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We present a detailed theoretical and experimental study on the opticalcontrol of a trapped-ion qubit subject to thermally induced fluctuations of theRabi frequency. The coupling fluctuations are caused by thermal excitation onthree harmonic oscillator modes. We develop an effective Maxwell-Boltzmanntheory which leads to a replacement of several quantized oscillator modes by aneffective continuous probability distribution function for the Rabi frequency.The model is experimentally verified for driving the quadrupole transition withresonant square pulses. This allows for the determination of the iontemperature with an accuracy of better than 2% of the temperature pertaining tothe Doppler cooling limit TD over a range from 0.5TD to 5TD. The theory is thenapplied successfully to model experimental data for rapid adiabatic passage(RAP) pulses. We apply the model and the obtained experimental parameters toelu- cidate the robustness and efficiency of the RAP process by means ofnumerical simulations.

Interaction of a Laser with a Qubit in Thermal Motion and its Application to Robust and Efficient Readout