tuning the rf frequency with extremely high precision, which may allow for ultra-sensitive measurements of molecular binding energies and scattering properties. Since rf fields can be switched in a very fast and controllable way [10], the rf-shifted Feshbach resonances offer the possibility of tuning the interaction between the atoms on a much shorter timescale than is possible using dc magnetic fields alone. The fast manipulation of ultracold atomic gases may be exploited to enhance the fidelity of quantum logic gates based on collisional interactions. In particular, a controlled phase gate, equivalent to a quantum CNOT, can be realized with nearly perfect fidelity by “activating” the atom-atom interaction, via rf fields, for the time needed for the system to acquire a π phase nonlinearity among the two-atom logical basis (i.e. hyperfine) states, see e.g. [30]. The ability to control spin-dependent interactions is also important in the context of simulating highly correlated many-body systems with ultracold atoms in optical lattices [3]. On atom chips, near-field rf control would add the capability of addressing individual pairs of atoms, an essential feature for universal quantum computation that is known to be difficult to realize with optical lattices. We thank J. Thywissen, P. Julienne, and T. Hanna for discussions and E. Tiesinga for providing the Rb$_{2}$ potentials. This work was supported by NSERC of Canada, the Austrian Science Foundation grant FWF-Z 118-N16, the EC (projects SCALA, CHIMONO), and the Chemical Science, Geoscience, and Bioscience Division of the Office of Basic Energy Science, Office of Science, U.S. Department of Energy and NSF grants to the Harvard-MIT CUA and ITAMP at Harvard University and Smithsonian Astrophysical Observatory. ∗ tshcherb@cfa.harvard.edu [1] C. Chin et al. , Rev. Mod. Phys., in press (2010), e-print arXiv:0812.1496. [2] I. Bloch, Nature (London) 453 , 1016 (2008). [3] S. Trotzky et al. , Science 319 , 295 (2008). [4] K. Xu et al. , Phys. Rev. Lett. 91 , 210402 (2003). [5] T. Weber et al. , Science 299 , 232 (2003). [6] P. O. Fedichev et al. , Phys. Rev. Lett. 77 , 2913 (1996); M. Theis et al. , Phys. Rev. Lett. 93 , 123001 (2004). [7] R. V. Krems, Phys. Rev. Lett. 96 , 123202 (2006); Z. Li and R. V. Krems, Phys. Rev. A 75 , 9