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.
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.
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 have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.
An analytical expression for the refractive index of atomic and molecular matter waves in ultracold gases is obtained. Asymptotic formulas for the refractive index are derived for high and low projectile velocities, and intermediate velocities are investigated with the eikonal approximation. The real and imaginary parts of the matter wave refractive index are expressed via the complex scattering length of elastic and superelastic collisions. It is shown that superelastic collisions dramatically influence the low-energy behavior of the refractive index. A discussion is given of proposed measurements of the real and imaginary parts of the scattering length using the interferometry of slow de Broglie waves.
Since the first interferometers for atoms and molecules were demonstrated in 1991, they have already been applied to measure atomic and molecular properties, to investigate fundamental aspects of quantum mechanics, and to measure inertial motion. This tutorial is designed to introduce those with a vague understanding of optical interferometers to atom interferometry. We outline the basic theory needed to calculate the observed phase shift, indicate how this phase shift is experimentally determined, and then describe how the phase shift is found in two particular cases: phase shifts caused by application of a uniform electric field to atoms on one side of the interferometer, and phase shift arising from the presence of a gaseous medium through which the atom wave on one side of the interferometer must propagate. We illustrate this presentation with a description of our three grating interferometer, including data taken with it.
The point of view of the electron How does the molecular target appear to the electron beam?Imagine yourself sitting on the electron wave as you accelerate towards the molecule.In order to understand your fate, you can think of yourself as refracted through the target with a refractive index of more than or less than unity.The former case corresponds to a weak interaction and the target appears closer than it truly is.The system is said to possess a "positive scattering length".If for a different target the PhotoIonlsatlon Region Four Element Zoom Lensphotoionisation of AI at 15.76 eV, using synchrotron radiation from the ASTRID storage ring, University ofAarhus.A beam of electrons,with a resolution which maybe better than 1 meV; passes through gas at room temperature, and the attenuation of the beam yields the scattering cross-section.A great variety of species has been studied with this apparatus, ranging from the simplest diatomics, H2, N2, O2 to more complex molecules such as benzene, hexafiuorobenzene and still larger species such as naphthalene or anthracene.These studies have revealed a number of fascinating quantum scattering phenomena, some known or strongly suspected from theory, such as powerful rotational excitation in polar molecules with cross-sections of several thousand A2, others unknown and which remain largely unexplained. - Collision RegionA. Fig. 1: The cold electron experiment on the ASTRID storage ring (Aarhus).The apparatus may be immersed in a magnetic field for measurement of backward scattering cross-sections.