Gerd Leuchs

We report on the first feedback cooling of a single trapped ion below the Doppler limit of $\hbarΓ/2 k_\mathrm{B}$. The motion of a single ion is monitored in real-time and cooled up to 9-times below the Doppler cooling temperature by applying electronic feedback. Real-time motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. The method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence.

We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the anomalous heating rate. In contrast to other established schemes for measuring the heating rate, one does not have to switch off the cooling but the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an $^{174}\text{Yb}^{+}$ ion. In the derivation of the expected phase shifts we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling.

Focusing with a 4$π$ parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. To determine these errors, we experimentally examine the focusing properties of a 4$π$ parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single $^{174}$Yb$^{+}$ ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4$π$ parabolic mirror.

We demonstrate the controlled creation of a $\mathrm{^{174}Yb^{2+}}$ ion by photo-ionizing $\mathrm{^{174}Yb^+}$ with weak continuous-wave lasers at ultraviolet wavelengths. The photo-ionization is performed by resonantly exciting transitions of the $\mathrm{^{174}Yb^+}$ ion in three steps. Starting from an ion crystal of two laser-cooled $\mathrm{^{174}Yb^+}$ ions localized in a radio-frequency trap, the verification of the ionization process is performed by characterizing the properties of the resulting mixed-species ion-crystal. The obtained results facilitate fundamental studies of physics involving $\mathrm{Yb^{2+}}$ ions.

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially, superpositions of many coherent states are achieved at a fraction of the time necessary to produce the cat state.

Small, controllable, highly accessible quantum systems can serve as probes at the single quantum level to study multiple physical effects, for example in quantum optics or for electric and magnetic field sensing. The applicability of trapped atomic ions as probes is highly dependent on the measurement situation at hand and thus calls for specialized traps. Previous approaches for ion traps with enhanced optical access included traps consisting of a single ring electrode or two opposing endcap electrodes. Other possibilities are planar trap geometries, which have been investigated for Penning traps and rf-trap arrays. By not having the electrodes lie in a common plane the optical access in the latter cases can be substantially increased. Here, we discuss the fabrication and experimental characterization of a novel radio-frequency (rf) ion trap geometry. It has a relatively simple structure and provides largely unrestricted optical and physical access to the ion, of up to 96% of the total 4pi solid angle in one of the three traps tested. We also discuss potential applications in quantum optics and field sensing. As a force sensor, we estimate sensitivity to forces smaller than 1 yN Hz^(-1/2).