A qubit is probed by a Ramsey sequence: a pulse

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantum Information & Technology · Data analysis and model fitting in the laboratory

Quantum Information and Technology, Ch What a qubit must do: requirements, tomography and benchmarking

Problem

A qubit is probed by a Ramsey sequence: a π/2\pi/2 pulse, free evolution for a time τ\tau, then a second π/2\pi/2 pulse and a measurement. At each τ\tau the fast oscillation of the fringe is fitted separately and its amplitude A(τ)A(\tau) recorded. The same qubit has also been characterised by two other sequences: inversion recovery gives T1=200 μsT_1 = 200\,\mu\mathrm{s} and a Hahn echo gives T2=80 μsT_2 = 80\,\mu\mathrm{s}. Data: τ=0,5,10,15,20 μs\tau=0,5,10,15,20\,\mu\mathrm{s} gives A(τ)=0.98,0.78,0.37,0.10,0.02A(\tau)=0.98,0.78,0.37,0.10,0.02 respectively. Shot-to-shot (quasi-static) frequency noise produces a Gaussian Ramsey envelope, A(τ)=A0exp⁡[−(τ/T2∗)2]A(\tau) = A_0\exp[-(\tau/T_2^*)^2]. ((a)) By fitting ln⁡A\ln A against τ2\tau^2 (least squares), extract T2∗T_2^* and A0A_0. ((b)) State, with a reason, whether this Ramsey decay is set by T1T_1, by the Hahn-echo T2T_2, or by something else, and name that something else.

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