Nonlinear atom optics: bosons vs fermions

Abstract

Nonlinear atom optics, the matter-wave analog of nonlinear optics, has recently been demonstrated in several experiments in quantum degenerate bosonic systems. Atomic four-wave mixing, as well as the nonlinear mixing between optical and matter waves, have been realized. In a parallel development, quantum degenerate atomic Fermi systems have become available. This leads one to ask whether nonlinear atom optical effects can occur in such systems, or whether they result from “Bose enhancement”, and hence are inherent to bosonic fields. To answer this question we compare atomic four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that in principle, matter-wave gratings formed from either bosonic or fermionic atoms can exhibit nearly identical Bragg scattering and four-wave mixing properties. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as “Bose enhancement.” This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases.