optical lattice
chapter
Hartree approximation
regime
Schrödinger equation
matter waves
prediction
cases
The experimental demonstration of Bose—Einstein condensation in atomic vapors [1–3] has rapidly lead to spectacular new advances in atom optics. In particular, it has enabled its extension from the linear to the nonlinear regime, very much like the laser lead to the development of nonlinear optics in the 1960s. It is now well established that two-body collisions play for matter waves a role analogous to that of a Kerr nonlinear crystal in optics. In particular, it is known that the nonlinear Schrödinger equation which describes the condensate in the Hartree approximation supports soliton solutions. For the case of repulsive interactions normally encountered in BEC experiments, the simplest solutions are dark solitons, that is, ‘dips’ in the density profile of the condensate. These dark solitons have been recently demonstrated in two experiments [4,5] which appear to be in good agreement with the predictions of the Gross—Pitaevskii equation.
2003
nonlinear Schrödinger equation
interaction
2003-01-01
301-319
approximation
waves
crystals
laser lead
2022-05-20T07:46
https://scigraph.springernature.com/explorer/license/
dark solitons
repulsive interactions
soliton solutions
solitons
equations
new advances
advances
nonlinear crystal
experimental demonstration
two-body collisions
development
extension
en
atomic solitons
solution
atomic vapor
true
atom optics
dip
Bose-Einstein condensation
linear
demonstration
Kerr nonlinear crystal
Atomic Solitons in Optical Lattices
experiments
agreement
good agreement
vapor
Gross-Pitaevskii equation
profile
collisions
condensate
role
condensation
nonlinear optics
chapters
lead
optics
BEC experiments
nonlinear regime
density profiles
lattice
https://doi.org/10.1007/978-3-662-05144-3_14
simple solution
E. M.
Wright
978-3-662-05144-3
Nonlinear Photonic Crystals
978-3-642-07867-5
Eggleton
Benjamin J.
S.
Pötting
Richard E.
Slusher
Atomic, Molecular, Nuclear, Particle and Plasma Physics
doi
10.1007/978-3-662-05144-3_14
P.
Meystre
dimensions_id
pub.1032166332
Physical Sciences
Springer Nature
Springer Nature - SN SciGraph project