Precision spectroscopy with 40 Ca + ions in a Paul trap

This thesis reports on experiments with trapped 40Ca+ ions related to the field of precision spectroscopy and quantum information processing. For the absolute frequency measurement of the 4s S1/2 − 3d D5/2 clock transition of a single, laser-cooled 40Ca+ ion, an optical frequency comb was referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and the frequency of an ultra-stable laser exciting this transition was measured with a statistical uncertainty of 0.5 Hz. The correction for systematic shifts of 2.4(0.9) Hz including the uncertainty in the realization of the SI second yields an absolute transition frequency of νCa+ = 411 042 129 776 393.2(1.0) Hz. This is the first report on a ion transition frequency measurement employing Ramsey’s method of separated fields at the 10−15 level. Furthermore, an analysis of the spectroscopic data obtained the Landé g-factor of the 3d D5/2 level as g5/2=1.2003340(3). The main research field of our group is quantum information processing, therefore it is obvious to use the tools and techniques related to this topic like generating multi-particle entanglement or processing quantum information in decoherence-free sub-spaces and apply them to high-resolution spectroscopy. As a first realization, the quadrupole moment θ(3d, 5/2) of the 40Ca+ 3d D5/2 state was measured with especially designed states that are sensitive to electric field gradients but insensitive to the linear Zeeman effect and related noise. Measurements with Ramsey-type experiments could be performed at the subHertz level despite the presence of strong technical noise, yielding θ(3d, 5/2) =1.82(1) ea0. In addition, the measurement technique was also used in preliminary experiments to determine the linewidth of the narrowband interrogation laser. While entanglement leads to enhanced signal-to-noise ratios, it is not an essential ingredient for this kind of method. The measurement result obtained with classically correlated but un-entangled states confirms the measured value previously obtained with maximally entangled states. This might be interesting for experiments suffering from short singleatom coherences where experiments with correlated atoms could substantially enhance the coherence time and thus allow for precision spectroscopy with high resolution.

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