Electric Field Gradient Gates for Quantum Logic with Molecular Ions

Molecular ions possess a rich internal structure which, while introducing technical challenges, can offer a fruitful environment as a quantum information platform. An intriguing feature of many molecular species is that they contain low-lying opposite-parity states, for example rotational or lambda-doublet states, with electric-dipole transitions in the radio frequency or microwave regime. Atomic ions do not have electric-dipole transitions between their long-lived ground states and transitions between these states must be performed via Raman lasers or magnetic field gradients.  Application of radio frequency voltages to the electrodes of an ion trap containing a molecular ion possessing these electric-dipole-connected low-lying states can implement a universal laser-free gate set (Phys Rev A 104, 042605). By appropriate configuration of these applied voltages we can create a uniform electric field to generate single-qubit rotations and electric field gradients to generate entanglement. In our experiment we have co-trapped H³⁵Cl⁺ with ⁴⁰Ca⁺ to demonstrate this technique and drive transitions between opposite-parity hyperfine molecular states.