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Physical Review A

Theory of an atomic beam splitter based on velocity-tuned resonances

S. Glasgow, Pierre Meystre, Martin Wilkens, Ewan M. Wright

Published Mar 1, 1991• 43 citations
Publisher

Abstract

We develop the theory of an atomic beam splitter in which a monoenergetic beam of two-level atoms is incident normally to a classical standing-wave light field. The incident atomic wave function can be split into two coherent components with transverse momenta \ifmmode\pm\else\textpm\fi{}(2n+1)\ensuremath{\Elzxh}k using velocity-tuned resonances, where n is the order of the resonance. We discuss the cases of zero- and first-order resonances in detail, and show that the velocity-tuned resonances are renormalized due to a high-frequency Stark shift. Numerical results that display the effects of a finite momentum spread in the incident atomic beam are presented.

DOI
10.1103/physreva.43.2455

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We develop the theory of an atomic beam splitter in which a monoenergetic beam of two-level atoms is incident normally to a classical standing-wave light field. The incident atomic wave function can be split into two coherent components with transverse momenta \ifmmode\pm\else\textpm\fi{}(2n+1)\ensuremath{\Elzxh}k using velocity-tuned resonances, where n is the order of the resonance. We discuss the cases of zero- and first-order resonances in detail, and show that the velocity-tuned resonances are renormalized due to a high-frequency Stark shift. Numerical results that display the effects of a finite momentum spread in the incident atomic beam are presented.
In this paper we review techniques to coherently split an atomic beam using the dipole force. We discuss the interaction of atoms with normal standing wave light field in the context of atomic beam splitters. The case where the atom enters the standing wave at a small angle such that Bragg diffraction and velocity selective resonances are observed is also considered. An alternative approach to realize a coherent beam splitter based on the optical Stern‐Gerlach effect is discussed. Finally we consider the interaction of atoms with a magneto‐optical potential formed by a polarization gradient light field and a static magnetic field. We show that the Stern‐Gerlach effect and the magneto‐optical potential produce a more effective beam splitting into states with high transverse momentum than diffraction from a normal standing wave.
A theory of an atom beam splitter is developed involving the interaction of standing-wave field pulses with $\ensuremath{\Lambda}$-type atoms. The beam splitter consists of two interaction zones, both treated in the Raman-Nath approximation. There is an initial, off-resonant field (or fields) that prepares the initial atomic state, followed by interaction with a pair of standing-wave field pulses. Using this configuration one is able to create a large-angle beam splitter with a significant suppression of unwanted momentum components. The roles of relaxation and a frequency chirp are investigated, as are initial conditions for which both ground states of the $\ensuremath{\Lambda}$ scheme are prepared by the first field. It is shown that the scheme is rather robust against fluctuations of system parameters.
We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.
Control in multi-zone atomic beam splitters needs for the practical realization of nanoscale lithography by coherent scattering of the atoms. We propose an effective atomic beam splitter based on the interaction of three-level atom with the field of the standing optical waves having relative spatial shifts. It is shown, that using of several interaction zones of the standing waves having the different spatial shift it make possible to reach the splitting 2n/spl planck/k (where n is the number of zone) in each of lower three-level /spl Lambda/-atom state.
Effective atomic beam splitters providing large scattering angles are central to atom optics and atom interferometry. Their most common optical realization relies on first-order Bragg scattering, which generates a splitting of the atomic wave function in momentum space. For typical atomic beam velocities of the order of 100 m/s, 2ħk produces very small scattering angles. Higher-order Bragg scattering is of questionable practicality, because of the need for atom–field interaction times that scale exponentially with the scattering order. Attempts at solving this problem include the introduction of multiple laser beams, the use of three-level transition schemes, and the application of velocity-tuned, or Doppleron, resonances. We present a novel scheme that uses a Doppleron resonance as a catalyst to speed up a high-order Bragg resonance by orders of magnitude. This effect occurs when the atom–field frequency detuning is such that the Bragg resonance and the Doppleron resonance become degenerate. Alternatively, in the band-theoretical description of the near-resonant Kapitza–Dirac effect, the Doppleron resonance is required to occur either at the center or at the boundary of the first Brillouin zone.