| Summary: | Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio-frequency radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the Hamiltonian describing this coupling in the presence of a resonant dynamic gradient, is identical, in a dressed state basis, to the Hamiltonian in the case of a static gradient. The coupling strength is in both cases described by the same effective Lamb-Dicke parameter. This insight can be used to overcome demanding experimental requirements when using a dynamic gradient field for state-of-the-art experiments with trapped ions, for example, in quantum information science. At the same time, this insight opens new experimental perspectives by way of using a single resonant or detuned dynamic gradient field, inducing long-range coupling, for conditional multi-qubit dynamics.
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