Using 'protected' modes in trapped ions to enable mid-algorithm measurements for CVQC

Measurements of the motional states of trapped ions require coupling the motion to the ions’ internal spin states. These measurements, however, require detection of spin-dependent fluorescence. Photon scattering, giving rise to fluorescence, causes the ion to recoil, which generally decoheres the ions’ motional modes. This decoherence prevents mid-algorithm measurements, which are necessary for processes that require classical feedback. Overcoming this challenge is likely necessary for the viability of practical continuous variable quantum computing (CVQC) in trapped ions.  To address this issue, we are investigating the use of ‘protected’ modes within chains consisting of an odd number of ions, where the center ion has zero displacement (3(N-2) protected modes with N ions).  As a demonstration we use a dual-species three-ion chain (⁸⁸Sr⁺ -⁴⁰Ca⁺ - ⁸⁸Sr⁺), which allows us to simply address the center ion with global laser fields. We perform measurements of the heating rate and coherence time, via Ramsey interferometry, of these protected modes, to determine how much the decohering effects of photon scattering are suppressed. We are also developing models to minimize the effects of symmetry breaking due to radiation pressure, and non-linear coupling between modes, on the coherence time of the protected modes.