Adaptive Measurements in Quantum Magnetometry

Abstract

We present an implementation of sequential Bayesian experiment design[1] for efficient Ramsey sequence magnetometry using NV centers in diamond. In the Ramsey sequence, the magnetic field is encoded as a phase difference between two spin states, where the phase accumulates over a selected precession time τ, and the experimental signal oscillates as a function of τ with precession frequency ω = γ B. The challenge is to choose values of τ that make efficient use of measurement time tm to reduce the field uncertainty σB. We use the equivalent noise sensitivity η = σB tm1/2 as a figure of merit. Sequential Bayesian experiment design chooses measurement settings (τ) by forecasting measurement outcomes and the effects they would have on the parameter distributions. The measurement benefit is quantified as the change in the information entropy of the parameter distribution and the measurement cost is the time required. With each measurement, more precise parameter distributions are inferred from new measurement data, improving forecasts and τ choices for later iterations. Results plotted in Fig. 1 compare the performance of sequential Bayesian experiment design with three other protocols: a non-adaptive variant of the quantum phase estimation algorithm (QPEA) [2], nonadaptive random selection of τ (Random), and an adaptive heuristic that chooses τ inversely proportional to the frequency uncertainty (Tau) [3]. For consistency, all measurement data is interpreted using Bayesian inference. The main figure plots the evolution of η against combined computation time and simulated measurement time. The vertical axis allows comparison of average uncertainty at a fixed measurement time. The inset plots η2, allowing comparison of time required to achieve a given uncertainty. The SBED protocol is faster than the Tau, Random, and QPEA protocols by factors of 2, 4 and 5, respectively.  Fig. 1. Comparison of equivalent noise sensitivity η = σB tm1/2 achieved by different measurement protocols. Initial measurements have small effects on the field uncertainty σB as tm increases. After 1 s of measurment, all protocols have converged to aymptotic σB∝ tm-1/2 behavior. The sequential Bayesian experiment design olffers the best performance.