A collaboration builds a magnetometer from ultracold atoms
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies
Quantum Information and Technology, Ch Quantum metrology and sensing
Problem
A collaboration builds a magnetometer from N=900 ultracold atoms, prepared in a 900-atom GHZ state for Ramsey interferometry, with each atom's independent dephasing time T2=2s. They compare it with 900 independent (unentangled) atoms under the same total averaging time, each scheme run with its own best free-precession (shot) time, and report: "Because the noiseless Heisenberg limit is N=30 times better than the standard quantum limit, our GHZ magnetometer is thirty times more sensitive than 900 independent atoms."
((a)) Identify the physical assumption behind the quoted noiseless Heisenberg limit that is violated by the atoms' finite T2.
((b)) Using the boxed result that both schemes, once each is optimised over its own free-precession time, reach the identical Δω=2e/(NTT2), state the improvement factor the GHZ state actually delivers over 900 independent atoms.
((c)) State the largest improvement factor any entangled state of these atoms could deliver under this noise model, and explain why the collaboration's figure of thirty is not attainable however the experiment is tuned.