Romain Dubessy

Advanced data analysis techniques have proved to be crucial for extracting information from noisy images. Here we show that principal component analysis can be successfully applied to ultracold gases to unveil their collective excitations. By analyzing the correlations in a series of images we are able to identify the collective modes which are excited, determine their population, image their eigenfunction, and measure their frequency. Our method allows to discriminate the relevant modes from other noise components and is robust with respect to the data sampling procedure. It can be extended to other dynamical systems including cavity polariton quantum gases or trapped ions.

We measured by laser spectroscopy the isotope shifts between naturally-occurring even-isotopes of strontium ions for both the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ (violet) and the $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing $10^3$--$10^4$ laser-cooled Sr$^+$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-level atom in interaction with two laser beams. This technique allowed us to increase the precision with respect to previously reported data obtained by optogalvanic spectroscopy or fast atomic-beam techniques. The results for the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ transition are $ν_{88}-ν_{84}=+378(4)$ MHz and $ν_{88}-ν_{86}=+170(3)$ MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ transition we find $ν_{88}-ν_{84}=-828(4)$ MHz and $ν_{88}-ν_{86}=-402(2)$ MHz. These results provide more data for stringent tests of theoretical calculations of the isotope shifts of alkali-metal-like atoms. Moreover, they simplify the identification and the addressing of Sr$^+$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.

We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on two-ion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows that the distribution rate of entanglement achievable with such an ion-based quantum repeater protocol is higher by orders of magnitude than the rates that are achievable with the best known schemes based on atomic ensemble memories and linear optics. The main reason is that for trapped ions the entanglement swapping operations are performed deterministically, in contrast to success probabilities below 50 percent per swapping with linear optics. The scheme requires efficient collection of the emitted photons, which can be achieved with cavities, and efficient conversion of their wavelength, which can be done via stimulated parametric down-conversion. We also suggest how to realize temporal multiplexing, which offers additional significant speed-ups in entanglement distribution, with trapped ions.

We present a model for the scaling laws of the electric field noise spectral density as a function of the distance, $d$, above a conducting surface. Our analytical approach models the patch potentials by introducing a correlation length, $ζ$, of the electric potential on the surface. The predicted scaling laws are in excellent agreement with two different classes of experiments (cold trapped ions and cantilevers), that span at least four orders of magnitude of $d$. According to this model, heating rate in miniature ion traps could be greatly reduced by proper material engineering.

This paper reports on photoionisation loading based on ultrafast pulses of singly-ionised strontium ions in a linear Paul trap. We take advantage of an autoionising resonance of Sr neutral atoms to form Sr+ by two-photon absorption of femtosecond pulses at a wavelength of 431nm. We compare this technique to electron-bombardment ionisation and observe several advantages of photoionisation. It actually allows the loading of a pure Sr+ ion cloud in a low radio-frequency voltage amplitude regime. In these conditions up to 4x10^4 laser-cooled Sr+ ions were trapped.