Applied Physics B manuscript No. (will be inserted by the editor) Atomic Nanofabrication with Complex Light Fields M. M¨ utzel 1 , U. Rasbach 1 , and D. Meschede 1 , C. Burstedde 2 , J. Braun 2 , and A. Kunoth 2 , K. Peithmann 3 , and K. Buse 3 1 Institut f¨ ur Angewandte Physik, Universit¨at Bonn, Wegelerstr. 8, D-53115 Bonn, Germany 2 Institut f¨ ur Angewandte Mathematik, Universit¨at Bonn, Wegelerstr. 6, D-53115 Bonn, Germany 3 Physikalisches Institut, Universit¨at Bonn, Wegelerstr. 8, D-53115 Bonn, Germany Received: date / Revised version: date Abstract The method of neutral atom lithography al- lows to transfer a 2D intensity modulation of an atomic beam imposed by an inhomogeneous light field to a sub- strate. The complexity of the pattern depends on the properties of the light field constructed from the super- position of multiple laser beams. For the design of suit- able light fields we present a mathematical model with a corresponding numerical simulation of the so called inverse problem. Furthermore, details of an experiment carried out with a holographically reconstructed light field are discussed. PACS: 02.60.Pn, 42.40.My, 42.40.Pa, 42.50.Vk MSC 2000: 65T50, 81V80 1 Introduction Laser cooling [1] and atom optics [2] have opened the route to manipulate atomic motion at the nanometer scale. In atomic nanofabrication (ANF) [3] optical dipole forces are used to steer an atomic beam into a pattern with sub-micrometer resolution. In this method, the in- homogeneous intensity distribution of the light field acts as an immaterial light mask. On impact, the atoms are either accumulated to directly grow a 2D structure (the so called direct deposition, or DD), or they modify a resist covered surface (the so called neutral atom lithog- raphy, or NAL) which is then prepared by chemical pro- cessing steps. In the first experiments by Timp et al. [4] and McClelland et al. [5] simple but extended and pre- cise arrays of lines were formed in a single step DD pro- cess. The pattern represented a one to one image of the laser interference pattern created immediately above the surface. In order to create more sophisticated 2D structures several light beams were superposed with beamsplitters and mirrors, cf. [6,7]. This arrangement however be- comes rapidly clumsy if more than 2 or 3 light beams are required. We have thus prepared and applied a hologram which is capable of simultaneously diffracting an incom- ing laser beam into multiple beams which may be very narrowly spaced [8]. Fig. 1 shows the resulting atom pat- tern. In principle this technique allows to generate any interference pattern which is consistent with Maxwell’s equations. 12μm Fig. 1 Atom nanofabrication with neutral atom lithography (from [8]). One essential aspect of image formation is the pat- terning contrast. Here we use a transfer function ap- proach to obtain a simple estimate of contrast to be expected by 1D and 2D focussing of atoms with light masks. Next, a mathematical model for the design of light fields generating the nanoscale light mask is intro- duced. Based on this model, numerical forward calcu- lations indicate what types of light intensity patterns are to be expected, if the directions of the beams and their amplitudes are known. We further investigate the solution of the inverse problem which serves as a basis for numerical backward simulations. Here the task is to (approximately) reconstruct from a given pattern the re- quired directions of the laser beams and their expansion coefficients. In this paper we specialize on a fixed set of beam directions. From a mathematical point of view,