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arXiv:physics/0201017

$λ/4$, $λ/8$, and higher order atom gratings via Raman transitions

B. Dubetsky, P. R. Berman

Published Jan 9, 2002• 0 citations
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Abstract

A method is proposed for producing atom gratings having period $λ/4$ and $λ/8$ using optical fields having wavelength $λ$. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\em another} Raman field having propagation vector -2 k, one, in effect, creates a standing wave Raman field \label{91}%which whose ``intensity'' varies as $\cos (4 k\cdot r).$ When atoms move through this standing wave field, atom gratings having period $λ/4$ are produced, with the added possibility that the total ground state population in a given ground state manifold can have $λ/8$ periodicity. The conditions required to produce such gratings are derived. Moreover, it is shown that even higher order gratings having periodicity smaller than $λ/8$ can be produced using a multicolor field geometry involving three (two-photon) Raman fields. Although most calculations are carried out in the Raman-Nath approximation, the use of Raman fields to create reduced period optical lattices is also discussed.

DOI
10.48550/arxiv.physics/0201017

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The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.
We propose a scheme to create high-contrast, periodic atom density distributions having period $\ensuremath{\lambda}/2n$ using the Talbot effect, where $\ensuremath{\lambda}$ is the wavelength of the optical fields that scatter the atoms and n is a positive integer. This filtered Talbot lens is comprised of two standing-wave optical fields. An atomic beam propagates perpendicular to the fields. The first field, which is far detuned from the atomic transition frequency, acts as an array of lenses that focuses the atoms. The second field, positioned at the atom optical focus of the first, is resonant with the atomic transition frequency and acts as an amplitude mask, leaving unperturbed only those atoms that pass through its nodes. At distances following the interaction with the second field that are equal to an integral fraction of the Talbot length, atomic density gratings having period $\ensuremath{\lambda}/2n$ are formed.
A novel type of electromagnetically induced gratings based on the Raman nonlinearity in the field of standing pump waves are proposed. Unlike electromagnetically induced absorption gratings, these gratings are based on the spatial modulation of Raman susceptibility. We present a theoretical study of the optical response of such a spatial periodically modulated three-level atomic medium. It is shown that transmission and reflection of a probe Raman wave can be simultaneously amplified in the grating. Transmission and reflection spectra can be controlled by varying the pump field intensity. The basic mechanism responsible for all-optical control of transmission and reflection in the samples of Raman driven atoms are discussed.
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An atom-field geometry is chosen in which an atomic beam traverses a field interaction zone consisting of three fields, one having frequency $\ensuremath{\Omega}=2\ensuremath{\pi}c/\ensuremath{\lambda}$ propagating in the $\mathbf{z\ifmmode \hat{}\else \^{}\fi{}}$ direction and the other two having frequencies $\ensuremath{\Omega}+{\ensuremath{\delta}}_{1}$ and $\ensuremath{\Omega}+{\ensuremath{\delta}}_{2}$ propagating in the $\ensuremath{-}\mathbf{z\ifmmode \hat{}\else \^{}\fi{}}$ direction. For ${n}_{1}{\ensuremath{\delta}}_{1}{+n}_{2}{\ensuremath{\delta}}_{2}=0$ and $|{\ensuremath{\delta}}_{1}|T,|{\ensuremath{\delta}}_{2}|T\ensuremath{\gg}1,$ where n1{n}_{1}n1​ and n2{n}_{2}n2​ are positive integers and T is the pulse duration in the atomic rest frame, the atom-field interaction results in the creation of atom amplitude and phase gratings having period $\ensuremath{\lambda}/[{2(n}_{1}{+n}_{2})].$ In this manner, one can use optical fields having wavelength \ensuremath{\lambda} to produce atom gratings having periodicity much less than \ensuremath{\lambda}.