Edward T. Smith

Determining the density matrix of a molecular beam using a longitudinal matter wave interferometer

Two separated oscillatory fields, if tuned to different frequencies, can generate or interrogate longitudinal momentum coherences in a beam of two-state particles. We demonstrate that use of differentially detuned separated oscillatory fields is an efficient method to determine the longitudinal density matrix of a particle beam.

Optics and Interferometry with Atoms and Molecules

Publisher Summary This chapter discusses recent accomplishments in the atom and molecular optics and interferometry at MIT. The chapter begins with a discussion of the details of an experimental apparatus and gives an overview of recent accomplishments in atom and molecular optics. It then describes the atom and molecule interferometer, which is unique in that the two interfering components of the atom wave are spatially separated and can be physically isolated by a metal foil. The interferometer is especially well suited for the study of atomic and molecular properties as it enables one to apply different interactions to each of the two components of the wave function, which in turn permits spectroscopic precision in the study of interactions that shift the energy or phase of a single state of the atom. The chapter also describes an experiment in which this capability is used to determine the ground state polarizability of sodium to 0.3%—an order of magnitude improvement—by measuring the energy shift due to a uniform electric field applied to one component of the wave function. The chapter also provides an overview of the relativistic effects in electromagnetic interactions, and differential force interferometry.

Coherence of large gratings and electron‐beam fabrication techniques for atom‐wave interferometry

We describe the fabrication of slotted, free‐standing structures used as amplitude gratings in a separated‐beam interferometer. Improvements in electron‐beam writing techniques have allowed us to compensate for electron‐beam system drift, making practical the exposure of 800×800 μm gratings with period as small as 0.14 μm. Alignment marks are used for periodic drift compensation. Finite element analysis of fracture formation in silicon nitride films gives us a tool for the prediction of structural failure in arbitrarily shaped free‐standing structures.

Coherence and Structural Design of Free-Standing Gratings for Atom-Wave Optics

Improvements in electron-beam writing techniques have allowed us to compensate for electron-beam system drift, making feasible the exposure of 800×800 µ m gratings with period as small as 0.14 µ m. Placement errors due to drift, calibration errors, and nonplanar substrates are measured with verniers. Gratings patterned with interferometric photolithography provide an absolute reference for a measure of stage nonlinearity (runout.) Simulation of fracture formation in silicon nitride films has given us a tool for the prediction of structures that will fail during fabrication, and a way of evaluating stress relief patterns in arbitrary structures. We have used two sets of simple patterns to identify the critical stress intensity factors in thin, free-standing films of nonstoichiometric silicon nitride.

Atom Interferometers and Atomic Coherence

Atom interferometers are powerful tools for the study of fundamental issues in quantum mechanics. This paper describes the use of our atom interferometer [1] for an experimental realization of Feynmans gedanken experiment in which the observation of photons scattered off of particles emerging from a double slit is used to obtain which path information. This determination, in principal, of the particles path, destroys any interference effects downstream. The interference can be regained by observing only those particles which scatter a photon into a small range of final directions.

Longitudinal Atom Interferometry

A detuned, radiofrequency field interacting with atoms in an atomic beam constitutes a beamsplitter in longitudinal momentum space. Using such beamsplitters, we have constructed a longitudinal atom interferometer in a generalization of Ramseys classic SOF configuration. This interferometer is well-suited to studying the longitudinal coherence properties of matter-wave beams. We report on two such experiments, including a deconvolution of the longitudinal density matrix of an atomic beam, and a search for longitudinal coherences coming from our supersonic beam source.

Using an atom interferometer to take the Gedanken out of Feynman’s Gedankenexperiment

We give a description of two experiments performed in an atom interferometer at MIT. By scattering a single photon off of the atom as it passes through the interferometer, we perform a version of a classic gedankenexperiment, a demonstration of a Feynman light microscope. As path information about the atom is gained, contrast in the atom fringes (coherence) is lost. The lost coherence is then recovered by observing only atoms which scatter photons into a particular final direction. This paper reflects the main emphasis of D. E. Pritchard’s talk at the RIS meeting. Information about other topics covered in that talk, as well as a review of all of the published work performed with the MIT atom/molecule interferometer, is available on the world wide web at http://coffee.mit.edu/.

Atomic beam propagation effects: index of refraction and longitudinal tomography

We present initial measurements of the dispersive index of refraction for sodium matter waves passing through argon. In addition, we describe a novel scheme for performing tomography on the longitudinal quantum state of particles in an atomic beam.

Interferometry with atoms and molecules: a tutorial

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.