Dark-state suppression and optimization of laser cooling and fluorescence in a trapped alkaline-earth-metal single ion

We study the formation and destabilization of dark states in a single trapped ⁸⁸Sr⁺ ion caused by the cooling and repumping laser fields required for Doppler cooling and fluorescence detection of the ion. By numerically solving the time-dependent density matrix equations for the eight-level system consisting of the sublevels of the 5s0.16em0ex²-0.16em0exS1/2, 5p0.16em0ex²-0.16em0exP1/2, and 4d0.16em0ex²-0.16em0exD3/2 states, we analyze the different types of dark states and how to prevent them in order to maximize the scattering rate, which is crucial for both the cooling and the detection of the ion. The influence of the laser linewidths and ion motion on the scattering rate and the dark resonances is studied. The calculations are then compared with experimental results obtained with an endcap ion trap system located at the National Research Council of Canada and found to be in good agreement. The results are applicable also to other alkaline-earth-metal ions and isotopes without hyperfine structure.