Fabian Wolf

Today's most sensitive experiments for detecting CP-violating permanent electric dipole moments (EDM) rely on molecular spectroscopy. The high sensitivity arises from large internal electric fields that interact with the constituents of the molecule. For molecular ions it has long been assumed that experiments with static polarization from dc electric fields are infeasible, as the ion's charge would either shift it to a field free region or eject it from the trap. This constraint appears to make single ion quantum-logic clocks, among the most precise measurement devices available, incompatible with EDM measurements. Here, we demonstrate that, under typical trapping conditions, heavy molecular ions with small $Ω/Λ$-doubling can be polarized by a static electric field while remaining confined in the Paul trap. This effect arises from a cancellation between the electrostatic force and the trap's ponderomotive force, resulting in an equilibrium position where the ion experiences a dc electric field component. Dynamic decoupling allows to implement co-magnetometry schemes in a single molecule and provides long interrogation times. This will allow the operation of a quantum-logic molecular radio-frequency clock in static electric fields, providing sensitivity to EDMs. Working with only a few ions and non-destructive detection techniques opens the door to the use of highly sensitive, rare, and radioactive molecular species as well as quantum-enhanced metrology schemes to achieve unprecedented levels of accuracy and precision.

Extending quantum control to increasingly complex systems is crucial for both advancing quantum technologies and fundamental physics. In trapped ion systems, quantum logic techniques that combine a well-controlled logic species with a more complex spectroscopy species have proven to be a powerful tool for extending the range of accessible species. Here, we demonstrate that a quantum system as complex as $^{48}$Ti$^+$ with its many metastable states can be controlled employing a combination of intrinsic thermalization due to collisions with background gas and quantum-logic techniques using a far-detuned Raman laser. The preparation of pure quantum states allows coherent manipulation and high resolution measurements of the Zeeman structure in $^{48}$Ti$^+$. The presented techniques are applicable to a wide range of ionic species giving access to a larger variety of systems for fundamental physics and constitute the first step for quantum-controlled spectroscopy of transition metals, relevant, e.g., for the interpretation of astrophysical spectra.

The demand for efficient preparation methods for dual-species ion crystals is rapidly expanding across quantum technology and fundamental physics applications with trapped ions. We present a deterministic and efficient technique to produce such crystals, utilizing the segmented structure of a linear Paul trap. By precisely tailoring the trapping potentials, we can split, move, and discard parts of an ion chain. This process is automated in a sequence that converts a larger ion sample into the desired configuration. A critical component of our approach is the accurate identification of crystal constituents. This is achieved by matching the measured positions of fluorescing ions against theoretical expectations for larger crystals, thus facilitating the detection of non-fluorescing ions and enabling accurate ion counting. We demonstrate that our method reliably produces two-ion crystals within minutes. These results represent a significant advance in the production of two-species ion crystals with applications ranging from quantum logic spectroscopy and optical clocks to quantum computing and simulation with trapped ions.

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows to reference the polarizability transfer to hydrogen-like ions for which the polarizability can be calculated with high precision.

Precision spectroscopy has been the driving force for progress of our physical understanding and still is a promising tool for the investigation of new physics. Molecules offer transitions which allow tests that are not possible in atomic systems. However, usually precision spectroscopy of molecules is challenging due to the lack of cycling transitions for state preparation and state detection. For molecular ions, this obstacle can be overcome by quantum logic spectroscopy, where dissipation for state preparation and detection is provided by a co-trapped atomic ion exploiting the shared eigenstates of motion. Here, we propose a full quantum logic spectroscopy scheme for molecular oxygen ions and theoretically investigate the feasibility of quantum logic assisted state detection and preparation. Furthermore, we provide coupling rates for a direct single-photon quadrupole excitation of a vibrational overtone transition that can serve as a sensitive transition for tests of a possible variation of the proton-to-electron mass ratio.

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

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.

Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in $^{25}$Mg$^+$, implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal state the STIRAP population transfer is more efficient than a stimulated Raman Rabi pulse on a motional sideband. In contrast to previous implementations, a large detuning of more than 200 times the natural linewidth of the transition is used. This approach renders STIRAP suitable for atoms in which resonant laser fields would populate fluorescing excited states and thus impede the STIRAP process. We use the technique to measure the wavefunction overlap of excited motional states with the motional ground state. This is an important application for photon recoil spectroscopy and other force sensing applications that utilize the high sensitivity of the motional state of trapped ions to external fields. Furthermore, a determination of the ground state population enables a simple measurement of the ion's temperature.

Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric dipole moment of the electron. Optical clocks based on molecular ions sensitive to some of these effects are expected to achieve uncertainties approaching the $10^{-18}$ level. While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling, quantum state control, and detection. Previously employed state detection techniques based on photo-dissociation or chemical reactions are destructive and therefore inefficient. Here we experimentally demonstrate non-destructive state detection of a single trapped molecular ion through its strong Coulomb coupling to a well-controlled co-trapped atomic ion. An algorithm based on a state-dependent optical dipole force(ODF) changes the internal state of the atom conditioned on the internal state of the molecule. We show that individual states in the molecule can be distinguished by their coupling strength to the ODF and observe black-body radiation-induced quantum jumps between rotational states. Using the detuning dependence of the state detection signal, we implement a variant of quantum logic spectroscopy and improve upon a previous measurement of the $\mathrm{X}^1Σ^+(J=1)\rightarrow\mathrm{A}^1Σ^+(J=0)$ transition in MgH, finding a frequency of 1067.74752(53)THz. We estimate that non-destructive state detection with near 100% efficiency could take less than 10 ms. The technique we demonstrate is applicable to a wide range of molecular ions, enabling further applications in state-controlled quantum chemistry and spectroscopic investigations of molecules serving as probes for interstellar clouds.

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with non-closed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a co-trapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the $^{2}$D$_{3/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition in $^{40}$Ca$^{+}$, resulting in a transition frequency of $f=346\, 000\, 234\, 867(96)$ kHz. Furthermore, we determine the isotope shift of this transition and the $^{2}$S$_{1/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition for $^{42}$Ca$^{+}$, $^{44}$Ca$^{+}$ and $^{48}$Ca$^{+}$ ions relative to $^{40}$Ca$^{+}$ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.