103.3 103.4  (a.u.) 18 20 22 24 26 28 10 -2 10 0 10 2  (a.u.) 24 26 28 30 32 34 36 rf frequency   (MHz) 10 -2 10 0  (a.u.) 103 103.5  (a.u.) (d) (b) (c) (a) A B C D E A F B C D E F Fig. 3: The real (a) and imaginary (b) parts of the scattering length for s -wave collisions of $^{87}$Rb atoms initially in the | 1 , 1 〉 ⊗ | 2 , − 1 〉 state as functions of the rf frequency at B = 2 G. (c), (d) Same as in (a), (b) but for the | 1 , − 1 〉 ⊗ | 2 , 1 〉 initial state and B = 3 . 23 G. The rf amplitude is 4 G [blue (light grey) lines] and 10 G (black lines). The rf-induced resonances are labeled after the bound states A-F in Fig. 1. frequencies given by Eqs. (4) are shifted from those corresponding to bare molecular states by the amount δω ( B$_{rf}$ ) ∼ B 2 rf [28]. Because the rf-induced coupling is weak and α$_{bg}$ is large, the real part of the scattering length does not vary appreciably in the vicinity of the resonances, increasing from 103.7 to 106.5 a$_{0}$ near the resonance D as the rf frequency is scanned from 31.405 to 31.413 MHz. The inelastic loss rate at the resonance is ∼ 10 − 12 cm $^{3}$/s. From Eqs. (4), it is clear that α can be controlled more efficiently in atomic systems with smaller α$_{bg}$ . Alternatively, α$_{bg}$ can be reduced using magnetic [1] or electric [7] Feshbach resonances. As follows from Eqs. (4), α and β peak at different rf detunings: Δ$_{α}$ = ± γ$_{ba}$/ 2 and Δ$_{β}$ = 0, with peak heights ∼ γ$_{ib}$/γ$_{ba}$ . Therefore, to induce an appreciable variation of α 7