Quantum Logic of Molecular States through Electric-field Gradients on a Cryogenic Ion Trap*

The rich state space of dipolar molecular ions in the microwave (MW) regime offers an intriguing laser-free platform to realize universal quantum gates. It was recently shown (PhysRevA. 2021, 104, 042605) that phonon-mediated quantum gates can be achieved by applying quadrupole microwave electric fields gradients via the electrodes of an ion trap, so called electric field gradient gates (EGGs). In order to suppress the chemical reaction due to background gas and reduce the blackbody radiation (BBR) for better rovibrational quantum state control, we have developed a cryogenic Paul trap with <30 nm displacement due to vibration at the ion trap. We have succeeded in cotrapping HCl⁺ with Ca⁺ in an ion chain. Moreover, we have applied sideband cooling and been able to cool all the motional modes less than 0.1 phonon. Finally, we will discuss how to use this new platform to pursue EGGs.