Precision frequency measurements with entangled ions

Summary form only given. The use of entangled states can provide an increased sensitivity in quantum-limited spectroscopic measurements, leading to an uncertainty that is inversely proportional to the number of particles instead of the usual square-law dependence. In this contribution, we show that spectroscopy with maximally entangled states of atoms also offers significant advantages over experiments done with single atoms. As a first example, we demonstrate that entanglement can be used to effectively eliminate first-order Zeeman shifts in spectroscopy with ⁴⁰Ca⁺ even though there are no m=0 -> m=0 transitions. Secondly, we discuss how maximally correlated states of two ⁴⁰Ca⁺ could be used for measuring tiny frequency shifts of the S1/2 - D5/2 transition arising from second-order Zeeman shifts and electric quadrupole shifts due to the trapping potential.