Sebastian Wolf

Modification of spontaneous decay in space and time is a central topic of quantum physics. It has been predominantly investigated in the context of cavity quantum electrodynamics (QED), gaining new interest recently in the domain of nano-optics. Beyond cavity-QED, spontaneous emission may be modified also in free space due to correlations among the photon emitters, a phenomenon known as super- and sub-radiance. Correlations may stem either from direct interactions between the particles, from long-range exchange of photons, or by measuring single photons in a common mode. Yet, the genuine spatial spontaneous emission pattern of an atomic ensemble in an entangled quantum state has not been observed so far, due to the lack of ultra-fast cameras with high spatial resolution suited for recording single photons from single atoms. Preparing two trapped ions in free space in entangled Dicke states via photon detection, we study the resulting collective spontaneous emission patterns. Depending on the symmetry of the Dicke states, associated with the direction of detection of the first state-determining photon, we observe fundamentally different emission patterns for the subsequently scattered photon, including super- and sub-radiance. Our results demonstrate that the detection of a single photon can profoundly modify the collective emission of an atomic array, here represented by its most elementary building block of two atoms in free space.

We implement three-dimensional polarization gradient cooling of trapped ions. Counter-propagating laser beams near $393\,$nm impinge in lin$\,\perp\,$lin configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in $^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap frequency of $2π\times 285\,$kHz and $3.3(4)$ at $2π\times480\,$kHz, in the axial and radial directions, respectively. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number, and thus works well for an initial ion motion far out of the Lamb-Dicke regime, for up to four ions, and for a micromotion modulation index $β\leq 0.1$. Still, we find that the spectral impurity of the laser field influences both, cooling rates and cooling limits. Thus, a Fabry-Pérot cavity filter is employed for efficiently suppressing amplified spontaneous emission of the diode laser.

We demonstrate super-resolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a sub-diffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped $^{40}\mathrm{Ca}^+$ ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of $4.2(1)\,μ$m we reach a spatial resolution which allows us to determine a wave packet size of $39(9)\,$nm for a near ground state cooled ion. This value matches an independently deduced value of $32(2)\,$nm, calculated from resolved sideband spectroscopy measurements. Finally, we discuss the ultimate resolution limits of our adapted GSD imaging technique in view of applications to direct quantum wave packet imaging.

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency $f_\text{spatial}=1490 \pm 2_{stat.}\pm 8_{syst.}\,\text{rad}^{-1}$, where the statistical uncertainty improves with the integrated number of correlation events as $N^{-0.51\pm0.06}$. We independently determine the spatial frequency to be $1494\pm 11\,\text{rad}^{-1}$, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record the spatially resolved autocorrelation function $g^{(2)}(τ)$ with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, $g^{(2)}(0) = 0.60(5)$ and a maximum of $g^{(2)}(0)=1.46(8)$ for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model of heralded entangled states and the observed maximum and minimum values are modeled, taking independently measured experimental parameters into account.

We demonstrate the efficient generation of Be$^+$ ions with a 60 ns and 150 nJ laser pulse near 235 nm for two-step photo-ionization, proven by subsequent counting the number of ions loaded into a linear Paul trap. The bandwidth and power of the laser pulse are chosen in such a way that a first, resonant step fully saturates the entire velocity distribution of beryllium atoms effusing from a thermal oven. The second excitation step is driven by the same light field causing efficient non-resonant ionization. Our ion-loading scheme is more than 15 times more efficient as compared to former pathways using two-photon continuous wave laser excitation.

We realize a single particle microscope by using deterministically extracted laser cooled $^{40}$Ca$^+$ ions from a Paul trap as probe particles for transmission imaging. We demonstrate focusing of the ions with a resolution of 5.8$\;\pm\;$1.0$\,$nm and a minimum two-sample deviation of the beam position of 1.5$\,$nm in the focal plane. The deterministic source, even when used in combination with an imperfect detector, gives rise to much higher signal to noise ratios as compared with conventional Poissonian sources. Gating of the detector signal by the extraction event suppresses dark counts by 6 orders of magnitude. We implement a Bayes experimental design approach to microscopy in order to maximize the gain in spatial information. We demonstrate this method by determining the position of a 1$\,μ$m circular hole structure to an accuracy of 2.7$\,$nm using only 579 probe particles.

We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.

We experimentally demonstrate nanoscopic transmission microscopy relying on a deterministic single particle source. This increases the signal-to-noise ratio with respect to conventional microscopy methods, which employ Poissonian particle sources. We use laser-cooled ions extracted from a Paul trap, and demonstrate remote imaging of transmissive objects with a resolution of 8.6 $\pm$ 2.0nm and a minimum two-sample deviation of the beam position of 1.5nm. Detector dark counts can be suppressed by 6 orders of magnitudes through gating by the extraction event. The deterministic nature of our source enables an information-gain driven approach to imaging. We demonstrate this by performing efficient beam characterization based on a Bayes experiment design method.

We discuss an experimental approach allowing to prepare antihydrogen atoms for the GBAR experiment. We study the feasibility of all necessary experimental steps: The capture of incoming $\bar{\rm H}^+$ ions at keV energies in a deep linear RF trap, sympathetic cooling by laser cooled Be$^+$ ions, transfer to a miniaturized trap and Raman sideband cooling of an ion pair to the motional ground state, and further reducing the momentum of the wavepacket by adiabatic opening of the trap. For each step, we point out the experimental challenges and discuss the efficiency and characteristic times, showing that capture and cooling are possible within a few seconds.