S. Ulmer

The BASE collaboration aims to measure antimatter systems with the highest precision in order to perform a rigorous test of CPT symmetry and search for physics beyond the Standard Model. As part of the BASE collaboration, we pursue the development of quantum logic inspired cooling and detection techniques for g-factor measurements of (anti-)protons. Implementing these methods requires full quantum-level control of individual antimatter particles confined in cryogenic Penning traps. By mapping the (anti-)proton's internal state onto a co-trapped 9Be+ "logic" ion via free Coulomb coupling in a double-well potential, we can accelerate measurement cycles and push g-factor precision measurements on (anti-)protons toward the quantum limit. Here, we present an overview of the proposed method and the current status of the project, with special emphasis on the new cryogenic multi-Penning-trap stack and the proton detection system.

We demonstrate efficient sub-thermal cooling of the modified cyclotron mode of a single trapped antiproton and reach particle temperatures $T_+=E_+/k_\text{B}$ below $200\,$mK in preparation times shorter than $500\,$s. This corresponds to the fastest resistive single-particle cyclotron cooling to sub-thermal temperatures ever demonstrated. By cooling trapped particles to such low energies, we demonstrate the detection of antiproton spin transitions with an error-rate $<0.000025$, more than three orders of magnitude better than in previous best experiments. This method will have enormous impact on multi-Penning-trap experiments that measure magnetic moments with single nuclear spins for tests of matter/antimatter symmetry, high-precision mass-spectrometry, and measurements of electron $g$-factors bound to highly-charged ions that test quantum electrodynamics.

High precision mass and $g$-factor measurements in Penning traps have enabled groundbreaking tests of fundamental physics. The most advanced setups use multi-trap methods, which employ transport of particles between specialized trap zones. Present developments focused on the implementation of sympathetic laser cooling will enable significantly shorter duty cycles and better accuracies in many of these scenarios. To take full advantage of these increased capabilities, we implement fast adiabatic transport concepts developed in the context of trapped-ion quantum information processing in a cryogenic Penning trap system. We show adiabatic transport of a single $^9\mathrm{Be}^+$ ion initially cooled to 2 mK over a 2.2 cm distance within 15 ms and with less than 10\,mK energy gain at a peak velocity of 3 m/s. These results represent an important step towards the implementation of quantum logic spectroscopy in the \ppbar system. Applying these developments to other multi-trap systems has the potential to considerably increase the data-sampling rate in these experiments.

We demonstrate optical sideband spectroscopy of a single $^9$Be$^+$ ion in a cryogenic 5 Tesla Penning trap using two-photon stimulated-Raman transitions between the two Zeeman sublevels of the $1s^{2}2s$ ground state manifold. By applying two complementary coupling schemes, we accurately measure Raman resonances with and without contributions from motional sidebands. From the latter we obtain an axial sideband spectrum with an effective mode temperature of (3.1 $\pm$ 0.4)~mK. This results are a key step for quantum logic operations in Pennings traps, applicable to high precision matter-antimatter comparisons tests in the baryonic sector of the standard model.

Currently, the only worldwide source of low-energy antiprotons is the AD/ELENA facility located at CERN. To date, all precision measurements on single antiprotons have been conducted at this facility and provide stringent tests of the fundamental interactions and their symmetries. However, the magnetic field fluctuations from the facility operation limit the precision of upcoming measurements. To overcome this limitation, we have designed the transportable antiproton trap system BASE-STEP to relocate antiprotons to laboratories with a calm magnetic environment. We anticipate that the transportable antiproton trap will facilitate enhanced tests of CPT invariance with antiprotons, and provide new experimental possibilities of using transported antiprotons and other accelerator-produced exotic ions. We present here the technical design of the transportable trap system. This includes the transportable superconducting magnet, the cryogenic inlay consisting of the trap stack and the detection systems, and the differential pumping section to suppress the residual gas flow into the cryogenic trap chamber.

Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled $^9$Be$^+$ in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, established methods such as feedback-enhanced resistive cooling with image-current detectors are limited to about 1 K in 100 s. Since the studied techniques are applicable to any trapped charged particle and allow spatial separation between the target ion and the cooling species, they enable a variety of precision measurements based on trapped charged particles to be performed at improved sampling rates and with reduced systematic uncertainties.

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments, to high-precision metrology, and to quantum technology. Until now, sympathetic cooling has required close-range Coulomb interactions, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image-current interactions, it can be easily applied to an experiment with antiprotons, facilitating improved precision in matter-antimatter comparisons and dark matter searches.

