Improving Estimation of Fock Probabilities And Parity of Trapped Ion Motional States

The motions of trapped ions can be used for quantum information protocols, and researchers are manipulating these motional states with increasing fidelity and complexity. In this work, we study the estimation of the parities and fidelities of ion motional states. Ion motion can be coupled to ion spin by applying laser pulses to either the carrier, blue, or red sidebands by adjusting the detuning of the laser. The probability of measuring the ion spin up after a particular laser pulse duration depends on the motional state's Fock distribution. We estimate the Fock distribution by fitting it to the spin-up probability versus the laser pulse duration curve. We seek to improve the estimation of Fock distribution and its parity by optimizing the choices of laser pulse durations, using both the carrier and blue sidebands. We present simulations of these measurements and estimates based on Beryllium ions. In future work we plan to apply these techniques to tomography of the motional state based on measuring the Fock parity after applying displacements.