Trap properties

In the bulk of this Section we will examine the atomic waveguide properties for light nearly resonant with the D2 line of cesium, using an optical guide of index 1.56 of the dimensions and from Section 8.2.2, and a substrate of unity index. The saturation intensity for cesium is 11.2W/m [2], and its resonant wavelength of 852nm requires that the physical guide size is 0.83m by 0.21m. (At the end of the Section we present preliminary calculations for a substrate and a different guide, and discuss how the atom waveguide properties are changed).

Given the guide, we are free to choose three experimental parameters, namely
the optical powers carried in the two modes,
and the detuning (assumed to be
symmetric, that is, to be of equal magnitude for red and blue beams,
because little advantage can be gained with an unsymmetric detuning).
The first two of these can usefully be reexpressed as total power
, and the power ratio
.
The trap shape will be affected by alone: we show
the trapping potential shapes achievable at the two practical extremes of
and
in Figure 8.3, where we have chosen
and to give
identical trap depths and coherence times.
Smaller values cause the trap minimum to move further from the surface
(a distinct advantage),
to be less ``bean'' shaped (*i.e.* to have smaller cubic deviations from
a 2D harmonic oscillator), and to cause a slight increase in collection area.
It is possible to achieve a trap minimum as distant as
from the
surface when .
The only disadvantage to implementing these smaller values is that a higher
is required to achieve the same trap depth and
coherence time (for instance a factor of 7.5 increase is required as we take
from 0.4 to 0.2).
This can be quantified within the exponential approximation,
and it can be found that the
total power required to maintain a given depth and coherence time with a fixed
trap geometry scales as
.

If we were purely interested in maximizing trap depth at a given and detuning, it would be best to make as large as possible, however if we take much larger than 0.4 the trap is brought so close that the corners of the ``bean'' shape touch the dielectric surface (see Figure 8.3, upper plot) and we will lose effective collection area due to sticking of atoms onto this surface.