We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion inter
actions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4$^2$S$_{1/2} leftrightarrow $ 4$^2$P$_{1/2}$ transition of $^{40}$Ca$^+$, for which we find the value 2.8928(43) ea$_0$. Moreover, the method allows us to deduce the lifetime of the 4$^2$P$_{1/2}$ state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a longstanding discrepancy between calculated values and experimental results.
We present a detailed theoretical and experimental study on the optical control of a trapped-ion qubit subject to thermally induced fluctuations of the Rabi frequency. The coupling fluctuations are caused by thermal excitation on three harmonic oscil
lator modes. We develop an effective Maxwell-Boltzmann theory which leads to a replacement of several quantized oscillator modes by an effective continuous probability distribution function for the Rabi frequency. The model is experimentally verified for driving the quadrupole transition with resonant square pulses. This allows for the determination of the ion temperature with an accuracy of better than 2% of the temperature pertaining to the Doppler cooling limit TD over a range from 0.5TD to 5TD. The theory is then applied successfully to model experimental data for rapid adiabatic passage (RAP) pulses. We apply the model and the obtained experimental parameters to elu- cidate the robustness and efficiency of the RAP process by means of numerical simulations.
