We show that a Bose-Einstein condensate and a portion of its surrounding thermal cloud can exhibit mutual self-trapping, supported by the attractive particle interactions, and not by the external confinement. This type of dynamics is characteristic of composite random-phase solitons.
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.
We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.
We discuss a method for creating bright matter solitons by loading a Bose-Einstein condensate of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focusing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than some critical value gmin, this self-focusing regime is followed by the formation of bright solitons. Increasing the interactions above another critical value gmax makes this process unstable. Instead of soliton formation one now meets the phenomenon of incoherent self-trapping. In this regime a fraction of atoms is trapped in incoherent localized wave packets, while the remaining atoms spread ballistically.
Solitons are non-dispersive wave packets that balance the wave dispersion with a focusing nonlinearity. They maintain their shape and velocity after collisions with other solitons, owing to the integrability of the underlying nonlinear partial differential equations. They appear in various physical systems, such as water waves, light waves in optical fiber, and matter waves. In our laboratory, we study solitons and their interactions in a Bose-Einstein condensate with an attractive nonlinearity, trapped in a quasi-one-dimensional waveguide. We investigate the collisions of a pair of solitons and explore the relative phase implications on the boundary of integrability. We study soliton train formation with the quench of the nonlinearity strength, and interactions between neighboring solitons in the train. We form a composite soliton, known as a breather, where multiple solitons overlap and the wavefunction ``breathes'' in time. We also explore the response of an elongated condensate to an external modulation of the nonlinearity. These experiments characterize the mean-field descriptions of solitons and Bose-Einstein condensates and explore the boundaries between the mean-field theory and quantum many-body theory.
We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and N-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature. PACS numbers: 03.75.Lm, 05.45.Yv, 67.80.Gb 1.
The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Nature (London) 417, 150 (2002)]] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales.