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Physical Review A

Retardation effects on quantum reflection from an evanescent-wave atomic mirror

Robin Côté, B. Segev, Mark G. Raizen

Published Nov 1, 1998• 35 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.3999

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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.
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.
We show that an attractive potential created by an evanescent wave quantum mechanically reflects an atom with nonzero probability if the atom’s incident de Broglie wavelength is larger than the decay length of the evanescent wave. The amplitude reflection coefficient is calculated by use of an analytical solution of the corresponding Schrödinger equation. We also discuss electromagnetic wave analog of the effect, the partial reflection of light at an exponentially increasing index. We interpret the quantum reflection in terms of a virtual turning point, by means of a complex stationary phase approximation. If the potential remains exponential until it becomes as deep as several hundred recoil energies, the reflection coefficient for a low-energy de Broglie wave is independent of the details of the potential far from the virtual turning point. This means that, if the evanescent wave is strong enough, interactions between the atom and the glass surface at which the evanescent wave is created can be neglected.
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.
The London-van der Waals potential experienced by an atom under reflection from an atomic mirror is modeled as a quantum dipole-dipole interaction between the atomic dipole induced by the evanescent wave and its image dipole in the dielectric mirror. The quantum dipole-dipole interaction arises from the combined effect of the evanescent field and spontaneous emission. It depends on the electronic structure of the atom and is described by an effective non-Hermitian Hamiltonian that yields dissipative effects under reflection. The analytical expression obtained here preserves the power-law dependence of the static van der Waals interaction at distances close to the wall, but its long-distance behavior reflects that of the evanescent wave.
We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data are compared to the theoretical predictions valid in the different regimes. They agree best with a full QED calculation.