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 20K 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.