Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in ${\mathrm{Pr}}^{3+}$ ions, doped into a ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Mølmer dark-state scheme [Roos and Mølmer, Phys. Rev. A 69, 022321 (2004)] Fidelities above $>90\%$, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Mølmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.

• Received 25 July 2007

DOI:https://doi.org/10.1103/PhysRevA.77.022307