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Physical Review A

Theory of evanescent mode atomic mirrors with a metallic layer

C. R. Bennett, J. B. Kirk, M. Babiker

Published Feb 13, 2001• 30 citations
Publisher

Abstract

Dielectric atomic mirrors are considered in which the repulsive force field owes its existence to an evanescent mode in the presence of a metallic capping layer. The theory of such an atomic mirror is constructed, assuming a finite thickness of the metallic layer with a finite plasma frequency and adopting the field-dipole orientation picture. The Rabi frequency together with the reflectivity for the light incident from within the substrate are evaluated, and their variations with the type of metal and layer thickness analyzed as useful indicators of the effectiveness of the system as an atomic mirror. A number of interesting features are pointed out, including a desirable enhancement. Solutions of the equation of motion for a given atom, subject to given initial conditions, lead to trajectories exhibiting reflection. The leading force fields controlling the dynamics include the average dipole image force plus the average light-induced forces due to the evanescent field. The parameters used to compute the trajectories are similar to those in recent experiments in which Rb atoms incident on a silver film deposited on a glass substrate have been shown to experience enhanced mirror action. The factors controlling the enhancement in general are pointed out and discussed.

DOI
10.1103/physreva.63.033405

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Dielectric atomic mirrors are considered in which the repulsive force field owes its existence to an evanescent mode in the presence of a metallic capping layer. The theory of such an atomic mirror is constructed, assuming a finite thickness of the metallic layer with a finite plasma frequency and adopting the field-dipole orientation picture. The Rabi frequency together with the reflectivity for the light incident from within the substrate are evaluated, and their variations with the type of metal and layer thickness analyzed as useful indicators of the effectiveness of the system as an atomic mirror. A number of interesting features are pointed out, including a desirable enhancement. Solutions of the equation of motion for a given atom, subject to given initial conditions, lead to trajectories exhibiting reflection. The leading force fields controlling the dynamics include the average dipole image force plus the average light-induced forces due to the evanescent field. The parameters used to compute the trajectories are similar to those in recent experiments in which Rb atoms incident on a silver film deposited on a glass substrate have been shown to experience enhanced mirror action. The factors controlling the enhancement in general are pointed out and discussed.
A theory of evanescent mode atomic mirrors utilising a metallic sheet on a dielectric substrate is described. The emphasis here is on the role of the metallic sheet and on the evaluation of atomic trajectories using the field- dipole orientation picture. At low intensity, the atomic reflection process is controlled by two separate mechanisms both of which are modified by the presence of the metallic sheet and influenced by the use of the field-dipole orientation picture. The first mechanism involves the spontaneous force which accelerates the atom parallel to the sheet plane. The second mechanism involves the combined dipole plus van der Waals force which acts to repel the atom from the surface, decelerating its motion until it attains an instantaneous halt before changing direction away from the surface at an appr opriate turning point in the trajectory. Various quantitative features arising from varying the controllable parameters of the system, including screening effects as well as desirable enhancement effects, are pointed out and discussed.
Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.
Recent studies have involved electric quadrupole effects in atoms interacting with the evanescent mode. This type of surface mode is usually produced by the total internal reflection in a dielectric-vacuum atz=0, and its intensity distribution is very close to the outer surface z>0 half-space. Coating the planar surface of a dielectric substrate with multilayer dielectric thin film of different thicknesses provides an enhanced in such evanescent modes. This type of mode can be used purely as an atomic mirror. We show that the use of such elements for atomic optics gives significant enhancement of the evanescent mode magnitude without degrading the quality of the atomic reflection process. In addition, the decay depth of the evanescent mode can be conveniently controlled by design parameters. This property keeps the atom-light interaction timeτ, and thus the probability of decay emission, very low, which means a high degree of coherence property.
There have been significant progresses in atom optics utilizing laser cooling techniques in recent years. Among them, we have been interested in an atomic mirror for silicon which can reflect silicon atoms. The atomic mirror consists of two layers on a sapphire substrate, and then atoms are reflected by the dipole forces from evanescent waves caused by the light reflected internally and totally at the interface of different refractive indices. In this study, we have constructed some structures of the atomic mirror. We tried atomic layer deposition techniques for preparation of both Al2O3 and TiO2 thin films, whose surface and interface roughnesses are well suppressed. In order to achieve the predicted enhancement of the evanescent waves, atomic layer deposition of the layer with the higher refractive index is especially important. It has found that absorption can be suppressed considerably by adding Al(CH3)3 precursor gas to the alternate introducing cycle of TiCl4 and H2O2 precursor gases. We use this effect which can improve homogeneity and flatness of layers significantly, to design an atomic mirror using atomic layer deposition.
We propose atom mirror schemes for a three-level atom of Λ-type interacting with two evanescent fields, which are generated as a result of the total internal reflection of two coherent Gaussian laser beams at the interface of a dielectric prism with vacuum. The forces acting on the atom are derived by means of optical Bloch equations, based on the atomic density matrix elements. The theory is illustrated by setting up the equations of motion for 23Na atom. Two types of excited schemes are examined, namely the cases in which the evanescent fields have polarization types of and . The equations are solved numerically and we get results for atomic trajectories for different parameters. The performance of the mirror for the two types of polarization schemes is quantified and discussed. The possibility of reflecting atoms at pre-determined directions is also discussed.
After a brief introduction to the field of atom optics and to atomic mirrors, we present experimental results obtained in our group during the last two years while studying the reflection of rubidium atoms by an evanescent wave. These involve the first measurement of the van der Waals force between an atom in its ground state and a dielectric wall, as well as the demonstration of a reflection grating for atoms at normal incidence. We also consider the influence of quantum reflection and tunnelling phenomena. Further studies using the atomic mirror as a probe of the van der Waals interaction, and of very small surface roughness are briefly discussed.