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Physical Review A

Multilayer “dielectric” mirror for atoms

Luis Santos, L. Roso

Published Sep 1, 1998• 14 citations
Publisher

Abstract

All existing atomic mirrors are conceptually similar to metallic mirrors in standard optics in the sense that they are constructed with repulsive potentials and thus produce an imaginary ``refraction index.'' Here a different kind of mirror for atoms that is similar to a multilayer dielectric mirror in standard optics is proposed. We show that a periodic attractive laser potential can reflect atoms of certain momenta due to the presence of gaps in the spectrum of energies, as in the photonic band-gap structures in light optics. Spontaneous emission and gravitational effects are also analyzed.

DOI
10.1103/physreva.58.2407

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All existing atomic mirrors are conceptually similar to metallic mirrors in standard optics in the sense that they are constructed with repulsive potentials and thus produce an imaginary ``refraction index.'' Here a different kind of mirror for atoms that is similar to a multilayer dielectric mirror in standard optics is proposed. We show that a periodic attractive laser potential can reflect atoms of certain momenta due to the presence of gaps in the spectrum of energies, as in the photonic band-gap structures in light optics. Spontaneous emission and gravitational effects are also analyzed.
We propose a laser arrangement that can allow a multipeaked laser profile with periodicity of the order of the laser wavelength. We analyse the reflection properties of atoms dropped onto this periodical laser. This periodicity produces bands in the reflection spectrum of the atoms. We have studied the case of repulsive and attractive laser potential. In particular we prove the feasibility of constructing an atom mirror with an attractive potential, i.e. a potential without turning points. We include in our calculations the gravitational effects. The spontaneous emission is also analysed as a lossy mechanism, and we have proved that for sufficiently large detuning the bands remain.
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.
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.
Quantum reflection of neutral atoms from a periodic far-detuned dipole potential is proposed and analyzed. This periodic atom mirror relies on constructive interference of small reflections from each cell to yield a high reflection coefficient even for very weak potentials. The reflected energy spectrum is calculated as a function of the potential height and the number of cells for both positive and negative potentials, and its relation to the reflection from one potential cell is derived. Two ways of increasing the reflection bandwidth, one based on changing the envelope of the potential and the other on changing its period gradually (chirp), are investigated. The phase of the reflected atoms and its dependence on experimental parameters are calculated, as well as the interaction time of the atoms with the potential and the spontaneous-emission rate during the reflection. Finally, it is shown that atoms with velocities of a few tens mm/s can be coherently reflected from a negative periodic potential with readily available laser diodes.
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.