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.
The present paper describes the experimental implementation of a measuring technique employing a slowly moving, near resonant, optical standing wave in the context of trapped ions. It is used to measure several figures of merit that are important for
quantum computation in ion traps and which are otherwise not easily obtainable. Our technique is shown to offer high precision, and also in many cases using a much simpler setup than what is normally used. We demonstrate here measurements of i) the distance between two crystalline ions, ii) the Lamb-Dicke parameter, iii) temperature of the ion crystal, and iv) the interferometric stability of a Raman setup. The exact distance between two ions, in units of standing wave periods, is very important for motional entangling gates, and our method offers a practical way of calibrating this distance in the typical lab situation.
