Dark-bright solitons in Bose-Einstein condensates at finite temperatures

We study the dynamics of dark-bright solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross-Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ("filling") soliton component is to partially stabilize "bare" dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on dark-bright soliton "molecules" (i.e., two in- and out-of-phase dark-bright solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.Comment: 24 pages, 13 figures, to appear in New J. Phy

Grey solitons in a strongly interacting superfluid Fermi Gas

The Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS to BEC) crossover problem is solved for stationary grey solitons via the Boguliubov-de Gennes equations at zero temperature. These \emph{crossover solitons} exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitary the velocity has a nearly linear dependence on phase difference over an extended range. For fixed phase difference the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power law relationship to express this fact: the density of grey crossover solitons varies as the square of the gap amplitude in the BEC limit and a power of about 1.5 at unitarity.Comment: 10 pages, 6 figures, part of New Journal of Physics focus issue "Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to QCD Plasmas," in pres