Figure 1

The energy spectra are plotted as functions of the dimensionless inverse scattering length in trap oscillator units $a_{ho}/a_{\mathrm{sc}}$ for the three few-body systems considered. The various classes and typical sublevels in each class are indicated by arrows on the figure. (a) BBF $L=0^{+}$. (b) BBFF $L=0^{+}$. (c) BBFF $L=1^{-}$. The inset shows a blowup of avoided crossings and a pictorial demonstration of our diabatization near unitarity.Reuse & Permissions

Figure 2

The final probability distributions are plotted vs the ramping speed. Starting from the ground state of the nearly noninteracting few-body system, as the dimensionless ramping speed $\chi =\frac{M}{\hslash \rho }\left|\frac{d\lambda }{dt}\right|$ [$\lambda =(1/a_{\mathrm{sc}})$] is varied, one can access various strongly interacting final states. On these figures, the plotted data points give the result of full numerical calculations, while the curves are our best fits using a analytical Landau-Zener model. The functional forms for each fit are given in Table . (a) BBF $L=0^{+}$. (b) BBFF $L=0^{+}$. (c) BBFF $L=1^{-}$.Reuse & Permissions

Figure 3

Some important $P$-matrix elements are shown, which have been numerically calculated as $P_{ij}=\langle {\Psi }_i|\frac{d}{d\lambda }{\Psi }_j\rangle$, where $\lambda =\frac{a_{ho}}{a_{\mathrm{sc}}}$. (a) BBF $L=0^{+}$. (b) BBFF $L=0^{+}$. (c) BBFF $L=1^{+}$. The inset of each figure contains an expanded view of the $P$-matrix elements except for $P_{12}$. Both numerical calculated $P$-matrix elements and their fitted curve by a Lorentzian profile are shown. The number labeling of $P$ matrix ($P_{ij}$) between different classes are: (a) 1: BBF, 2: BF+B, 3: B+B+F, (b) 1: BBF+F, 2: BF+B+F, 3: B+B+F, and (c) 1: BBF+F, 2: BF+BF, 3: BF+B+F, 4: B+B+F+F.Reuse & Permissions

Figure 4

The molecule formation percentage is depicted as a function of the dimensionless ramp speed for (a) $L=0^{+}$ and (b) $L=1^{-}$ BBFF systems. Since the trimer and dimer were not distinguished experimentally, two separate analyses are presented here. In one analysis, a trimer is counted as a molecule (dashed line) and in the other analysis the trimer formed is excluded from the molecules counted (solid line).Reuse & Permissions

Figure 5

Comparison of our numerical calculation carried out in the adiabatic representation of a two-level system (red squares) with the numerical calculation in the diabatic representation for a multilevel system (blue diamonds). Also shown is the analytical Landau-Zener model's prediction for the asymptotic behavior of the transition probability as a solid curve. (a) The probability to form a trimer state as a function of ramping speed $\alpha =\frac{d{V}_0}{dt}$ is shown in the two-level adiabatic calculation, the unit of $\alpha$ is $\frac{\hslash {\omega }^2}{2\pi }$. The levels included are the lowest BBF+F channel and lowest BF+B+F channel. (b) The cosine function of the phase accumulated during the transition is shown, where the phase is defined as the phase of the wave function minus the semiclassical phase. (This test is carried out in the BBFF $L=0$ case.)Reuse & Permissions