Non-destructive parity measurement of a motional cat state

Non-destructive parity measurements enable mid-circuit projections into eigenstates of parity. They can for example be used in quantum error correction as part of stabilizer error correction schemes. Trapped ions feature harmonic oscillator modes of motion and internal (electronic ) degrees of freedom, which make them suitable for quantum information processing. However, measurement typically relies on conditional fluorescence of an ion, “bright” or “dark”, to detect its internal state. Information in a motional mode will generally not be preserved after “bright” detection due to motional heating when the ion experiences thousands of photon recoils. We aim to demonstrate non-destructive parity measurements and apply them to create and characterize motional “Schrödinger’s cat” states in a mixed-species ion crystal of ⁹Be⁺-²⁵Mg⁺-⁹Be⁺. During fluorescence readout, the motional state will be held in a “protected” motional mode, in which the fluorescing Mg⁺ ion does not participate, to avoid the effects of photon recoil. A coherent state of motion whose parity is measured this way will be projected into either an even or odd motional cat state, with the cat-state parity heralded by the measurement. The parity can subsequently be verified by a second (destructive or non-destructive) measurement. I will discuss progress of critical steps needed to realize this protocol.