The cyclotron frequency ratio of $^{187}\mathrm{Os}^{29+}$ to $^{187}\mathrm{Re}^{29+}$ ions was measured with the Penning-trap mass spectrometer PENTATRAP. The achieved result of $R=1.000\:000\:013\:882(5)$ is to date the most precise such measurement performed on ions. Furthermore, the total binding-energy difference of the 29 missing electrons in Re and Os was calculated by relativistic multiconfiguration methods, yielding the value of $ΔE = 53.5(10)$ eV. Finally, using the achieved results, the mass difference between neutral $^{187}$Re and $^{187}$Os, i.e., the $Q$ value of the $β^-$ decay of $^{187}$Re, is determined to be 2470.9(13) eV.

Current precision experiments with single (anti)protons to test CPT symmetry progress at a rapid pace, but are complicated by the need to cool particles to sub-thermal energies. We describe a cryogenic Penning-trap setup for $^9$Be$^+$ ions designed to allow coupling of single (anti)protons to laser-cooled atomic ions for sympathetic cooling and quantum logic spectroscopy. We report on trapping and laser cooling of clouds and single $^9$Be$^+$ ions. We discuss prospects for a microfabricated trap to allow coupling of single (anti)protons to laser-cooled $^9$Be$^+$ ions for sympathetic laser cooling to sub-mK temperatures on ms time scales.

We present methods to manipulate and detect the motional state and the spin state of a single antiproton or proton which are currently under development within the BASE (Baryon Antibaryon Symmetry Experiment) collaboration. These methods include sympathetic laser cooling of a single (anti-)proton using a co-trapped atomic ion as well as quantum logic spectroscopy with the two particles and could be implemented within the collaboration for state preparation and state readout in the antiproton $g$-factor measurement experiment at CERN. In our project, these techniques shall be applied using a single $^9\text{Be}^+$ ion as the atomic ion in a Penning trap system at a magnetic field of 5 T. As an intermediate step, a controlled interaction of two beryllium ions in a double-well potential as well as sympathetic cooling of one ion by the other shall be demonstrated.

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 $7.5(3.4)\times 10^{-20}\,\text{V}^{2}\text{m}^{-2} \text{Hz}^{-1}$, which corresponds to a scaled noise spectral density below $8.8(4.0)\times 10^{-12}\,\text{V}^{2}\text{m}^{-2}$, results which are more than two orders of magnitude smaller than those reported by other ion trap experiments.

We present an experiment to sympathetically cool protons and antiprotons in a Penning trap by resonantly coupling the particles to laser cooled beryllium ions using a common endcap technique. Our analysis shows that preparation of (anti)protons at mK temperatures on timescales of tens of seconds is feasible. Successful implementation of the technique will have immediate and significant impact on high-precision comparisons of the fundamental properties of protons and antiprotons. This in turn will provide some of the most stringent tests of the fundamental symmetries of the Standard Model.

The novel five-Penning trap mass spectrometer PENTATRAP is developed at the Max-Planck-Institut für Kernphysik (MPIK), Heidelberg. Ions of interest are long-lived highly charged nuclides up to bare uranium. PENTATRAP aims for an accuracy of a few parts in 10^12 for mass ratios of mass doublets. A physics program for PENTATRAP includes Q-values measurements of β-transitions relevant for neutrino physics, stringent tests of quantum electrodynamics in the regime of extreme electric fields, and a test of special relativity. Main features of PENTATRAP are an access to a source of highly charged ions, a multi-trap configuration, simultaneous measurements of frequencies, a continuous precise monitoring of magnetic field fluctuations, a fast exchange between different ions, and a highly sensitive cryogenic non-destructive detection system. This paper gives a motivation for the new mass spectrometer PENTATRAP, presents its experimental setup, and describes the present status.

A novel Penning trap tower consisting of five compensated cylindrical Penning traps is developed for the PENTATRAP mass spectrometer at the Max-Planck-Institut für Kernphysik in Heidelberg, Germany. An analytical expression for the electrostatic potential inside the trap tower is derived to calculate standard Penning trap properties like the compensation of anharmonicities and an orthogonal geometry of the trap electrodes. Since the PENTATRAP project described in the preceding article aims for ultra high-precision mass-ratio measurements of highly charged ions up to uranium, systematic effects for highly charged ions inside the trap tower are considered for the design process as well. Finally, a limit due to remaining anharmonic shifts at large amplitudes is estimated for the resulting geometry, which is important for phase-sensitive measurements of the reduced cyclotron frequency of the ions.