Optimal interrogation time
Longer phase accumulation helps until coherence loss outweighs the gain.
$$F(T)\propto T^2e^{-2T/T_2}$$
Physical intuition
Longer phase accumulation helps until coherence loss outweighs the gain.
Deep dive: physical mechanism
Optimize the Fisher information per unit wall-clock time, including preparation, dead time and readout overhead.
What is measured experimentally?
Sensitivity versus T typically has a finite optimum.
Assumptions, noise and limitations
The stated envelope assumes simple exponential dephasing.
Research and simulation exercise
Find the best Ramsey time with finite preparation and readout overhead.
Connect the ideas
Explore the chapter overview, learning path, and references.