268 Ion traps
Fig. 12.4A string of calcium ions in a
linear Paul trap. The ions have an aver-
age separation of 10μm and the strong
fluorescence enables each ion to be de-
tected individually. The minimum size
of the image for each ion is determined
by the spatial resolution of the imaging
system. Courtesy of Professor Andrew
Steane and co-workers, Physics depart-
ment, University of Oxford.
Fig. 12.5The fluorescence signal from
a single calcium ion undergoing quan-
tum jumps. The ion gives a strong sig-
nal when it is in the ground state and
it is ‘dark’ while the ion is shelved in
the long-lived metastable state. Data
courtesy of Professors Andrew Steane
and Derek Stacey, David Lucas and co-
workers, Physics department, Univer-
sity of Oxford.
δ=−Γ/2andI=2Isat,sothatRscattΓ
4
4 × 107 photon s−^1. (12.21)In a typical experiment the lens that images the fluorescence onto the
detector has anf-number (ratio of focal length to diameter) of about 2,
so it collects 1.6% of the total number of fluorescence photons (the solid
angle subtended over 4π). A reasonable detector could have an efficiency
of 20%, giving an experimental signal ofS=0. 016 × 0. 2 ×Rscatt=
105 photon s−^1 that can easily be measured on a photomultiplier as in
Fig. 12.5. (The signal is lower than the estimate because fluorescent
photons are lost by reflection at the surfaces of optical elements, e.g.
windows or lenses.)
Laser cooling on a strong transition reduces the ion’s energy to the
Doppler cooling limitΓ/2. In a trap with a spacing ofωtrapbetween
vibrational energy levels, the ions occupy about∼Γ/ωtrapvibrational
levels; typically this corresponds to many levels. The minimum energy
occurs when the ions reside in the lowest quantum level of the oscillator
where they have just the zero-point energy of the quantum harmonic
oscillator. To reach this fundamental limit experiments use more so-
phisticated techniques that drive transitions with narrow line widths, as
described in Section 12.9.