Momentum-space interferometry with trapped ultracold atoms

Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructively or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as many-body effects, to determine the potential applicability of momentum-space interferometry. For a broad range of parameters and conditions it is found that a "dark notch" in the momentum distribution depends linearly on the phase imprinted, with maximal sensitivity for noninteracting atoms in the ground state of tight traps.