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Molecules have vibrational, rotational, spin-orbit and hyperfine degrees offreedom, each of which responds in a unique fashion to external electromagneticradiation. The coherent control over superpositions of these quantum states iskey to manipulation of molecules. For example, the better the coherence timethe longer quantum simulations can last. The important quantity for controllinga molecule with laser light is its complex-valued molecular dynamicpolarizability. Its real part determines the tweezer potential as felt by themolecule, while its imaginary part contributes to the coherence time. Ourstudies show that efficient trapping of a molecule in an optical potential canbe achieved by a selecting laser frequency that has a small detuning (on theorder of tens of GHz) relative to an electric-dipole-forbidden moleculartransition. Close proximity to this transition allows us to significantlymodify the trapping potentials for multiple rotational states withoutsacrificing coherences among these states. We demonstrate that magic trappingconditions for multiple rotational states in ultracold 23Na87Rb polar moleculecan be created. In addition, we show that spin-decoupled magic trapping can beachieved with an applied static electric field oriented along the magneticfield direction.

Magic Traps for Multiple Rotational States of NaRb Molecule