A two-dimensional four-beam annular accordion optical lattice for ultra-cold atoms

In his seminal 1976 paper\footnote{D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976).} ``Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,'' Hofstadter suggested that his intriguing fractal spectrum be tested experimentally by creating a lattice with a larger period than Nature provides us. In his words: ``This is not to say that the idea is easy; but such an intriguing spectrum deserves a good experimental test.'' To measure this spectrum we developed a technique for creating artificial magnetic fields for neutral atoms, and now are constructing a wide-range two-dimensional accordion optical lattice\footnote{L. Fallani et al., Opt. Express 13, 4303-4313 (2005).}$^,$\footnote{T.C. Li et al., Opt. Express 16, 5465-5470 (2008).}$^,$\footnote{R.A. Williams et al., Opt. Express 16, 16977-16983.} by steering four paraxial laser beams onto an atom cloud using a single large annular lens. In addition to eliminating spherical aberration, this novel design leaves the central solid angle surrounding the optical axis completely unobstructed for imaging and other purposes.