  Many ion species commonly used for laser-cooled ion trapping studies have a
low-lying metastable 2D3/2 state that can become populated due to spontaneous
emission from the 2P1/2 excited state. This requires a repumper laser to
maintain the ion in the Doppler cooling cycle. Typically the 2D3/2 state, or
some of its hyperfine components if the ion has nuclear spin, has a higher
multiplicity than the upper state of the repumping transition. This can lead to
dark states, which have to be destabilized by an external magnetic field or by
modulating the polarization of the repumper laser. We propose using
unpolarized, incoherent amplified spontaneous emission (ASE) to drive the
repumping transition. An ASE source offers several advantages compared to a
laser. It prevents the buildup of dark states without external polarization
modulation even in zero magnetic field, it can drive multiple hyperfine
transitions simultaneously, and it requires no frequency stabilization. These
features make it very compact and robust, which is essential for the
development of practical, transportable optical ion clocks. We construct a
theoretical model for the ASE radiation, including the possibility of the
source being partially polarized. Using 88Sr+ as an example, the performance of
the ASE source compared to a single-mode laser is analyzed by numerically
solving the eight-level density matrix equations for the involved energy
levels. Finally a reduced three-level system is derived, yielding a simple
formula for the excited state population and scattering rate, which can be used
to optimize the experimental parameters. The required ASE power spectral
density can be obtained with current technology.
