Novel ion traps that employ magnetic gradient fields allow for the application of conditional quantum logic, the essential prerequisite for quantum computing, by the use of radio-frequency radiation that can be generated by off-the-shelf electronics.
We show that the Hamiltonian describing the necessary couplings 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.
Our insights 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, we show new experimental perspectives by way of using a single dynamic gradient field, inducing long-range coupling, for conditional multi-qubit dynamics.