Holger Kracke

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.

Resolution of single spin flips of a single proton.

The spin magnetic moment of a single proton in a cryogenic Penning trap was coupled to the particles axial motion with a superimposed magnetic bottle. Jumps in the oscillation frequency indicate spin flips and were identified using a Bayesian analysis.

Direct high-precision measurement of the magnetic moment of the proton

One of the fundamental properties of the proton is its magnetic moment, µp. So far µp has been measured only indirectly, by analysing the spectrum of an atomic hydrogen maser in a magnetic field. Here we report the direct high-precision measurement of the magnetic moment of a single proton using the double Penning-trap technique. We drive proton-spin quantum jumps by a magnetic radio-frequency field in a Penning trap with a homogeneous magnetic field. The induced spin transitions are detected in a second trap with a strong superimposed magnetic inhomogeneity. This enables the measurement of the spin-flip probability as a function of the drive frequency. In each measurement the proton’s cyclotron frequency is used to determine the magnetic field of the trap. From the normalized resonance curve, we extract the particle’s magnetic moment in terms of the nuclear magneton: μp = 2.792847350(9)μN. This measurement outperforms previous Penning-trap measurements in terms of precision by a factor of about 760. It improves the precision of the forty-year-old indirect measurement, in which significant theoretical bound state corrections were required to obtain µp, by a factor of 3. By application of this method to the antiproton magnetic moment, the fractional precision of the recently reported value can be improved by a factor of at least 1,000. Combined with the present result, this will provide a stringent test of matter/antimatter symmetry with baryons.

The quality factor of a superconducting rf resonator in a magnetic field

The quality factor of a superconducting NbTi resonator at 1.6 MHz in a magnetic field up to 1.2 T as well as its temperature dependence is investigated. A hysteresis effect in the superconducting surface resistance as a function of the magnetic field is observed. An unloaded Q-value of the resonator of 40,500 is achieved at 3.9 K. It is shown that this Q-value is limited by dielectric losses in the FORMVAR insulation of the coils wire. The details of the Q-value optimization are discussed. In the temperature dependence of the Q-value a steep decrease is observed above T approximately = 7.5 K. Finally, the implications of these measurements for real trap experiments are discussed in detail.

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

A new apparatus has been designed that aims at a direct precision measurement of the g-factor of a single isolated proton or antiproton in a Penning trap. We present a thorough discussion on the trap design and a method for the experimental trap optimization using a single stored proton. A first attempt at the g-factor determination has been made in a section of the trap with a magnetic bottle. The Larmor frequency of the proton has been measured with a relative uncertainty of 1.8◊10 6 and the magnetic moment has been determined with a relative uncertainty of 8.9◊10 6 . Ag-factor of 5.585696(50) has been obtained, which is in excellent agreement with previous measurements and predictions. Future experiments shall drive the spin-flip transition in a section of the trap with a homogeneous magnetic field. This has the potential to improve the precision of the measured g-factor of the proton and the antiproton by several orders of magnitude.

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 Greens 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 Dirichlets 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 5 Author to whom any correspondence should be addressed. 6 This article comprises part of the PhD thesis of S Kreim.

g-factor experiments on simple systems in Penning traps

Penning traps serve for the precise measurement of magnetic moments of simple atomic systems and fundamental particles. Here we present attempts to measure the magnetic moment of the electron bound in hydrogen-like or lithium-like heavy ions as well as of the proton and antiproton. While the first experiment aims for a more stringent test of bound-state quantum-electrodynamic calculations the second experiment provides a new high-precision test of the CPT theorem in the baryonic sector.

Demonstration of the Double Penning Trap Technique with a Single Proton

Abstract 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.

The Magnetic Moments of the Proton and the Antiproton

Recent exciting progress in the preparation and manipulation of the motional quantum states of a single trapped proton enabled the first direct detection of the particles spin state. Based on this success the proton magnetic moment μp was measured with ppm precision in a Penning trap with a superimposed magnetic field inhomogeneity. An improvement by an additional factor of 1000 in precision is possible by application of the so-called double Penning trap technique. In a recent paper we reported the first demonstration of this method with a single trapped proton, which is a major step towards the first direct high-precision measurement of μp. The techniques required for the proton can be directly applied to measure the antiproton magnetic moment μp. An improvement in precision of μp by more than three orders of magnitude becomes possible, which will provide one of the most sensitive tests of CPT invariance. To achieve this research goal we are currently setting up the Baryon Antibaryon Symmetry Experiment (BASE) at the antiproton decelerator (AD) of CERN.

Towards a direct measurement of the g-factor of a single isolated proton

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 measure- ments 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.