"optics" .
_:Ncfe53fd6a6af4bf2b1799ca67017484e .
"waves" .
_:Nad00bf1740e744e286889df0afda621c .
"role" .
.
"https://doi.org/10.1007/978-3-662-05144-3_14" .
"development" .
.
"2003-01-01" .
"matter waves" .
_:N502b4a47906c4a87a5ed5c3ea81adac8 "Richard E." .
"regime" .
.
_:Na3bb8cb3ae2548fab7f820da0cb64107 .
"crystals" .
"solitons" .
_:N049f7388553945808f0fed01468c4a6b "Springer Nature - SN SciGraph project" .
_:N737ca7d33b324544a6ec74d9f5ede9b7 .
.
_:N049f7388553945808f0fed01468c4a6b .
"Meystre" .
"nonlinear Schr\u00F6dinger equation" .
.
"nonlinear optics" .
_:N502b4a47906c4a87a5ed5c3ea81adac8 .
"repulsive interactions" .
"Schr\u00F6dinger equation" .
_:N502b4a47906c4a87a5ed5c3ea81adac8 "Slusher" .
_:N15a1bdaa60294320a868b945a6c3591b .
"extension" .
_:N15a1bdaa60294320a868b945a6c3591b .
_:Nad00bf1740e744e286889df0afda621c .
"BEC experiments" .
"two-body collisions" .
_:N049f7388553945808f0fed01468c4a6b .
"laser lead" .
"P." .
"profile" .
"approximation" .
_:N8797258cc3dd4549818c7290314422ce .
_:N0cb5f83cc139457b903997b08a2dafcc .
"atom optics" .
.
.
"Wright" .
"E. M." .
"demonstration" .
"Gross-Pitaevskii equation" .
"Hartree approximation" .
"Physical Sciences" .
"en" .
"dark solitons" .
"lattice" .
"301-319" .
"cases" .
"new advances" .
_:N0cb5f83cc139457b903997b08a2dafcc "Benjamin J." .
"equations" .
_:N0cb5f83cc139457b903997b08a2dafcc "Eggleton" .
.
.
"Kerr nonlinear crystal" .
"collisions" .
"linear" .
"The experimental demonstration of Bose\u2014Einstein condensation in atomic vapors [1\u20133] 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 Schr\u00F6dinger 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, \u2018dips\u2019 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\u2014Pitaevskii equation." .
"vapor" .
_:Nc90f1639bd284f8e9a078844150d3873 "978-3-662-05144-3" .
"density profiles" .
"condensate" .
"solution" .
_:N8797258cc3dd4549818c7290314422ce "doi" .
_:Nad00bf1740e744e286889df0afda621c "dimensions_id" .
_:Nad00bf1740e744e286889df0afda621c "pub.1032166332" .
"dip" .
"chapter" .
_:Ncfe53fd6a6af4bf2b1799ca67017484e "Springer Nature" .
.
_:Nc90f1639bd284f8e9a078844150d3873 "978-3-642-07867-5" .
_:N737ca7d33b324544a6ec74d9f5ede9b7 _:N9627f03293ed4974858b73a6340c0c06 .
.
.
"advances" .
_:N737ca7d33b324544a6ec74d9f5ede9b7 _:N502b4a47906c4a87a5ed5c3ea81adac8 .
.
_:Nc90f1639bd284f8e9a078844150d3873 .
_:N9627f03293ed4974858b73a6340c0c06 .
_:N8797258cc3dd4549818c7290314422ce "10.1007/978-3-662-05144-3_14" .
"soliton solutions" .
"atomic solitons" .
_:Nc90f1639bd284f8e9a078844150d3873 .
_:Nfe0bd1e5b7d94ab0a336c7bbed6421ab .
"agreement" .
"2022-05-20T07:46" .
"Atomic, Molecular, Nuclear, Particle and Plasma Physics" .
"Atomic Solitons in Optical Lattices" .
"experimental demonstration" .
.
.
"simple solution" .
_:Na3bb8cb3ae2548fab7f820da0cb64107 _:Nfe0bd1e5b7d94ab0a336c7bbed6421ab .
"interaction" .
"optical lattice" .
"condensation" .
"2003" .
"lead" .
"P\u00F6tting" .
"nonlinear crystal" .
"https://scigraph.springernature.com/explorer/license/" .
"prediction" .
"true"^^ .
_:Nc90f1639bd284f8e9a078844150d3873 "Nonlinear Photonic Crystals" .
"S." .
_:N9627f03293ed4974858b73a6340c0c06 _:N0cb5f83cc139457b903997b08a2dafcc .
_:Nfe0bd1e5b7d94ab0a336c7bbed6421ab .
_:Ncfe53fd6a6af4bf2b1799ca67017484e .
"good agreement" .
"atomic vapor" .
"chapters" .
_:N8797258cc3dd4549818c7290314422ce .
"nonlinear regime" .
"Bose-Einstein condensation" .
_:N15a1bdaa60294320a868b945a6c3591b _:Na3bb8cb3ae2548fab7f820da0cb64107 .
"experiments" .
.