Coherent scattering from a free gas

We investigate decoherence in atom interferometry due to scattering from a background gas and show that the supposition that residual coherence is due to near-forward scattering is incorrect. In fact, the coherent part is completely unscattered, although it is phase shifted. This recoil-free process leaves both the atom and the gas in an unchanged state, but allows for the acquisition of a phase shift. This is essential to understanding decoherence in a separated-arm atom interferometer, where a gas of atoms forms a refractive medium for a matter wave. Our work elucidates the actual microscopic, many-body, quantum-mechanical scattering mechanism that gives rise to prior phenomenological results for the phase shift and decoherence.

Figure 1

A Mach-Zender interferometer with the gas cell serving as a which-way detector. The atom beam is coherently split into the two arms of the interferometer by the leftmost diffraction grating. The initial state of the gas is $\mid D⟩$, which evolves into $\mid D_1⟩$ or $\mid D_2⟩$ depending on whether an atom from the beam passes through the cell. An interference pattern forms on the screen at right where the arms overlap.

Figure 2

Details of the gas cell appearing in Fig. 1. The cell has length $l$ and is embedded in a waveguide. The $j\text{th}$ slab, running from $z=(j-1)w$ to $z=jw$, is illustrated. The waveguide in which the projectile is confined is an infinite tube with a square cross section of dimensions $a\times a$.