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

Pendellösung oscillations in second-order Bragg scattering of atoms from a standing light wave

Stephan Dürr, Stefan Kunze, Gerhard Rempe

Published Jun 1, 1996• 47 citations
Publisher

Abstract

Bragg scattering of atoms from a standing light wave exhibits Pendellösung oscillations in the scattering probability. For second-order scattering, we have recently observed significant deviation of the oscillation frequency from the prediction for a pure four-photon-type process. To give a quantitative explanation for this behaviour, we present an analytical calculation which takes into account lowest energy momentum states. Our calculation suggests that a transition between a four-photon-type process at low light intensity to a two-photon-type process at higher light intensity is responsible for this behaviour.

DOI
10.1088/1355-5111/8/3/016

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Bragg scattering of atoms from a standing light wave exhibits Pendellösung oscillations in the scattering probability. For second-order scattering, we have recently observed significant deviation of the oscillation frequency from the prediction for a pure four-photon-type process. To give a quantitative explanation for this behaviour, we present an analytical calculation which takes into account lowest energy momentum states. Our calculation suggests that a transition between a four-photon-type process at low light intensity to a two-photon-type process at higher light intensity is responsible for this behaviour.
Slow atoms from a magneto-optical trap are used to study diffraction from a near-resonant standing-wave light field. Long interaction times make it possible to observe unidirectional Bragg scattering. In particular, the Pendellösung interference effect between two resonant momentum states is demonstrated for first- and second-order diffraction. The oscillation frequency of second-order scattering shows a transition from a four-photon–type process at low light intensity to a two-photon–type process at higher intensity. The data are in quantitative agreement with a theoretical description which takes into account lowest-energy momentum states.
Slow atoms from a magneto-optical trap are used to study difiraction from a near-resonant standing-wave light fleld. Long interaction times make it possible to observe unidirectional Bragg scattering. In particular, the Pendellosung interference efiect between two resonant momentum states is demonstrated for flrst- and second-order difiraction. The oscillation frequency of second-order scattering shows a transition from a four-photon{type process at low light intensity to a two-photon{type process at higher intensity. The data are in quantitative agreement with a theoretical description which takes into account lowest-energy momentum states.
Multiphoton Bragg scattering of atoms in a sufficiently strong field of a standing wave is treated within the framework of the WKB approximation for recurrence relations describing discrete momentum-state amplitudes. The time evolution of the momentum-state probabilities was found. The obtained results are valid for arbitrary atom-field coupling and show good agreement with experimental data, including the so-called Pendellosung effect, i.e., the oscillatory behavior of the scattering probability with an increase in the interaction parameter or the effective transit time. We also study damped Pendell6sung oscillations originating from irreversible spontaneous emission.
We performed extensive measurements on the scattering efficiency of atomic Bragg scattering on a standing light wave up to sixth order and developed a two-state Demkov model to explain the results. Using an effective 2N2N2N-photon coupling between the original and the reflected momentum states and the assumption of a mostly adiabatic transfer we derived the scattering probability. This probability has two factors: an oscillating part which represents the well-known Pendell\"osung oscillation and a part that is peaked in the energy difference between the two momentum states. This last part describes the tolerance on the Bragg condition for angular misalignment. Comparison of the measurements and numerical simulations with this model shows good agreement.