Kurt Franke

High-precision comparison of the antiproton-to-proton charge-to-mass ratio

Invariance under the charge, parity, time-reversal (CPT) transformation is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry—that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime—although it is model dependent. A number of high-precision CPT and Lorentz invariance tests—using a co-magnetometer, a torsion pendulum and a maser, among others—have been performed, but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available. Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H−) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton to that for the proton and obtain . The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-to-proton mass comparisons as well as the respective figure of merit of the standard model extension by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of <720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of < 8.7 × 10−7.

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.

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.

Noninvasiveness and time symmetry of weak measurements

Measurements in classical and quantum physics are described in fundamentally different ways. Nevertheless, one can formally define similar measurement procedures with respect to the disturbance they cause. Obviously, strong measurements, both classical and quantum, are invasive—they disturb the measured system. We show that it is possible to define general weak measurements, which are noninvasive: the disturbance becomes negligible as the measurement strength goes to zero. Classical intuition suggests that noninvasive measurements should be time symmetric (if the system dynamics is reversible) and we confirm that correlations are time-reversal symmetric in the classical case. However, quantum weak measurements—defined analogously to their classical counterparts—can be noninvasive but not time symmetric. We present a simple example of measurements on a two-level system which violates time symmetry and propose an experiment with quantum dots to measure the time- symmetry violation in a third-order current correlation function.

Exploiting boundary states of imperfect spin chains for high-fidelity state transfer

We study transfer of a quantum state through XX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material.

Towards a high-precision measurement of the antiproton magnetic moment

The recent observation of single spins flips with a single proton in a Penning trap opens the way to measure the proton magnetic moment with high precision. Based on this success, which has been achieved with our apparatus at the University of Mainz, we demonstrated recently the first application of the so called double Penning-trap method with a single proton. This is a major step towards a measurement of the proton magnetic moment with ppb precision. To apply this method to a single trapped antiproton our collaboration is currently setting up a companion experiment at the antiproton decelerator of CERN. This effort is recognized as the Baryon Antibaryon Symmetry Experiment (BASE). A comparison of both magnetic moment values will provide a stringent test of CPT invariance with baryons.

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.

Time asymmetry in weak measurements

In classical physics, the microscopic dynamics is invariant under time reversal. In quantum mechanics, it is only the measurement process that renders the dynamics irreversible. However, for non-invasive measurements, one should expect that the time-reversal symmetry is restored. We show that, counterintuitively, the symmetry is broken even in the non-invasive limit.