EXACT SOLUTION FOR THE REFLECTION AND DIFFRACTION OF ATOMIC DE BROGLIE WAVES BY A TRAVELLING EVANESCENT LASER WAVE

@article{Witte1998EXACTSF,
title={EXACT SOLUTION FOR THE REFLECTION AND DIFFRACTION OF ATOMIC DE BROGLIE WAVES BY A TRAVELLING EVANESCENT LASER WAVE},
author={Nicholas S. Witte},
journal={Journal of Physics A},
year={1998},
volume={31},
pages={807-832}
}
• N. Witte
• Published 16 January 1998
• Physics
• Journal of Physics A
The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore, we give the limiting cases of the amplitudes in the uniform…

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References

SHOWING 1-10 OF 35 REFERENCES

• Physics
• 1996
We present two results in an investigation of reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both results use the bare-state rather
• Physics
Physical review. A, Atomic, molecular, and optical physics
• 1993
The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states the into account internal and
• Physics
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
• 1952
The calculation of reflexion coefficients for long wireless waves incident obliquely on the ionosphere requires an exact solution of the differential equations governing the propagation of
• Physics
Physical review. A, Atomic, molecular, and optical physics
• 1993
We propose a beam splitter for atomic de Broglie waves combining atomic reflection from an evanescent laser wave with induced transitions between ground-state sublevels in a homogeneous magnetic
An exact analytical solution is obtained for coupled time-independent Schrodinger equations with model potentials: , and . This is made possible by solving a single fourth-order ordinary differential
• Physics
Physical review. A, Atomic, molecular, and optical physics
• 1994
An exact analytical solution in terms of the Meijer functions is obtained from the quantum Rosen-Zener-Demkov model for nonadiabatic transitions for elastic and inelastic atomic collision channels.
Abstract. The modiﬁed Bessel function of the third kind of purely imaginaryorder:K iν (x) = Z ∞0 e −xcosht cosνtdt,is considered for real values of the parameters ν,x, x > 0. This function playsan