Non-demolition readout of a mechanical oscillator state in a symmetric linear ion crystal

Continuous-variable (CV) systems are an alternative to approaches using two-level systems for quantum information processing. An infinite-dimensional (or CV) Hilbert space, such as that of a harmonic oscillator (HO), can be used to encode "logical" qubit states (mutually orthogonal superpositions of energy eigenstates) for which quantum error correction (QEC) is possible through coupling to an auxiliary quantum system. Trapped-ion systems are a candidate for CV QEC by encoding information in motional degrees of freedom, which can be treated as HOs, while reading out error syndromes via internal electronic states. However, atomic motion is affected by photon recoil such that any information stored in motional modes is typically destroyed during fluorescence readout. Readout schemes that do not affect the motional state are thus an important prerequisite for motional-state verification in trapped-ion CV QEC. We demonstrate that the axial out-of-phase (OOPH) mode in a Be+-Mg+-Be+ crystal is nearly unaffected after scattering thousands of photons off the Mg+ ion. We also demonstrate a projective measurement that leaves the OOPH mode in number state |0> or |1> with high fidelity. It may be possible to modify this measurement to accommodate error syndrome readout for bosonic codes.