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Physical Review Letters

Velocity Rephased Longitudinal Momentum Coherences with Differentially Detuned Separated Oscillatory Fields

Edward T. Smith, Al-Amin Dhirani, David A. Kokorowski, Richard A. Rubenstein, Tony Roberts, Huan Yao, David E. Pritchard

Published Sep 1, 1998• 21 citations
Publisher

Abstract

Localized oscillating fields are beam splitters that can entangle internal and longitudinal momentum states in an atomic beam. Differentially detuned separated oscillatory fields and an am modulator constitute a ``white fringe'' longitudinal interferometer which rephases velocity averaging by a process analogous to half a spin echo. Differentially detuned separated oscillatory fields are used to produce a downstream coherence or rephase an upstream coherence in an atomic beam.

DOI
10.1103/physrevlett.81.1996

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Localized oscillating fields are beam splitters that can entangle internal and longitudinal momentum states in an atomic beam. Differentially detuned separated oscillatory fields and an am modulator constitute a ``white fringe'' longitudinal interferometer which rephases velocity averaging by a process analogous to half a spin echo. Differentially detuned separated oscillatory fields are used to produce a downstream coherence or rephase an upstream coherence in an atomic beam.
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.
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.
We present a generalized excitation scheme and achromatic geometries for coherent diffraction of three-level atoms from a nonmagnetic, blazed phase grating. The phase grating is formed by differentially detuned standing waves with a relative spatial phase shift of π/2 and can be realized for transitions other than J = 0/1 → J = 1. The use of the differential detuning to create the phase grating allows for geometries in which the longitudinal atomic motion is coupled to the diffraction process. We describe a geometry that yields two regimes of beam splitting in which all longitudinal atomic velocities receive the same momentum transfer from the phase grating. We propose to call this type of beam splitter achromatic.
We have used a separated beam atom interferometer to investigate magnetically-induced phase shifts of the different magnetic substates of the sodium ground state. We have observed periodic rephasing of the 8 independent magnetic substates present in an unpolarized sodium beam as the differential magnetic field is increased on opposite sides of the interferometer. We have also demonstrated that two phase shifts with similar velocity dependences can be used to cancel each other, creating an interference pattern from one magnetic substate although an unpolarized beam is sent into the interferometer. Finally we discuss some applications of these techniques.