For coherent guiding, we can define a more physically meaningful
figure of merit,
, which tells us the typical number of
coherent transverse oscillations we can expect multiplied by
(i.e. it is the Q-factor of the transverse oscillations).
We should choose
since this is
the smaller of the transverse frequencies in our case.
For
the transverse atomic modes will be well resolved, and our guide
can be a useful interferometric device.
Using (8.10), in conjunction with the
fact that when the trapping potential shape is fixed then
is proportional to the square root of the depth,
tells us that for a given trap and detuning,
.
For a higher
we should choose smaller transverse oscillation frequencies,
that is, shallower traps.
For example, the 2mK trap discussed above has
, but
if we reduce it to a 20
K trap of the same
(by changing
or
the laser powers), the
is 10 times larger.
Increasing
would allow even higher
to be realized.
The dependence on detuning in (8.11)
is another way of
expressing the advantages already known about using far off-resonant
beams[2,85].
However, our single-resonance approximation will break down if the
detuning is too large: we have (somewhat arbitrarily) chosen
a detuning limit of 15nm, as compared to
nm
for cesium.
At this limit, the additional dipole potential created due to the
detunings from the D1 line is very significant.
However, by removing the detuning symmetry
(changing
from +15nm to +12.07nm and
from -15nm to -17.14nm), the desired
D2 single-resonance approximation
potential is recovered in the true physical situation of both resonances
present.
(These required shifts, which are of order
, can
easily be found using the expression for the sum of dipole potentials
from the two lines.)
An additional necessity for our limit is the fact that any larger detunings
start to demand separate bound-mode calculations for the two colors, a
treatment we reserve for the future.
This detuning limit in turn limits the depths,
coherence times and Q-factors we quote here,
but
we anticipate similar
future EW atom waveguide designs which explore the region
(or even
),
and achieve much better coherence.