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Physical Review A

Quantum reflection from an atomic mirror

B. Segev, Robin Côté, Mark G. Raizen

Published Nov 1, 1997• 47 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.r3350

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We calculate the reflection probability for ultracold sodium atoms incident on an evanescent-wave atomic mirror. For low enough energies the reflection probability curves exhibit quantum effects that are sensitive to the long-range part of the potential and can therefore be used to resolve Casimir retardation effects. We also explore the accuracy of model potentials approximating the exact atom-wall effective potential.

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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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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.

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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.

Physical Review A•Feb 1, 1997•35 citations
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 explore the design of atom-optic components, such as mirrors, to manipulate ultracold atoms. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the interaction potential between atoms and the component. We illustrate the concept by calculating the reflection probability for ultracold sodium atoms incident on a bichromatic evanescent-wave atomic mirror created by lasers red and blue detuned from resonance with intensities and detunings chosen to enhance quantum reflection of a purely attractive potential. With realistic parameters for sodium atoms incident on glass at 10 cm/s, up to 30% reflection can be obtained.
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.
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.
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.
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.