Next: Effect of a realistic
Up: Trap properties
Previous: Depth, coherence time, and
Other properties
We estimate the collection area of the trap as the crosssectional region
within which the potential is deeper than the typical cesium
MOT energy
.
For our example 100K traps of Figure 8.3
this area is about
1m.
However, it is not possible to do much better than this with our design:
if
one tries to increase the area by increasing the overall trap depth,
the
contour touches the substrate, indicating that atoms at this energy
can reach the substrate surface, where they will stick,
limiting the effective collection area.
To investigate the lifetime of atoms transported incoherently (the
multimode regime), we can calculate the heating rate
along similar lines as Grimm and Weidemüller[85].
We start with their equation (23) which gives the rate of change of
the average of the total energy of atomic motion
as

(8.12) 
being the recoil temperature,
and use the assumption that in an equilibrated 3D trap
.
Since there is harmonic motion in two directions but free motion in the third,
the virial theorem gives us
.
Combining this with
from (8.8) gives the heating rate

(8.13) 
which is of the order of one recoil temperature per coherence time.
For our 100K depth trap at nm the rate is
4.4Ks,
implying that storage and transport for many seconds is possible.
For simplicity, we have ignored the fact that there
may be distinct longitudinal and transverse temperatures which do not
equilibrate over the trapping timescales.
Next: Effect of a realistic
Up: Trap properties
Previous: Depth, coherence time, and
Alex Barnett
20011003