  We present experimental results on adiabatic cooling of a single 40Ca+ ion in
a linear radiofrequency trap. After a period of laser cooling, the secular
frequency along the rf-field-free axis is adiabatically lowered by nearly a
factor of eight from 583 kHz to 75 kHz. For an ion originally Doppler laser
cooled to a temperature of 0.65 +/- 0.03 mK, a temperature of 87 +/- 7 \mu K is
measured after the adiabatic expansion. Applying the same adiabatic cooling
procedure to a single sideband cooled ion in the ground state (P0 = 0.978 +/-
0.002) resulted in a final ground state occupation of 0.947 +/- 0.005. Both
results are in excellent agreement with an essentially fully adiabatic
behavior. The results have a wide range of perspectives within such diverse
fields as ion based quantum information science, high resolution molecular ion
spectroscopy and ion chemistry at ultra-low temperatures.
