# SOLITONS GRIS, PHONONS ET DISSIPATION DANS UN CONDENSAT DE BOSE-EINSTEIN QUASI-UNIDIMENSIONNEL

Abstract : Since the experimental realization of the first Bose-Einstein condensates (BEc's), in $1995$, in ultra-cold ($T=0\,^(\mathrm(o))\!\mathrm(K)$) dilute vapor of alkali-metal atoms $\left( ^(87)Rb\,, \ ^(23)Na\,, \ ^(7)Li\right)$, confined in three-dimensional ($3D$) magnetic traps, the physics of the BEc's and of the Fermi has known a remarkable development both experimentally and theoretically. The purpose of this thesis has been fixed in the general frame of the recent progress accomplished in the study of the dynamical evolution of the repulsive BEc's and the reduction of their dimensionality. This thesis contains two parts. In the first, we describe the Bose-Einstein condensation phenomenon like it was predicted in $1925$ by Einstein in an ideal gas of bosonic atoms, and then realized in $1995$ in a dilute gas of alkali-metal atoms. We point out that the dynamical evolution of a dilute Bose-Einstein condensate at $T=0\,^(\mathrm(o))\!\mathrm(K)$ is accurately described by the non-linear Schr\"(o)dinger equation (NLSE), also known as the Gross-Pitaevskii equation (GPE). In the second part, we study the dynamical, dissipative and superfluid behaviours of a quasi-1D repulsive dilute Bose-Eintein condensate
confined in an elongated nonharmonic trap (elongated trap with parabolic boundaries). Our numerical results show that : i) the effect of the trap parabolic boundaries and of a Gaussian hump placed in the flat part of the same trap, is anti-damping on the uniform propagation of a gray soliton in the condensate. This effect manifests by a spontaneous emission of phonons
; ii) the production of a rectiline oscillating uniform motion by a Gaussian obstacle in the condensate, leads to the creation of gray solitons and phonons when the obstacle constant velocity exceeds a critical value. In this case, the Bose-Einstein condensate becomes a dissipative medium. We have illustrated that the dissipative behaviour of the condensate increases with the increase of the obstacle velocity, attains its maximum, then decreases and disappears at high values of the obstacle constant velocities. In this limit, the Bose-Einstein condensate behaves as a quasi-superfluid.
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https://tel.archives-ouvertes.fr/tel-00009805
Submitted on : Friday, July 22, 2005 - 7:18:59 PM
Last modification on : Thursday, December 10, 2020 - 12:38:42 PM
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• HAL Id : tel-00009805, version 1

### Citation

Abdelaziz Radouani. SOLITONS GRIS, PHONONS ET DISSIPATION DANS UN CONDENSAT DE BOSE-EINSTEIN QUASI-UNIDIMENSIONNEL. Matière Condensée [cond-mat]. Faculté des sciences de Rabat, 2004. Français. ⟨tel-00009805⟩

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