# High-dynamic-range magnetometry with a single nuclear spin in diamond

One main application of the nitrogen-vacancy defect in diamond is a sensor which can detect weak magnetic and electric fields at the nanoscale. This is done by measuring the field dependent shift in the Lamor frequency of the spin states using Ramsey interferometry: First, a ?/2 pulse creates a superposition of two spin states. The phase of this superposition will then undergo so called Ramsey oscillations, i.e. it will evolve periodically from 0 to 2? with a field dependent frequency. After a certain phase accumulation time, a second ?/2 pulse maps the accumulated phase onto spin state population, which is then measured. From the measurement result, one can deduce the accumulated phase, the Lamor frequency, and the applied field. However, due to the periodic modulation of the phase, such a measurement is ambiguous, which means that the applied field must be known within certain limits to unambiguously determine its value. Effectively, this limits the dynamic range of the sensor.

On the one hand, these limits are less severe for shorter phase accumulation times. On the other hand, longer phase accumulation times lead to a higher measurement precision, even for the same amount of total measurement time: By repeating a measurement with phase accumulation time τ for n times, the precision of the result scales as 1/ τ⋅n ^{0.5}, whereas the precision of a single measurement with phase accumulation time n⋅τ scales as 1/n⋅τ. By using a recently proposed phase estimation algorithm, we combined short, unambiguous measurements with long, high precision measurements. The performance of the algorithm can be seen in the Figure, which shows the probability that a certain phase (which depends on the applied field) was accumulated. For short phase accumulation times (bright region), the distribution is broad but has an unambiguous maxima. As measurements with longer phase accumulation times are included (darker regions), this maxima becomes more narrow.

With this algorithm, we achieved a precision scaling of a magnetic field measurement of T ^{-0.85}. For high precision measurements, the dynamic range of the sensor was thereby increased by a factor of 130.

**High-dynamic-range magnetometry with a single nuclear spin in diamond**

Nature Nanotechnology 10.1038/nnano.2011.224

G. Waldherr ^{1}, J. Beck ^{1}, P. Neumann ^{1}, R. S. Said ^{2}, ^{3}, M. Nitsche ^{1}, M. L. Markham ^{4}, D. J. Twitchen ^{4}, J. Twamley ^{2}, F. Jelezko ^{1}, ^{5} and J. Wrachtrup ^{1}

^{1} 3. Physikalisches Institut, Research Center SCOPE, and MPI for Solid State Research, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany,

^{2} Centre for Engineered Quantum Systems, Department of Physics & Astronomy, Faculty of Science, Macquarie University, Sydney, NSW 2109, Australia,

^{3} Institut für Quanten-Informationsverarbeitung, Universität Ulm, 89081 Ulm, Germany,

^{4} Element Six Ltd, King’s Ride Park, Ascot SL5 8BP, UK,

^{5} Institut für Quantenoptik, Universität Ulm, 89073 Ulm, Germany.