The EW trap has the benefit of creating high field gradients near a surface, but along with this comes the disadvantage that interactions with that surface that can alter the trap potential and even cause heating and loss of trapped atoms.
An atom's change in potential near a surface is
known as the van der Waals interaction () or the Casimir
interaction (
), depending on the distance
from the surface
compared to
, the dominant wavelength responsible for the
polarizability of the atom (in our case of Cs this is the D line resonance,
the same as our trapping resonance).
There is a smooth
cross-over from van der Waals (
, which can be viewed
as the atom's electrostatic interaction with the
image of its own fluctuating dipole) to Casimir (
,
which can be viewed as a retarded van der Waals attraction
or equally well as an atomic level
shift due to a cavity QED effect) at
[96].
In the case of a perfect mirror surface, the full form is known for any
,
but for a dielectric surface, the expression becomes much more
complicated to evaluate[184].
Since our trapping distances are larger than this cross-over point, we will use
the Casimir form, which is correct for asymptotically large , and
is always an overestimate of the true potential[96].
The dependence of the coefficient with dielectric constant is complicated
[68,207], but
we will use the simpler approximate
form given by Spruch and Tikochinsky[184], to give
Figure 8.1b shows the effect
of this potential on a
typical trap of depth 150K and distance
nm.
It is clear that the change is negligible further than 100nm from the
surface,
and a WKB
tunneling calculation along this straight-line path (at
) shows that
even if all atoms that reach the surface stick, the loss rate from the
first few transverse modes is entirely negligible.
However, care should be taken with the multi-mode regime, or in the case of
high-
traps, since the tunneling via the
corners of the ``bean'' shape may dominate for
(Figure 8.3).
The issue of energy transfer to trapped atoms due to a finite (and possibly room) temperature nearby surface is far less well understood, and may be a problem with many surface-based particle traps, as discussed by Henkel and Wilkens [92]. However, since we are trapping neutral particles and the conductivity of our surface is low, we expect a decoherence rate negligible compared to that already present from spontaneous absorption and emission cycles.