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Reflection Spectrum of Two Level Atoms by an Evanescent Laser Wave

Weihan Tan, Qingning Li

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

An exact solution and numerical calculation of the reflection of two level atoms by atomic mirror are presented. The curve of reflection coefficient against Rabi frequency calculated shows some new features, and the physical machanism underlying is analyzed.

Related papers

On the General and Resonant Solutions of Atoms Reflected by an Evanescent Laser Wave

Weihan Tan, Qiang-ning Li

Usually the reflection of two level atoms by a detuning evanescent laser wave was studied in past few years. In previous paper we have presented an exact solution for this model based on the matrix Laplace transformation technique, and proceeded the numerical calculations for a given set of parameters. However in the special case of resonance interaction considered in this paper, the solution for Schrödinger wave equation and reflectivity calculation can be greatly simplified; besides, the resonant solution provides a check to the numerical data based on the general solution of the previous paper.

Chinese Physics Letters•Aug 1, 1996•0 citations

Evanescent Wave Atomic Mirror

S. Ghezali, A. Taleb, El-Hachemi Amara +2 more

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.

AIP conference proceedings•Jan 1, 2008•0 citations

Phase shifts of atomic de Broglie waves at an evanescent wave mirror

Carsten Henkel, J.-Y. Courtois, Robin Kaiser +2 more

A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.

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V. I. Balykin, Vladilen S Letokhov

In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.

CRC Press eBooks•Apr 23, 2020•0 citations

Quantum reflection from an atomic mirror

B. Segev, Robin Côté, Mark G. Raizen

We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.

Physical Review A•Nov 1, 1997•47 citations

Atomic mirrors for aΛ-type three-level atom

Nuha Felemban, Omar Marzook Al-Dossary, V. E. Lembessis

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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 2014•5 citations
Usually the reflection of two level atoms by a detuning evanescent laser wave was studied in past few years. In previous paper we have presented an exact solution for this model based on the matrix Laplace transformation technique, and proceeded the numerical calculations for a given set of parameters. However in the special case of resonance interaction considered in this paper, the solution for Schrödinger wave equation and reflectivity calculation can be greatly simplified; besides, the resonant solution provides a check to the numerical data based on the general solution of the previous paper.
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.
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.
In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.
We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.
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.