State selective detection of hyperfine qubits

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, state selective scattering of resonance fluorescence is well established. The simplest way to read out this measurement and assign a state is the threshold method. The detection error can be decreased by using more advanced detection methods like the time-resolved method (Myerson et al 2008 Phys. Rev. Lett. 100 200502) or the π-pulse detection method (Hemmerling et al 2012 New. J. Phys. 14 023043). These methods were introduced to qubits with a single possible state change during the measurement process. However, there exist many qubits like the hyperfine qubit of ¹⁷¹Y{{b}⁺} where several state change are possible. To decrease the detection error for such qubits, we develop generalizations of the time-resolved method and the π-pulse detection method for such qubits. We show the advantages of these generalized detection methods in numerical simulations and experiments using the hyperfine qubit of ¹⁷¹Y{{b}⁺}. The generalized detection methods developed here can be implemented in an efficient way such that experimental real time state discrimination with improved fidelity is possible.