Conclusion

We have presented a novel substrate-based neutral atom waveguide, based on the optical dipole force, which combines the features of a planar far-detuned two-color evanescent trap[156] with the ability to confine strongly along two axes. We utilized the differing vertical decay lengths of the two bound-mode polarizations of a submicron-sized optical waveguide near cut-off. We have shown that only a few milliwatts of guided laser power can create atomic potential depths $\sim 100\,\mu$K with transverse oscillation frequencies $\sim 100\,$kHz, a coherence time $\sim 10\,$ms and a trap minimum 200-400nm above the optical guide surface, for Cs atoms in the $m_F = 0$ state. Laser powers greater than ten milliwatts can give a transverse mode spacing greater than the temperature of a Cs MOT, opening up the single-mode waveguide regime. The advantages of guiding optical trapping fields on a substrate include mechanical stability and reliability, mass production and the potential for transport along complicated paths.

We have given some design criteria for guided-lightwave two-color atom waveguides (chiefly the maximization of the evanescent decay lengths, and of their normalized difference $\alpha_L$), and shown that a substrate of low refractive index can be very beneficial. We modelled in detail the trapping potentials for a general rectangular guide of index 1.56 above a unity-index substrate, and have shown that a realistic substrate choice of index 1.32 poses few problems to the viability of the device. We predict that the effect of the surface interaction is generally small, and that coherent guiding is possible around corners of radii $\sim 1\,$mm for a longitudinal velocity $\sim 1\,$ms$^{-1}$. We also believe that the magnetic part of the potential felt by nonzero $m_F$ atoms could be used to increase the depth and oscillation frequencies further.

This preliminary work (specifically equation (8.10)) indicates that utilizing detunings much larger than the 15nm we limit ouselves to here will be very advantageous for coherent guiding. We have only scratched the surface of the design variations possible; for instance, equalizing the horizontal and vertical oscillation frequencies is yet to be attempted. The use of two polarizations is our solution to the problem of maximizing $\alpha_L$ when the detuning is very small compared to the wavelength, but we suspect that there will exist other fruitful schemes where these are comparable ( $\Delta \sim \omega_0$, very far-detuning) and where a large $\alpha_L$ is caused simply by the different optical cut-off conditions at the two wavelengths. We have reserved investigation of cooling schemes for future work (although this has already been demonstrated in an EW mirror[61] and proposed in EW traps[157,62]). We believe that the potential shapes capable of being produced by guided waves on a substrate also include the possibility of funnel-type loading schemes and coherent atom couplers, allowing for a complete ``integrated'' atom-optical experiment on a substrate.