Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Bragg scattering of slow atoms from a standing light wave

S Kunze, Stephan Dürr, Gerhard Rempe

Published May 10, 1996• 78 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i1996-00462-x

Related papers

Bragg Scattering of Slow Atoms from NaStanding Light Wave

Gerhard Rempe, S. Kunze, Stephan Dürr

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.

European Quantum Electronics Conference (EQEC)•Jan 1, 1996•0 citations

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

Stephan Dürr, Stefan Kunze, Gerhard Rempe

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.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1996•47 citations

Off-resonance atomic Bragg scattering

M. A. H. M. Jansen, K.F.E.M. Domen, Herman C. W. Beijerinck +1 more

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 $2N$-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.

Physical Review A•Nov 30, 2007•7 citations

Experimental possibilities for observation of unidirectional momentum transfer to atoms from standing-wave light

David E. Pritchard, P. L. Gould

We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.

Journal of the Optical Society of America B•Nov 1, 1985•31 citations

Multiphoton Bragg scattering: Pendellosung effect for momentum-state probabilities

Sergey Petropavlovsky, Yakovlev, VP

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.

•Mar 1, 2004•0 citations

Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect

P. L. Gould, George A. Ruff, David E. Pritchard

We have observed the Kapitza-Dirac effect in the scattering of sodium atoms by a nearly resonant standing-wave laser field. The data clearly show diffraction peaks of the atomic momentum transfer at even multiples of the photon momentum. Theoretical predictions for an off-resonant, adiabatic interaction with a two-state system are in reasonable agreement with the data.

Physical Review Letters•Feb 24, 1986•408 citations
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.
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.
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.
We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.
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.