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 $W = 0.97 \,\lambda$ and $H = 0.25 \,\lambda$ from Section 8.2.2, and a substrate of unity index. The saturation intensity for cesium is 11.2W/m$^2$ [2], and its resonant wavelength of 852nm requires that the physical guide size is 0.83$\mu$m by 0.21$\mu$m. (At the end of the Section we present preliminary calculations for a $n_s = 1.32$ 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 $\Delta$ (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 $P_{\rm tot} \equiv P_{\rm red} + P_{\rm blue}$, and the power ratio $p \equiv P_{\rm red} / P_{\rm blue}$. The trap shape will be affected by $p$ alone: we show the trapping potential shapes achievable at the two practical extremes of $p=0.4$ and $p=0.2$ in Figure 8.3, where we have chosen $P_{\rm tot}$ and $\Delta$ to give identical trap depths and coherence times. Smaller $p$ 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 $y_0 = 0.52\,\lambda$ from the surface when $p=0.2$. The only disadvantage to implementing these smaller $p$ values is that a higher $P_{\rm tot}$ is required to achieve the same trap depth and coherence time (for instance a factor of 7.5 increase is required as we take $p$ 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 $P_{\rm tot} \sim (1+p)/p^{1 + 1/\alpha_L}$.

If we were purely interested in maximizing trap depth at a given $P_{\rm tot}$ and detuning, it would be best to make $p$ as large as possible, however if we take $p$ 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.