  Efficient preparation and detection of the motional state of trapped ions is
important in many experiments ranging from quantum computation to precision
spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP)
technique for the manipulation of motional states in a trapped ion system. The
presented technique uses a Raman coupling between two hyperfine ground states
in $^{25}$Mg$^+$, implemented with delayed pulses, which removes a single
phonon independent of the initial motional state. We show that for a thermal
state the STIRAP population transfer is more efficient than a stimulated Raman
Rabi pulse on a motional sideband. In contrast to previous implementations, a
large detuning of more than 200 times the natural linewidth of the transition
is used. This approach renders STIRAP suitable for atoms in which resonant
laser fields would populate fluorescing excited states and thus impede the
STIRAP process. We use the technique to measure the wavefunction overlap of
excited motional states with the motional ground state. This is an important
application for photon recoil spectroscopy and other force sensing applications
that utilize the high sensitivity of the motional state of trapped ions to
external fields. Furthermore, a determination of the ground state population
enables a simple measurement of the ion's temperature.
