  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 5s 2S1/2, 5p 2P1/2, and 4d 2D3/2 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 ions and isotopes without
hyperfine structure.
