We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit [T2=1.2(2)\s], and in external motional states of a single \Ca{40} trapped-ion qubit [T2′=0.18(4)\s], in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state T2 time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on \Ca{40} ions. Using a single spin-echo pulse to ``re-phase'' the internal state, we can detect no decoherence after 1\s, implying an effective coherence time T2\mboxSE\gtish45\s. This compares with timescales in this trap for single-qubit operations of \ish 1\us, and for two-qubit operations of \ish 10\us.
@article{arxiv.0710.4421,
title = {A long-lived memory qubit on a low-decoherence quantum bus},
author = {D. M. Lucas and B. C. Keitch and J. P. Home and G. Imreh and M. J. McDonnell and D. N. Stacey and D. J. Szwer and A. M. Steane},
journal= {arXiv preprint arXiv:0710.4421},
year = {2007}
}