mathematical formalism developed goes beyond the mere design of novel Penning traps and has potential applications in other fields of physics and engineering.

Continuous Stern–Gerlach effect and the magnetic moment of the antiproton

The measurement of the magnetic moment (or g-factor) of the antiproton and of the proton is a sensitive test of CPT invariance. We discuss the possibility of applying the continuous Stern–Gerlach effect to detect quantum jumps between the two spin states (spin up and spin down) of the antiproton. The measurement will be performed on a single antiproton stored in a Penning trap. The g-factor of the antiproton is determined by measuring its cyclotron frequency and its spin precession frequency in the magnetic field of the trap. With the double Penning trap method the g-factor of the antiproton can be determined with an accuracy of 1 ppb.

The magnetic moment anomaly of the electron bound in hydrogen-like oxygen16O7+

The measurement of the g-factorof the electron bound in a hydrogen-like ion is a high-accuracy test of the theory ofquantum electrodynamics (QED) in strong fields. Here we report on the measurement ofthe g-factorof the bound electron in hydrogen-like oxygen (16O7+). In our experimenta single highly charged ion is stored in a Penning trap. The electronicspin state of the ion is monitored via the continuous Stern–Gerlacheffect in a quantum non-demolition measurement. Quantum jumpsbetween the two spin states (spin up and spin down) are induced by amicrowave field at the spin precession frequency of the bound electron. Theg-factorof the bound electron is obtained by varying the microwave frequency and countingthe number of spin flips. The comparison of our experimental values for theg-factorof the bound electron with the theoretical values shows excellent agreement andconfirms the recent non-perturbative QED calculations.

Correlation and Relativistic Effects on LandégJFactors of Atomic Ions

We investigate relativistic effects on the Lande gJ factors of atomic ions using Multiconfiguration Dirac-Fock technique and Relativistic Many-Body perturbation theory. The role of Breit interaction, negative energy continuum and correlation effects is studied in Li-like, B-like, N-like ions and Ca+ ground-states. We also investigate Ti-like ions which have a long-lived excited state with J = 4. Those ions are all good candidates for employing the continuous Stern-Gerlach effect to measure their gJ -factor and provide accurate tests of relativistic many-body calculations.

Measurement of the gJ factor of a bound electron in hydrogen-like oxygen 16O7+

The magnetic moment of the electron bound in hydrogen-like oxygen O7+ has been determined using the "continuous Stern–Gerlach effect" in a double Penning trap. We obtained a relative precision of 2 x 10–9. This tests calculations of bound-state quantum electrodynamics and nuclear correction. PACS No.: 32.10Dk