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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Atomic beamsplitter based on Raman transitions in four standing light waves

Eugeny Korsunsky

Published Jun 1, 1998• 3 citations
Publisher

Abstract

We propose a new atomic beamsplitter which uses Raman transitions via the far detuned excited state of an atom induced by four standing light waves. The splitting is not restricted to the Raman-Nath regime, and spontaneous emission is strongly suppressed. Therefore this scheme can be applied even for very slow atoms with strong transitions.

DOI
10.1088/1355-5111/10/3/006

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We propose a new atomic beamsplitter which uses Raman transitions via the far detuned excited state of an atom induced by four standing light waves. The splitting is not restricted to the Raman-Nath regime, and spontaneous emission is strongly suppressed. Therefore this scheme can be applied even for very slow atoms with strong transitions.
We investigate schemes for the clean splitting of beams of three-level atoms using two standing-wave laser fields within an optical cavity. The proposed beam splitter is shown to work for atoms in the \ensuremath{\Lambda} ladder, and ssV configurations. For appropriate values of Rabi frequencies and detunings, we obtain a triangular type of potential for the atomic states of interest. As well as modeling the coherent evolution of the systems, we have used quantum Monte Carlo wave-function methods to model the effects of spontaneous emission on the resulting diffraction pattern, finding significant differences between the three configurations. We also investigate the limits of the Raman-Nath approximation for our systems, using the symmetric split-operator technique to include the effects of the kinetic term in the Hamiltonian. We also present the results of calculations in which the split output beams are recombined, demonstrating the expected interference for differently prepared input beams. In comparison with two-level beam splitters using a single standing wave, we obtain a superior splitting, while, in comparison with magneto-optical beam splitters, our system possesses the worthwhile practical advantages of experimental simplicity.
We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicularly to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.
We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.
We study atomic-beam deflection by adiabatic passage between Zeeman ground levels via Raman transitions induced by counterpropagating ${\mathrm{\ensuremath{\sigma}}}^{\ifmmode\pm\else\textpm\fi{}}$-polarized lasers. We show that complete population transfer between the ground states can be achieved, which corresponds to the scattering of the atomic wave packet into a single final momentum state by absorption and induced emission of laser photons. Although the lasers can be resonant, the excited state(s) are never populated during the adiabatic transfer, which suppresses the effects of spontaneous emission and preserves the coherence of the atomic wave function. This scheme has attractive features as a beam splitter and mirror for atomic interferometry.
In a recent experiment (Wang et al., e-print cond-mat/0407689), it was observed that a sequence of two standing-wave square pulses can split a Bose-Einstein Condensate at rest into $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\hbar}\mathbf{k}$ diffraction orders with almost 100% efficiency. By truncating the Raman-Nath equations to a two-state model, we provide an intuitive picture that explains this double-square-pulse beam-splitter scheme. We further show it is possible to optimize a standing-wave multiple-square-pulse sequence to efficiently diffract an atom at rest to a symmetric superposition of $\ifmmode\pm\else\textpm\fi{}2n\ensuremath{\hbar}\mathbf{k}$ diffraction orders with n>1n>1n>1. The approach is considered to be qualitatively different from the traditional light-pulse schemes in the Bragg or the Raman-Nath region, and can be extended to more complex atomic optical elements that produce various tailored output momentum states from a cold atom source.