A trapped ion is read out by state-dependent fluorescence
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies
Quantum Information and Technology, Ch Trapped ions, neutral atoms, photons, NMR and spins in solids
Problem
A trapped 88Sr+ ion is read out by state-dependent fluorescence. When the ion is in the bright (fluorescing) state, the detector registers a Poisson-distributed number of photons with mean 9 during the readout window. When the ion is in the dark state, it registers a Poisson-distributed background with mean 0.05 counts. The threshold rule is: call the result 'bright' if 2 or more counts are recorded, and 'dark' otherwise.
((a)) Find the probability that a bright ion is wrongly registered as dark.
((b)) Find the probability that a dark ion is wrongly registered as bright.