Roton-mediated soliton bound states in binary dipolar condensates

Abstract

We investigate the formation of bound states between dark-antidark solitary waves in two-component dipolar Bose-Einstein condensates. The excitation spectrum contains density and spin branches, and a rotonic feature of the spin branch enables long-range soliton interactions, giving rise to multiple bound states for a single pair, each with a distinct separation. We show that these bound states originate from periodic modulations of the inter-soliton potential, while individual solitons are surrounded by spatial spin-density oscillations. Both features provide direct signatures of the spin roton. Collisions between unbound solitons probe this potential, with dipolar interactions enforcing universal bouncing at low velocities, independent of soliton sign, whereas nondipolar solitons may either transmit or bounce. This distinct behavior offers a realistic path to confirming spin rotons experimentally.

Figures (5)

• Figure 1: An isolated dark-antidark soliton in a binary dipolar condensate. (a) Density profiles: component 1 (solid) and component 2 (dot-dashed). (b) Wave function phase profiles. (c) Total-density profile. (d) Spin-density profile. Colors match the spin densities shown in Figs. \ref{['Fig:Pot']}(i-iii) and \ref{['Fig:Coll']}(b). Scattering lengths: $\{a_{11},a_{12},a_{22}\}/a_0 = \{140,105,140\}$.
• Figure 2: Relationship between the dispersion relations (left) and spin density (right) for a soliton in a binary condensate, shown without (a) and with (b) dipolar interactions. (a1) Dispersion relations for nondipolar mixtures with $a_{12} = [70, 95, 99]\,a_0$ from dark to light, and fixed intraspecies interactions $a_{11}=a_{22}=100\,a_0$. Solid (dashed) lines denote spin (density) branches; thin dashed line shows free-particle reference. (a2) Corresponding spin density profiles of dark-antidark solitons. (b1) Dispersion relations for binary dipolar condensate with $a_{12} = [70, 105, 108.4]\,a_0$, from dark to light, with $a_{11}=a_{22}=140\,a_0$. (b2) Corresponding spin-density profiles of dark-antidark solitons.
• Figure 3: (Main panel) Inter-soliton potential versus separation and interspecies scattering length for binary dipolar condensate. Crosses mark local minima where stationary-state bound states exist. Panels (i-iii) show oscillations of two solitons about the first, second, and third minima, respectively, for selected $a_{12}$ values (see double-headed arrows), with spin-density color coding as in Fig. \ref{['Fig1:Dens']}(d). The spin density is shown as a function of position and time. Intraspecies scattering lengths are fixed at $a_{11}=a_{22}=140a_0$.
• Figure 4: Inter-soliton potential versus soliton separation for a binary dipolar condensate. Three minima are present, corresponding to three regions where bound states can form. The insets show the density of component 1 (solid) and component 2 (dashed) of soliton pairs with separations $\Delta x/l\approx1.35$ and $\Delta x/l\approx2.7$, corresponding to a maximum (i) and a minimum (ii) in $V$, respectively. Contact interaction parameters: $\{a_{11},a_{12},a_{22}\}/a_0 = \{140,105,140\}$.
• Figure 5: Unbound collisional dynamics involving two initially nonmoving positive-core (blue) and two initially moving negative-core (red) dark-antidark solitons, shown (a) without and (b) with dipolar interactions. Spin density is shown as a function of position and time. Contact interaction parameters: (a) $\{a_{11},a_{12},a_{22}\}/a_0 = \{100,95,100\}$; (b) $\{a_{11},a_{12},a_{22}\}/a_0 = \{140,95,140\}$.