Spin-dependent inelastic collisions in spin-2 Bose-Einstein condensates

We studied spin-dependent two-body inelastic collisions in $F=2$ ${}^{87}\text{R}\text{b}$ Bose-Einstein condensates both experimentally and theoretically. The ${}^{87}\text{R}\text{b}$ condensates were confined in an optical trap and selectively prepared in various spin states in the $F=2$ manifold at a magnetic field of 3.0 G. The measured atom loss rates depend on the spin states of colliding atoms. We measured two fundamental loss coefficients for two-body inelastic collisions with total spins of 0 and 2. The loss coefficients determine the loss rates of all the spin pairs. The experimental results for mixtures of all spin combinations are in good agreement with numerical solutions of the Gross-Pitaevskii equations that include the effect of a magnetic field gradient.

Figure 1

(Color online) Inelastic collision rates $K_2^{\left(m,m^{\prime }\right)}$ for all combinations of $m$ and $m^{\prime }$ in a spin-2 BEC. A rectangle that connects two ellipses corresponds to a collision between two different components, whereas a rectangle linked to one ellipse corresponds to a collision between the same component.

Figure 2

(Color online) Time dependence of the number of atoms in a single-component BEC initially prepared in $|2,0⟩$ (filled circles), $|2,-1⟩$ (open squares), and $|2,-2⟩$ (open triangles) states. The inset shows the decay of $|2,-2⟩$ atoms for a longer period. The experimental data are fitted by Eq. (17) (dashed lines). The theoretical curves are calculated from the GP equation (solid lines).

Figure 3

(Color online) Time dependence of numbers of condensed atoms for various initially populated spin states (a) $\left(2,-1\right)+\left(2,-2\right)$, (b) $\left(2,0\right)+\left(2,-2\right)$, (c) $\left(2,+1\right)+\left(2,-2\right)$, (d) $\left(2,+2\right)+\left(2,-2\right)$, (e) $\left(2,0\right)+\left(2,-1\right)$, and (f) $\left(2,+1\right)+\left(2,-1\right)$ pairs. The theoretical curves are calculated from Eq. (23) with the SMA (dotted and dashed lines) or the GP equations that include the effect of a magnetic field gradient (solid and dot-dashed lines).

Figure 4

(Color online) Relative center-of-mass positions of (a) $\left(2,0\right)+\left(2,-1\right)$ pair (open circles) and $\left(2,0\right)+\left(2,-2\right)$ pair (closed circles), (b) $\left(2,+1\right)+\left(2,-2\right)$ pair (closed triangles) and $\left(2,-1\right)+\left(2,-2\right)$ pair (open triangles), (c) $\left(2,+1\right)+\left(2,-1\right)$ pair (open squares), and $\left(2,+2\right)+\left(2,-2\right)$ pair (open triangles).

Figure 5

(Color online) Axial profiles of averaged density distributions for various spin states at an evolution time of 100 ms. Initially populated to (a) $\left(2,-1\right)+\left(2,-2\right)$, (b) $\left(2,0\right)+\left(2,-2\right)$, (c) $\left(2,+1\right)+\left(2,-2\right)$, (d) $\left(2,+2\right)+\left(2,-2\right)$, (e) $\left(2,0\right)+\left(2,-1\right)$, and (f) $\left(2,+1\right)+\left(2,-1\right)$ states with equal population.