Gaëtan Hagel

We propose a joint experimental and theoretical approach to measure the self-diffusion in a laser-cooled trapped ion cloud where part of the ions are shelved in a long-lived dark state. The role of the self-diffusion coefficient in the spatial organisation of the ions is deciphered, following from the good agreement between the experimental observations and the theoretical predictions. This comparison furthermore allows to deduce the temperature of the sample. Protocols to measure the self-diffusion coefficient are discussed, in regard with the control that can be reached on the relevant time scales through the dressing of the atomic levels by laser fields.

A novel protocol of interrogation based on coherent population trapping in an N-level scheme atomic system leads to dark resonances involving three different photons. An ensemble of several hundreds of radiofrequency-trapped ions is probed by three lasers simultaneously locked onto the same optical frequency comb, resulting in high-contrast spectral lines referenced to an atomic transition in the THz domain. We discuss the cause of uncertainties and limitations for this method and show that reaching a sub-kHz resolution is experimentally accessible via this interrogation protocole.

The interrogation of an ultra-narrow clock transition of a single trapped ion for optical frequency metrology requires a laser stabilized to a couple of Hz per second with a linewidth of the same order of magnitude. Today, lasers in the visible have reached the Hz-range in frequency stability, if locked onto a high-finesse, ultra-stable reference cavity. Vertical mounting of the reference cavity can reduce its sensitivity to vibrations as described in \cite{notcutt05}. We have designed a comparable vertical cavity with an overall length of 150 mm resulting in a Free Spectral Range of 1GHz. Optimisation of the cavity design has been carried out with a Finite-Elements Method, leading to expected relative length variations below 10$^{-14}$ under the influence of gravity acceleration (1 $g$). The variation of different geometric parameters has been studied. The analysis of the different noise sources shows that, for a regime superior to a tenth of a hertz, the fast linewidth of the laser will not be limited by the cavity characteristics.

A recent evaluation of the frequency uncertainty expected for an optical frequency standard based on a single trapped $^{43}$Ca$^+$ ion was published in Phys. Rev. A {\bf 72} (2005) 043404. The paper contains some interesting information like systematic frequency shifts but fails to depict their uncertainty, leading to confuse accuracy and precision. The conclusions about the major contribution to the frequency shift are not consistent with the presented calculations and omit comparisons with data published previously.

The lifetime of the 3d^2D_5/2-level in singly-ionized calcium has been measured by the electron-shelving technique on different samples of rf trapped ions. The metastable state has been directly populated by exciting the dipole-forbidden 4S_1/2 - 3D_5/2 transition. In ion clouds, the natural lifetime of this metastable level has been measured to be (1095+-27) ms. For the single-ion case, we determined a lifetime of (1152+-20) ms. The 1sigma-error bars at the 2%-level have different origins for the two kinds of experiments: data fitting methods for lifetime measurements in an ion cloud and control of experimental parameters for a single ion. De-shelving effects are extensively discussed. The influence of differing approaches for the processing of the single-ion quantum jump data on the lifetime values is shown. Comparison with recent measurements shows excellent agreement when evaluated from a given method.