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Physical Review Letters

Search for Off-Diagonal Density Matrix Elements for Atoms in a Supersonic Beam

Richard A. Rubenstein, Al-Amin Dhirani, David A. Kokorowski, Tony Roberts, Edward T. Smith, W. W. Smith, Herbert Joseph Bernstein, Jana Lehner, Subhadeep Gupta, David E. Pritchard

Published Mar 8, 1999• 19 citations
Publisher

Abstract

We demonstrate the absence of off-diagonal elements for the density matrix of a supersonic Na atomic beam, thus showing that there are no coherent wave packets emerging from this source. We used a differentially detuned separated oscillatory field longitudinal interferometer to search for off-diagonal density matrix elements in the longitudinal energy/momentum basis. Our study places a stringent lower bound on their possible size over an off-diagonal energy range from 0 to 100 kHz.

DOI
10.1103/physrevlett.82.2018

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We demonstrate the absence of off-diagonal elements for the density matrix of a supersonic Na atomic beam, thus showing that there are no coherent wave packets emerging from this source. We used a differentially detuned separated oscillatory field longitudinal interferometer to search for off-diagonal density matrix elements in the longitudinal energy/momentum basis. Our study places a stringent lower bound on their possible size over an off-diagonal energy range from 0 to 100 kHz.
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 Ramsey's 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.
A supersonic beam of noble gas atoms is a source of unprecedented brightness. A novel short pulse supersonic nozzle is developed with beam intensity that is higher by at least an order of magnitude than other available sources. We show how this beam can be coherently slowed and focused using elastic reflection from single crystals. Simulations show beam fluxes of 10 11 atoms s −1 at velocities of 50 m s −1 and temperatures of less than 20 μK in the longitudinal direction. Possible applications of this slow beam to the study of atom–surface interactions and atom interferometry are discussed.
This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the n=3n=3n=3 state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\ensuremath{\alpha}$ photons at 90\ifmmode^\circ\else\textdegree\fi{} to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to n=3n=3n=3 excitation of hydrogen.
We provide a fully quantal treatment of a beam of two-state particles interacting with temporally oscillating potentials, and propose a number of longitudinal atom optics devices. A single oscillatory potential, in coupling the two internal states, generally entangles each with a different longitudinal momentum. An oscillatory potential can also act as an amplitude modulator, creating momentum coherences within a single internal state. Two successive oscillatory fields (DSOF's), if differentially detuned, can couple an initially monochromatic state to a coherent momentum superposition, or alternatively may be used to detect a pre-existing momentum superposition. DSOF's can create amplitude modulation which, despite the presence of a broad velocity distribution, rephases at a selected distance downstream of the device. Phase modulation generates coherent momentum sidebands which can evolve into amplitude modulation at a particular location downstream.