By measuring the cyclotron frequency ratios of (3)He(+) to HD(+) and T(+) to HD(+), and using HD(+) as a mass reference, we obtain new atomic masses for (3)He and T. Our results are M[(3)He]=3.016 029 322 43(19)  u and M[T]=3.016 049 281 78(19)  u, where the uncertainty includes an uncertainty of 0.12 nu in the mass reference. Allowing for cancellation of common systematic errors, we find the Q value for tritium β decay to be (M[T]-M[(3)He])c(2)=18 592.01(7)  eV. This allows an improved test of systematics in measurements of tritium β decay that set limits on neutrino mass.

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 particle's spin state. Based on this success the proton magnetic moment mu(p) 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 mu(p). The techniques required for the proton can be directly applied to measure the antiproton magnetic moment mu((p) over bar). An improvement in precision of mu((p) over bar) 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.

The magnetic moment of the proton is directly measured with unprecedented precision using a double Penning trap.

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

A highly sensitive detection system for the non-destructive measurement of the cyclotron frequency of a single proton stored in a cryogenic Penning trap is described. The detector consists of a low noise GaAs field effect transistor amplifier combined with a copper helical resonator with high quality factor. The resonance frequency can be tuned with a GaAs-varactor diode. Connected to the Penning trap a quality factor of 1250 at 28.9MHz is achieved. With this detection system the signal of a single proton at a cyclotron mode-energy of only 10meV was resolved.

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 1.8x10(-6) and the magnetic moment has been determined with a relative uncertainty of 8.9x10(-6). A g-factor of 5.585 696(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.

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.

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.

A measurement scheme for the direct determination of the free cyclotron frequency ν(c) of a single particle stored in a Penning trap is described. The method is based on the dressed states of mode coupling. In this novel measurement scheme both radial modes of the single trapped particle are simultaneously coupled to the axial oscillation mode.

This experiment is aimed at measuring the magnetic moment org-factor of a single, isolated proton stored in a cylindrical Penning trap with a relative uncertainty of below 10 [1]. It will be conducted in a double Penning trap and constitutes the first direct and self-contained measure ment ever performed. Besides the proton g-factor, future experiments aim at determining the antiproton g-factor. Comparison of the two experimental values will provide a stringent test of CPT invariance on the baryonic sector. The g-factor results from an accurate measurement of its cyclotron(νc) and spin precession frequency (νL): g = 2 νL/νc. The former being deduced from the eigenfrequencies(νi) of the particle motion in the trap using the relation ν c = ν + +ν 2 z +ν − [2], where the eigenfrequencies will be measured by detecting the image currents induced in the trap electrodes. Since the spin motion is an internal degree of freedom, a magnetic bottle is exploited to imprint the spin state information onto an external degree of freedom, namely the axial eigenmotion of the particle. This so-called continuous Stern-Gerlach effect is used to detec t the resulting frequency shift and thus the spin state nondestructively [3]. The value of the frequency shift scales with the magnetic moment of the particle and the strength of the magnetic bottle. Thus, a novel trap design was developed, which we call hybrid Penning trap [4], to increase the axial frequency jump to a detectable range. To realize a high-precision experiment, long storage times are required which is realized by performing the experiment in a closed horizontal setup at cryogenic temperatures yielding an extremely low background pressure (p < 10 mbar). The double Penning trap installed in a 1.8 T superconducting magnet is housed in the trap chamber, in which a temperature of 3.9 K is reached using a low vibrational Gifford-MacMahon pulse tube cooler. Protons are created from a black polyethylene target inside thi s sealed system by electron beam impact ionization. The experimental environment bears great challenges for the elec tronics needed to non-destructively detect the trapped pro ton, however, it leads to a low electronic noise. To obtain a high signal-to-noise ratio (SNR), a detection system with a high quality factorQ is required. For the detection of the axial frequency at νz = 680 kHz aQ-value ofQz = 5500 is reached using a resonator with coil and shield made out of type II superconducting NbTi. This permits placing the detector near the trap in the high magnetic field thus reduc-

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 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.

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.

The precise determination of the g-factor of the proton and the antiproton together with their comparison is a stringent test of the CPT invariance theorem on the baryonic sector [1]. In our experiment, which is part of the FLAIR collaboration, theg-factor of a single, isolated (anti)proton will be determined by utilizing the continuou s Stern-Gerlach effect [2] in a hybrid double Penning trap setup [3]. Measuring the free cyclotron frequency ωc and the Larmor frequencyωL the g-factor can be determined via the relation

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.

S. Kreim†1, K. Blaum1,2, H. Kracke1, W. Quint2, S. Ulmer1,3, and J. Walz1 1Institut für Physik, Universität Mainz, 55099 Mainz; 2GSI, 64291 Darmstadt, Germany; 3Ruprecht-Karls-Universität, 69047 Heidelberg Determining the g-factor of a single, isolated (anti)proton in a double Penning trap results from an accurate measurement of its cyclotron and spin precession frequency. The Larmor frequency can be determined by inducing radio frequency transitions between the two spin states and detecting the resulting spin state in the magnetic bottle field of the analysis trap [1]. The spin direction is monitored by measuring the respective axial frequency non-destructively with a high-Q tank circuit. The cyclotron frequency is detected in the same manner in the homogeneous magnetic field region of the precision Penning trap. To achieve a high-precision determination of the proton g-factor long storage times are required. This is realized by performing the experiment in a closed setup at 4 K yielding an ultra-high vacuum. A low vibrational Gifford-MacMahon cooler provides the cryogenic environment.