We report the first observation of Bragg scattering from atomic ions confined in an electromagnetic trap. The results reveal long-range order and give evidence for bulk behavior in a strongly coupled collection of laser-cooled
9Be+ ions in a Penning trap. Long-range order emerges in approximately spherical clouds with as few as 5 \ifmmode\times\else\texttimes\fi{}
104 ions (cloud radius ${r}_{0}\ensuremath{\approx}37a$ where $a\ensuremath{\equiv}\mathrm{W}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{r}\ensuremath{-}\mathrm{S}\mathrm{e}\mathrm{i}\mathrm{t}\mathrm{z}\phantom{\rule{0ex}{0ex}}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}$). Bulk behavior is evident with 2.7 \ifmmode\times\else\texttimes\fi{}
105 trapped ions (${r}_{0}\ensuremath{\approx}65a$), with Bragg scattering patterns characteristic of a body-centered cubic lattice.
In this work, laser-cooled ion crystals containing 1000 to 100000 singly charged magnesium ions (Mg+) were prepared in a Penning trap. The properties of the ion crystals and their structure displaying long-range ordering were analyzed by various non-destructive techniques. After creation of the Mg + ions in the form of ion bunches in an external source, the ions were injected into the Penning trap where their temperature was reduced by eight orders of magnitude within seconds using a combination of buffer gas cooling and Doppler laser cooling. The achieved temperatures in the millikelvin-regime were close to the theoretical Doppler-cooling limit and sufficiently low to induce the transition to a crystal phase exhibiting long-range ordering. The structure of these mesoscopic ion crystals is in agreement with a model describing the crystal as a set of planar shells. This allows for a derivation of properties such as the charge density or the temperature of the observed crystals. For the process of combined buffer-gas and Doppler laser cooling an analytical model has been developed, which explains the time development of the temperature and the fluorescence signal in agreement with the experimental results.
We outline the theory of a practical Bragg scattering technique for studying the long-range spatial order of atoms localized in one-dimensional optical lattices and we demonstrate the technique using and F = 1 → 1 transitions with lin ⊤ lin laser cooling fields. The latter transition gives a dark optical lattice. We show that the scattering by a spin grating, which may also be present, can be completely or partially filtered out by varying the polarizations of the cooling fields while holding the polarization of the probe and the detector analyser fixed. This allows the fraction of atoms that are localized to be measured. The probe field is treated as a pulse and so the technique also allows time-resolved details of the spatial structure to be studied.