We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov--de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.
We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.
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.
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. © Springer Science+Business Media, LLC 2007.
Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.
Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.
We study the matter-wave solitons in Bose-Einstein condensate (BEC) trapped on a M\"obius st rip (MS), based on the respective Gross-Pitaevskii (GP) equation with the mean-field theory. In the linear regime, vortex states are characterized by quantum numbers,
n and
m, corresponding to the transverse and circumferential directions, with the phase structure determined by the winding number (WN)
m. Odd and even values of
n must associate, respectively, with integer and half-integer values of
m, the latter ones requiring two cycles of motion around MS for returning to the initial phase. Using variational and numerical methods, we solve the GP equation with the attractive nonlinearity, producing a family of ground-state (GS) solitons for values of the norm below the critical one, above which the collapse sets in. Vortex solitons with
n=1,m=1 and
n=2,m=1/2 are obtained in a numerical form. The vortex solitons with
n=1,m=1 are almost uniformly distributed in the azimuthal direction, while ones with
n=2,m=1/2 form localized states. The Vakhitov-Kolokolov criterion and linear-stability analysis for the GS soliton solutions and vortices with
n=1,m=1 demonstrates that they are completely stable, while the localized states with
n=2,m=1/2 are completely unstable. Finally, the motion of solitons on the MS and the collision of two solitons are discussed.