Two-mode squeezing and SU(1,1) interferometry with trapped ions

We experimentally implement circuits of one- and two-mode operations on two motional modes of a single trapped ion. This is achieved by implementing the required displacement, squeezing, two-mode squeezing, and beam-splitter operations using oscillating electric potentials applied to the trap electrodes. The resulting electric fields drive the modes resonantly or parametrically without the need for optical forces. As a demonstration, we implement SU(2) and SU(1,1) interferometers with phase sensitivities near the Cram & eacute;r-Rao bound. We report a maximum sensitivity of a SU(2) interferometer within 0.67(5) dB of the standard quantum limit (SQL) as well as a single- and two-mode SU(1,1) sensitivity of 5.9(2) dB and 4.5(2) dB below the SQL, respectively.