Marius Schulte

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.

We discuss quantum variational optimization of Ramsey interferometry with ensembles of $N$ entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean square error of the estimated phase for a given prior distribution, i.e. we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.

We demonstrate the experimental realization of a two-qubit Mølmer-Sørensen gate on a magnetic field-insensitive hyperfine transition in $^9$Be$^+$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm1.2\,\%$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer.

In photon recoil spectroscopy, signals are extracted from recoils imparted by the spectroscopy light on the motion of trapped ions as demonstrated by C. Hempel et al., Nature Photonics 7, 630 (2013) and Y. Wan et al., Nature Communications 5, 3096 (2014). The method exploits the exquisite efficiency in the detection of phonons achievable in ion crystals, and is thus particularly suitable for species with broad non-cycling transitions where detection of fluorescence photons is impractical. Here, we develop a theoretical model for the description of photon recoil spectroscopy based on a Fokker-Planck equation for the Wigner function of the phonon mode. Our model correctly explains systematic shifts due to Doppler heating and cooling as observed in the experiment. Furthermore, we investigate quantum metrological schemes for enhancing the spectroscopic sensitivity based on the preparation and detection of nonclassical states of the phonon mode.

Non-vanishing fluctuations of the vacuum state are a salient feature of quantum theory. These fluctuations fundamentally limit the precision of quantum sensors. Nowadays, several systems such as optical clocks, gravitational wave detectors, matter-wave interferometers, magnetometers, and optomechanical systems approach measurement sensitivities where the effect of quantum fluctuations sets a fundamental limit, the so-called standard quantum limit (SQL). It has been proposed that the SQL can be overcome by squeezing the vacuum fluctuations. Realizations of this scheme have been demonstrated in various systems. However, protocols based on squeezed vacuum crucially rely on precise control of the relative orientation of the squeezing with respect to the operation imprinting the measured quantity. Lack of control can lead to an amplification of noise and reduces the sensitivity of the device. Here, we experimentally demonstrate a novel quantum metrological paradigm based on phase insensitive Fock states of the motional state of a trapped ion, with applications in frequency metrology and displacement detection. The measurement apparatus is used in two different experimental settings probing non-commuting observables with sensitivities beyond the SQL. In both measurements, classical preparation and detection noise are sufficiently small to preserve the quantum gain in a full metrological protocol.

Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. We show that the readout algorithm can be implemented with a single application of a multi-species quantum gate, which we describe in detail for a crystal of Aluminum and Calcium ions.