Atomic combination clocks

Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, partially cancel leading to improved stability and a reduction in the corresponding systematic shifts. We present and analyze two examples of such combinations. The first uses the optical quadrupole transitions in a Ca-40(+)-Yb-174(+) two-ion system. The second is a superposition of optical quadrupole transitions in one Sr-88(+) ion and three Hg-202(+) ions. These combinations have reduced susceptibility to external magnetic fields and blackbody radiation.