Chapter 8: Waveguides for neutral atoms using evanescent light fields

The fourth and final part is a self-contained proposal for a new design of coherent atom waveguide, using the forces exerted on atoms by near-resonant laser fields. As an independent project, it does not connect directly with other theoretical work in this thesis. However it shares many common themes: the motion of atoms in the trapping potential is a 2D quantum bound mode problem (in a smooth potential), and the optical waveguide bound mode calculation is also similar to this same problem (dielectric constant playing the role of a negative potential). Because the optical `potential' is not hard-walled, and because the fields are vector rather than scalar, the efficient methods of Chapter 5 or 6 do not apply; rather Finite Elements[56] will be used.

There has been much recent progress in the trapping and cooling of neutral atoms, opening up new areas of ultra-low energy and matter-wave physics [45,51,159]. Waveguides for such atoms are of great interest for atom optics, atom interferometery, and atom lithography. Multimode atom waveguides act as incoherent atom pipes that could trap atoms, transport them along complicated paths or between different environments, or deliver highly localized atom beams to a surface. Single-mode waveguides (or multimode guides populated only by atoms in the transverse ground-state) could be used for coherent atom optics and interferometry [151,2], as well as a tool for one-dimensional physics such as boson-fermion duality [190,152,44] and low-dimensional Bose-Einstein condensation effects [115].

In Chapter 8 we propose a dipole-force linear waveguide which confines neutral atoms up to $\lambda/2$ above a microfabricated single-mode dielectric optical guide. The optical guide carries far blue-detuned light in the horizontally-polarized TE mode and far red-detuned light in the vertically-polarized TM mode, with both modes close to optical cut-off. A trapping minimum in the transverse plane is formed above the optical guide due to the differing evanescent decay lengths of the two modes. This design allows manufacture of mechanically stable atom-optical elements on a substrate.

We find that a rectangular optical guide of 0.8$\mu$m by 0.2$\mu$m carrying 6mW of total laser power (detuning $\pm$15nm about the D2 line) gives a trap depth of 200$\mu$K for cesium atoms ($m_F = 0$), transverse oscillation frequencies of $f_x = 40$kHz and $f_y = 160$kHz, collection area $\sim 1\,\mu$m$^{2}$ and coherence time of 9ms. The laser powers required are orders of magnitude less than those commonly needed for dipole traps. The large tranverse frequencies achieved allow the possibility of atomic single-mode occupation (hence coherent guiding) when fed from a source at cesium MOT temperature ( $\approx 3\mu K$). We present design equations allowing optimal parameter choices to be made. We also discuss the effects of non-zero $m_F$, the D1 line, surface interactions, heating rate, the substrate refractive index $n_s$, and the limits on waveguide bending radius. It emerges that lowering $n_s$ is the main goal if large trap depths are desired of order an optical wavelength from the guide surface.

As known in the engineering community, the optical bound mode problem is notoriously hard [56]. We calculate the full vector bound modes for an arbitrary guide shape using two-dimensional non-uniform finite elements in the frequency-domain, allowing us to optimize atom waveguide properties. We chose rectangular guide cross-sections for this optimization, for simplicity. There are many other shapes possible; the fabrication technique will be the determining factor on what is practical.

This work on atom waveguides, an admittedly far-fetched topic for a student of Rick Heller, was in fact a collaboration with the following members of the Prentiss Group: Steve Smith (my principal collaborator), Maxim Olshanii, Kent Johnson, Allan Adams (who introduced me to the problem), and Mara Prentiss. I also benefitted from discussions with Joseph Thywissen and Yilong Lu.