Simulating unsharp measurements and state estimation using trapped ytterbium ions*

In this paper, we investigate the feasibility of experimentally performing unsharp quantum measurements using a system of two trapped ytterbium ions. The goal of the unsharp measurement protocol is to track the state of a trapped target ion qubit as it evolves in time by weakly coupling its state to an auxiliary ion and projectively measuring the auxiliary ion’s state. For this study, the goal was to track Rabi oscillations of the target ion, Yb-171, while measuring the auxiliary ion, Yb-174. This paper focuses on the approach to unsharp measurements described by Choudhary et al. [1] where the state of the target ion is weakly coupled to the vibrational mode of the ions that can be determined by a measurement on the auxiliary ion.

We investigate the implementation of the theory in a specific cost-effective experiment using two isotopes Yb-171 and Yb-174 as target and auxiliary systems respectively. We use an optical Bloch model to simulate the optical pumping sequence performed on the target ion during the unsharp measurement protocol. This simulates the evolution of the target state and calculates the probabilities for all outcomes of the unsharp measurement, including spontaneous decay via all decay paths. This improves on previous work [1] where spontaneous decay was considered only generally and estimated with an upper limit. Furthermore, we consider electron shelving, instead of quantum logic spectroscopy, for the measurement on the auxiliary.

Using these simulation results, we developed an independent simulation to estimate the qubit evolution which is informed by the outcomes of the unsharp measurements. This was done by modifying an updating scheme described in Konrad et al. [2]. The state estimation process is tested by comparing the estimated state to the simulated target state to show the feasibility of this measurement scheme in the case of the target qubit undergoing Rabi oscillations.

Conclusions are drawn on the feasibility of experimentally implementing the unsharp measurement theory, both generally and in our laboratory at Stellenbosch University.

[1] S.K. Choudhary, et al, Phys. Rev. A 87 (2013).

[2] T. Konrad, et al, Phys. Rev. A 85 (2012).