Progress Toward Microwave- and RF-Based Mixed-Species Quantum Logic in Trapped Ions

We report progress on quantum logic implemented using microwave and radiofre-

quency magnetic fields together with magnetic field gradients in a mixed-species trapped-

ion system. This approach avoids direct optical interactions on the data ion, thereby

mitigating spontaneous-emission-induced errors and surface charging associated with

short-wavelength laser light. Our platform consists of a co-trapped ²⁵Mg⁺ data ion and

⁴⁰Ca⁺ helper ion confined in a surface-electrode trap. A key challenge in mixed-species

control arises from charge-to-mass ratio mismatch, which leads to imbalanced motional

mode participation, particularly in radial modes relevant for magnetic-field-gradient-

based spin–motion coupling. To address this, we can implement mode–mode coupling

between a Mg-dominant motional mode and a Ca-dominant motional mode, allow-

ing controlled hybridization and redistribution of mode participation. This capability

provides a route toward sympathetic cooling of data-ion-dominant motional modes

mediated by the helper ion and offers a means of controlling the effective spin–motion

coupling in the mixed-species crystal. Building on these capabilities, we are pursuing

quantum logic state preparation of Mg⁺ based on microwave sideband pumping within

its hyperfine manifold, with dissipation provided indirectly through repeated ground-

state cooling of the shared motional modes using Ca⁺. Together, mode hybridization

via mode–mode coupling, microwave-based spin–motion interactions, and prospective

quantum logic state preparation and readout mediated by the helper ion establish the

essential ingredients for mixed-species quantum logic and provide a pathway toward

mixed-species entangling gate operations between the data and helper ion mediated by

magnetic field gradients.