Dynamics of fermionic four-wave mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due to the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the technique of “atom echoes.”