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arXiv:0801.4951 · Physical Review A

Coherent scattering from a free gas

Scott N. Sanders, Florian Mintert, Eric J. Heller

Published Feb 6, 2009• 3 citations
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Abstract

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.

DOI
10.1103/physreva.79.023610

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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.
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.
We study the decoherence of a system of NNN noninteracting heavy particles (atoms) due to coherent scattering with a background gas. We introduce a framework for computing the induced phase shift and loss of contrast for arbitrary preparations of NNN-particle quantum states. We find phase shifts that are inherently $(N\ensuremath{\ge}2)$-body effects and may be searched for in future experiments. We analyze simple setups, including a two-mode approximation of an interferometer. We study fully entangled N00NN00NN00N states, which resemble the correlated positions in a matter interferometer, as well as totally uncorrelated product states that are representative of a typical state in an atom interferometer. We find that the extent to which coherent enhancements increase the rate of decoherence depends on the observable of interest, state preparation, and details of the experimental design. In the context of future ultralow-recoil (e.g., light dark matter) searches with atom interferometers we conclude that (i) there exists a coherently enhanced scattering phase which can be searched for using standard (i.e., contrast/visibility and phase) interferometer observables; (ii) although decoherence rates of one-body observables are not coherently enhanced, a coherently enhanced loss of contrast can still arise from dephasing; and (iii) higher statistical moments (which are immediately accessible in a counting experiment) are coherently enhanced and may offer a new tool with which to probe the soft scattering of otherwise undetectable particles in the laboratory.
Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.
The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.
We describe a method for measuring the forward-scattering amplitude for electron collisions with atoms or molecules. Our scheme uses a gas cell in one arm of an electron interferometer and measures the resulting attenuation and phase shift of the electron matter wave. The complex index of refraction of the gas is determined along with the forward-scattering amplitude. Calculations of the scattering of electrons by atoms are performed using a self-energy potential obtained by treating the atom as an inhomogeneous electron gas. The results indicate that the proposed experiments are feasible.