Experimental Demonstration of Entanglement-Enhanced Rotation Angle Estimation Using Trapped Ions

We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the ``standard quantum limit'' for nonentangled states. All methods use a form of quantum mechanical ``squeezing.'' In a system of two entangled trapped ⁹Be⁺ ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.