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International Journal of Physics and Astronomy

A Detailed Study of a Dielectric Waveguide Structure for an Enhanced Evanescent Wave Atom Mirror

S. Ghezali, A. Taleb

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We are interested in a coherent atom mirror (specular atomic reflections in vacuum).A resonant dielectric waveguide structure is placed upon the prism so that a large energy is confined into the waveguide which is placed between two mediums of low index medium.The incident laser beam is resonantly coupled to a waveguide mode, through the gap, by frustrated total internal reflection.We obtain a large amplitude evanescent wave in the vacuum above the waveguide.We study the influence of the thickness of the gap and the losses inside the waveguide.

DOI
10.15640/ijpa.v2n3-4a3

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We are interested in a coherent atom mirror (specular atomic reflections in vacuum).A resonant dielectric waveguide structure is placed upon the prism so that a large energy is confined into the waveguide which is placed between two mediums of low index medium.The incident laser beam is resonantly coupled to a waveguide mode, through the gap, by frustrated total internal reflection.We obtain a large amplitude evanescent wave in the vacuum above the waveguide.We study the influence of the thickness of the gap and the losses inside the waveguide.
We have realized a resonant waveguide structure which enhances the intensity of an evanescent wave at a dielectric - vacuum interface by more than three orders of magnitude. We present a simple theoretical model including the effect of the losses in the waveguide, which gives a good description of the observed behaviour of the structure. We experimentally determine the enhancement factor by analysing the resonance of the reflected light intensity. This characterization technique allows for an easy in situ monitoring of the enhancement, which is a key feature for the understanding of atomic mirror experiments.
A research project at the “Laboratoire d’électronique quantique” consists in a theoretical study of the reflection and diffraction phenomena via an atomic mirror. This poster presents the principle of an atomic mirror. Many groups in the world have constructed this type of atom optics experiments such as in Paris‐Orsay‐Villetaneuse (France), Stanford‐Gaithersburg (USA), Munich‐Heidelberg (Germany), etc. A laser beam goes into a prism with an incidence bigger than the critical incidence. It undergoes a total reflection on the plane face of the prism and then exits. The transmitted resulting wave out of the prism is evanescent and repulsive as the frequency detuning of the laser beam compared to the atomic transition δ = ωL−ω0 is positive. The cold atomic sample interacts with this evanescent wave and undergoes one or more elastic bounces by passing into backward points in its trajectory because the atoms’ kinetic energy (of the order of the μeV) is less than the maximum of the dipolar potential barrier ℏΩ2/Δ where Ω is the Rabi frequency [1]. In fact, the atoms are cooled and captured in a magneto‐optical trap placed at a distance of the order of the cm above the prism surface. The dipolar potential with which interact the slow atoms is obtained for a two level atom in a case of a dipolar electric transition (D2 Rubidium transition at a wavelength of 780nm delivered by a Titane‐Saphir laser between a fundamental state Jf = l/2 and an excited state Je = 3/2). This potential is corrected by an attractive Van der Waals term which varies as 1/z3 in the Lennard‐Jones approximation (typical atomic distance of the order of λ0/2π where λ0 is the laser wavelength) and in 1/z4 if the distance between the atom and its image in the dielectric is big in front of λ0/2π. This last case is obtained in a quantum electrodynamic calculation by taking into account an orthornormal base [2]. We’ll examine the role of spontaneous emission for which the rate is inversely proportional to the detuning δ and is responsible of the non specular aspect of the atomic reflection (atomic diffusion). In the contrary, we note that the specularity of the reflection preserve the coherence of the atomic wave packet. The atoms will constitute a probe of the rugosity of the prism surface which can be imperfect or super‐polished.
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.
We present a theoretical analysis of the influence of surface roughness on the atomic reflection from an evanescent wave mirror. In our calculations we assume that light scattered at the rough dielectric surface interferes with the evanescent wave, creating a rough potential that scatters the atoms. We calculate the probability of diffuse reflection and the momentum distribution of the scattered atoms with a statistical model for the rough surface. The atomic reflection is diffuse rather than specular if the surface roughness is comparable to the wavelength of the incident atoms. We discuss the spatial coherence of the reflected matter waves. We indicate how to generalize our treatment to the case of multilevel atoms.
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.