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The invention of the laser ushered in a new field of experimental study in
the early 1960s--non-linear optics. Because laser light can be so intense,
it can actually change the index of refraction of a material through which
it passes. Thus, the behavior of a transparent medium can depend on how
intense the light is, a "non-linearity" that has led to such interesting
phenomena as self-focusing of light, and optical harmonic generation--the
creation of new colors of light from a single color.
Atomic-gas Bose-Einstein condensation, first observed in 1995 at NIST-Boulder and the Univ. of Colorado at Boulder, makes possible the "atom laser" beam, atomic matter waves of sufficient intensity and purity to observe non-linear effects in "atom optics"--the atomic analog to ordinary or "photon" optics. A key difference is that while non-linear photon optics requires a non-linear medium through which the light can propagate, the non-linearity is automatically present in atom optics because of atom-atom collisional interactions, something that is virtually absent for photons in vacuum. One important non-linear optics phenomenon is four-wave-mixing (4WM), in which three optical fields mix in a non-linear medium and create a fourth wave. The frequency and momentum of the fourth wave's photons is equal to a sum or difference among the three input frequencies and momenta. In experiments at the National Institute of Standards and Technology in Gaithersburg, Maryland, we have performed four wave mixing of atomic matter waves, the first non-linear optics with de Broglie waves. From a single Bose-Einstein condensate we create three coherent matter waves with different velocities. These three waves mix with one another because of their collisional interactions (intrinsic non-linearity) and produce a fourth wave. We conserve the total number of atoms because for each atom appearing in the new, fourth wave, an atom disappears from each of two other waves and one atom is added to the remaining wave. The process of matter wave 4WM can be understood as stimulated elastic scattering (analogous to stimulated emission of radiation, the basis for the optical laser) in which two atoms collide in the presence of a strong atomic matter wave, and one of the atoms is stimulated to scatter into the already-present matter wave, amplifying it. The other atom must scatter into the previously non-existent fourth wave because of energy and momentum conservation. This fourth wave is the phase conjugate of the wave that is amplified. An alternative way of explaining atomic 4WM is that two of the original matter waves create a standing wave, a spatial corrugation of the atomic density. The third de Broglie wave Bragg-reflects from this grating, creating the fourth wave. Satisfying the condition for Bragg reflection is equivalent to satisfying energy and momentum conservation. One of the fundamental tenets of quantum mechanics is the concept of wave-particle duality: sometimes things act like particles, and sometimes like waves. This work now extends the wave-like character of atoms into the non-linear domain. Non-linearity has been key in the development of quantum optics, which explores the uniquely quantum mechanical aspects of light. We can now look forward to the analogous development of quantum atom optics. This work is reported in the 18 March 1999 issue of Nature: "Four-wave mixing of matter waves," L. Deng, E. Hagley, J. Wen, M. Trippenbach, Y. Band, P. Julienne, J. Simsarian, K. Helmerson, S. Rolston and W. Phillips. |
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