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Quantum control of $^{88}$Sr$^+$ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the $S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions' external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar n=0.05$ and a heating rate of $\dot{\bar n}=0.016$ ms$^{-1}$ is measured.