Entanglement and decoherence in a trapped-ion quantum register

This thesis describes the construction of a small quantum register using laser-cooled 9Be+ ions in a linear RF trap. Each qubit corresponds to a single trapped ion, with the two qubit levels being two hyperfine sublevels of the ground electronic state. I outline the basics of ion trapping and cooling and describe the operation of single-qubit logic gates using Raman transitions. I then review work performed during my tenure. We have realized an entangling gate and have produced entangled states of up to four ions. This gate enables universal quantum logic on two qubits in our system. We investigated several applications of this two-qubit register. We demonstrated a violation of a Bell inequality that closes the detector loophole. This experiment was the first to perform a complete set of Bell correlation measurements on massive particles. We also demonstrated rotation angle estimation with precision better than the standard quantum limit (SQL) using a two-ion entangled state. As a special case, we performed Ramsey spectroscopy at precision better than the SQL, opening a possibility for improvement of atomic clocks. We observed a number of decoherence mechanisms in our register, the most prominent being magnetic field fluctuations and heating of the ion motion. We propose a way to eliminate the effects of heating Finally, we implemented a decoherence-free quantum memory that was shielded from the effects of magnetic field fluctuations. Encoding one qubit's worth of information in the decoherence-free subspace of two ions increased the memory lifetime by a factor of three under ambient conditions.