K. Ott

We study the behavior of a single laser-driven trapped ion inside a microscopic optical Fabry-Perot cavity. In particular, we demonstrate a fiber Fabry-Perot cavity operating on the principal $S_{1/2}\to P_{1/2}$ electric dipole transition of an Yb$^+$ ion at $369\,$nm with an atom-ion coupling strength of $g=2π\times 67(1)\,$MHz. We employ the cavity to study the generation of single photons and observe cavity-induced back-action in the Purcell-enhanced emission of photons. Tuning of the amplitude and phase of the back-action allows us to enhance or suppress the total rate of photoemission from the ion-cavity system.

The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding of ions provided by laser addressing, it becomes possible to synthesize stripes of both triangular and Kagome lattices. Besides, the degree of frustration of the phonon-mediated spin interactions can be controlled by shaping the trap frequencies. We support our theoretical considerations by initial experiments with planar ion crystals, where a high and tunable anisotropy of the radial trap frequencies is demonstrated. We take into account an extensive list of possible error sources under typical experimental conditions, and describe explicit regimes that guarantee the validity of our scheme.