An ensemble of atoms is used to estimate an unknown angular frequency by Ramsey…

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

An ensemble of N=8N=8 atoms is used to estimate an unknown angular frequency ω\omega by Ramsey interferometry, either as NN independent atoms or as a single NN-atom GHZ state, each atom dephasing independently with coherence time T2=4 sT_2=4\,\mathrm{s}. A total measurement time T=20 s\mathcal{T}=20\,\mathrm{s} is available, and each scheme's free-precession shot length is separately optimised to maximise the total Fisher information about ω\omega. Both optimised schemes then reach the same best achievable uncertainty, Δω=2eNTT2.\Delta\omega=\sqrt{\frac{2e}{N\mathcal{T}T_2}}. ((a)) Evaluate Δω\Delta\omega for the numbers above. ((b)) State whether the GHZ state gives any advantage over independent atoms here, once dephasing is included.

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