# Quantum reflection: atomic matter wave optics in an attractive exponential potential

C. Henkel, C. I. Westbrook, and A. Aspect
*J. Opt. Soc. Am. B* **13** (1996) 233-243.
**Abstract**

We show that an attractive potential created by an evanescent wave quantum mechanically reflects an atom with a 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 the 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 with the evanescent wave is created can be neglected.

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