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Journal of Experimental and Theoretical Physics

Dissipative light mask generated by a nonuniformly polarized field for atomic lithography

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Jun 1, 2007• 13 citations
Publisher

Abstract

The localization of atoms in a deep optical potential is analyzed in the framework of the completely quantum description of the motion of the atoms using the kinetic equation for the density matrix. It is shown that the laser cooling of the neutral atoms in the deep optical potential at a relatively large detuning of the light field from resonance can be used as a method for forming spatially localized atomic structures with a high contrast for atomic lithography. This method is alternative to nondissipative light masks.

DOI
10.1134/s1063776107060015

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The localization of atoms in a deep optical potential is analyzed in the framework of the completely quantum description of the motion of the atoms using the kinetic equation for the density matrix. It is shown that the laser cooling of the neutral atoms in the deep optical potential at a relatively large detuning of the light field from resonance can be used as a method for forming spatially localized atomic structures with a high contrast for atomic lithography. This method is alternative to nondissipative light masks.
Generally, conditions for deep sub-Doppler laser cooling do not match conditions for strong atomic localization, that takes place in a deeper optical potential and leads to higher temperature. Moreover, for a given detuning in a deep optical potential the secular approximation, which is frequently used for a quantum description of laser cooling, fails. Here we investigate the atomic localization in optical potential, using a full quantum approach for atomic density matrix beyond the secular approximation. It is shown that laser cooling in a deep optical potential, created by a light field with polarization gradients, can be used as an alternative method for the formation of high contrast spatially localized structures of atoms for the purposes of atom lithography and atomic nanofabrication. Finally, we analyze possible limits for the width and contrast of localized atomic structures that can be reached in this type of light mask.
An analysis of general characteristics of light-induced forces is presented for arbitrary monochromatic masks in which optical pumping of atoms and spontaneous emission play an important role. Dependence of regions of localization on detuning and ellipticity is determined for cyclic transitions of two types: J å J with half-integer J and J å J + 1 with arbitrary J . Numerical simulations of atomic beam focusing with one-and two-dimensional light masks show that spatial atom distributions with narrow features and high contrast can be formed in dissipative masks. In particular, spherical aberration is substantially reduced when the pumping field is tuned to a J å J + 1 transition with large J in lin ∼ lin configuration as compared to nondissipative masks.
In atom lithography, neutral atoms are focused by laser light to form a periodic pattern on a substrate. We have realized two-dimensional structuring of chromium on a silicon substrate employing a polarization gradient light mask with uniform intensity. The generated structures exhibit peak-to-peak distances below half the laser wavelength. The results are explained by a theoretical model which takes into account the magnetic substructure of the atomic transition employed and the influence of a static magnetic field.
Summary form only given.Using neutral atoms for lithography is a new method of generating nanostructures on a substrate. This method is based on light masks formed by interfering laser beams perpendicular to the atomic beam. One- and two-dimensional periodic structures have been fabricated by various groups using light masks with intensity gradients and uniform polarization. The resulting periods are half the laser wavelength or greater. Atoms with a magnetic substructure in the electronic ground state are strongly sensitive to light polarization and static magnetic fields. Our work presents a detailed investigation of possible two-dimensional light field configurations including polarization gradients and static magnetic fields. The resulting nanostructures obtained in an experimentally realistic situation are simulated.
The theoretical description of the kinetics of neutral atoms in the polarized light fields with all the atomic levels, the coherence, the recoil effect is both important and challenging problem. The first step toward understanding mechanisms of interaction between atoms and light was called quasi-classical approach. [1,2] It lies in the fact that the equations for the density matrix can be reduced to the Fokker-Planck equation for the Wigner function in the phase space. But the semiclassical approximation is inapplicable for investigating the cooling of atoms at clock transitions, because the quasiclassical parameter (the recoil frequency) is not small (in comparison with the natural line width). Later quantum methods were developed [3], for example, the secular approach which describes cooling and localization of atoms in the optical potential. Secular approximation fails high vibrational levels and for atoms in high vibrational states.
The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.