Localization of a magnetic moment using a two-qubit probe

Abstract: A nanomagnet precessing in an external magnetic field can be treated as a source of narrow-bandwidth magnetic noise, that leaves characteristic fingerprints in decoherence of a nearby spin qubit undergoing dynamical decoupling. We show how, by measurements of two-qubit coherence, a noise sensor composed of qubit pair can be used to reconstruct the position of the nanomagnet. Such localization of noise source is possible with only two qubit probes, because the course of coherence decay under appropriately designed dynamical decoupling sequences contain information not only about noises experienced by each qubit, but also about their cross-correlations. We test the applicability of the proposed protocol on an example of two qubits coupled to the nanomagnet via dipolar interaction. We also show how, using a two-qubit sensor possessing a particular symmetry, one can localize the nanomagnet even when the sensor-magnet coupling law is unknown.