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

arXiv:cond-mat/0005021 · Physical Review Letters

Elastic Scattering Loss of Atoms from Colliding Bose-Einstein Condensate Wave Packets

Y. B. Band, Marek Trippenbach, J. P. Burke, Paul S. Julienne

Published Jun 12, 2000• 73 citations
arXivHTMLPDF

Abstract

Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.

DOI
10.1103/physrevlett.84.5462

Related papers

Elastic scattering losses from colliding Bose-Einstein condensates

Paweł Zin, Jan Chwedeńczuk, Marek Trippenbach

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.

Physical Review A•Mar 6, 2006•28 citations

Theory of four-wave mixing of matter waves from a Bose-Einstein condensate

Marek Trippenbach, Y. B. Band, Paul S. Julienne

A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low-momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum, and energy conservation (i.e., phase matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.

arXiv:cond-mat/0002119•Physical Review A•Jul 19, 2000•93 citations

Suppression of elastic scattering loss for slowly colliding Bose-Einstein condensates

Y. B. Band, John H. Burke, Andrea Simoni +1 more

Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an $|F=2,{M}_{F}=2〉$ with an $|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}$ condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the ${M}_{F}=1$ wave packet for suitable experimental conditions.

Physical Review A•Jul 1, 2001•11 citations

INVESTIGATION OF FOUR-WAVE MIXING OF MATTER WAVES IN BOSE–EINSTEIN CONDENSATES

CHUNLIU SUN, Chao Hang, Guoxiang Huang +1 more

We investigate the four-wave mixing of matter wave packets created from a Bose–Einstein condensate, realized experimentally by utilizing light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary condensate. Based on the Gross–Pitaevskii equation, a set of nonlinearly coupled envelope equations including self- and cross-phase modulational effects are derived systematically using a method of multiple-scales. The exact and explicit analytical solutions are provided for the coupled envelope equations and the evolution of the wave packets after turning off trapping potential is discussed and compared with experiment.

Modern Physics Letters B•Apr 10, 2004•5 citations

Elastic scattering losses from colliding BEC's

Paweł Zin, Jan Chwedeńczuk, Marek Trippenbach

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) have introduced a model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first order approximation we derive analytical expressions for the density matrix and anomalous density which provides excellent insight into correlation properties of scattered atoms.

arXiv:cond-mat/0512082•Dec 5, 2005•0 citations

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics

Valentina Krachmalnicoff, Jean-Christophe Jaskula, Marie Bonneau +8 more

We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

arXiv:0911.4564•Physical Review Letters•Apr 15, 2010•81 citations
Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.
A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low-momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum, and energy conservation (i.e., phase matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.
Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an ∣F=2,MF=2〉|F=2,{M}_{F}=2〉∣F=2,MF​=2〉 with an ∣F=2,MF=1〉87Rb|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}∣F=2,MF​=1〉87Rb condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the MF=1{M}_{F}=1MF​=1 wave packet for suitable experimental conditions.
We investigate the four-wave mixing of matter wave packets created from a Bose–Einstein condensate, realized experimentally by utilizing light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary condensate. Based on the Gross–Pitaevskii equation, a set of nonlinearly coupled envelope equations including self- and cross-phase modulational effects are derived systematically using a method of multiple-scales. The exact and explicit analytical solutions are provided for the coupled envelope equations and the evolution of the wave packets after turning off trapping potential is discussed and compared with experiment.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) have introduced a model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first order approximation we derive analytical expressions for the density matrix and anomalous density which provides excellent insight into correlation properties of scattered atoms.
We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.