Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate

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.

Figure 1

(a) Matter-wave dispersion, i.e., evolution of the gas density without interactions present. (b) Coherent matter-wave solitonic evolution with GP equation. (c) Evolution of the gas with the TDHFB model; attractive interactions among atoms are present in figures (b) and (c). (d) The condensate fraction (black solid line) and the fraction of noncondensed atoms (blue dashed line). (e) The complex degree of coherence $\mu (x,x^{\prime },t)$ of a matter wave at $t=0$ (black dot-dashed line), and $t{\omega }_{\perp }=63.9$ [$\mathrm{Re}\mu (x,x^{\prime },t)$ blue solid line, and $\mathrm{Im}\mu (x,x^{\prime },t)$ red dashed line]; $x^{\prime }$ is placed at the position of the left peak. (f) The kinetic energies of the condensate $E_{\mathrm{kin},c}$ (blue solid line), thermal cloud $E_{\mathrm{kin},\mathrm{th}}$ (red dotted line), and total interaction energy $E_{\mathrm{int}}$ (green dashed line); total energy $E_{\mathrm{total}}=E_{\mathrm{kin},c}+E_{\mathrm{kin},\mathrm{th}}+E_{\mathrm{int}}$ is conserved (black dot-dashed line); energy is in units of $|E_{\mathrm{total}}|$.

Figure 2

(a) Evolution of the gas density with TDHFB. (b) The condensate fraction (black solid line) and the fraction of noncondensed atoms (blue dashed line) during TDHFB evolution. (c) Double peaked total density (solid line), and condensate density (dashed line) at $t{\omega }_{\perp }=37.6$. (d) The complex degree of coherence $\mu (x,x^{\prime },t)$ at $t{\omega }_{\perp }=37.6$ [$\mathrm{Re}\mu (x,x^{\prime },t)$ blue solid line, and $\mathrm{Im}\mu (x,x^{\prime },t)$ red dashed line]; $x^{\prime }$ is placed at the position of the left peak.