Magnetic sensors capable of detecting nanoscale volumes of spins allow for non-invasive, element-specific probing. The error in such measurements is usually reduced by increasing the measurement time, and noise averaging the signal. However, achieving the best precision requires restricting the maximum possible field strength to much less than the spectral linewidth of the sensor. Quantum entanglement and squeezing can then be used to improve precision (although they are difficult to implement in solid-state environments). When the field strength is comparable to or greater than the spectral linewidth, an undesirable trade-off between field strength and signal precision occurs. Here, we implement novel phase estimation algorithms on a single electronic spin associated with the nitrogen-vacancy defect centre in diamond to achieve an ∼8.5-fold improvement in the ratio of the maximum field strength to precision, for field magnitudes that are large (∼0.3 mT) compared to the spectral linewidth of the sensor (∼4.5 µT). The field uncertainty in our approach scales as 1/T(0.88), compared to 1/T(0.5) in the standard measurement approach, where T is the measurement time. Quantum phase estimation algorithms have also recently been implemented using a single nuclear spin in a nitrogen-vacancy centre. Besides their direct impact on applications in magnetic sensing and imaging at the nanoscale, these results may prove useful in improving a variety of high-precision spectroscopy techniques.
Non-invasive magnetic field sensing using optically -detected magnetic resonance of nitrogenvacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi2B2C, Ba0.6K0.4Fe2As2, Ba(Fe0.93Co0.07)2As2, and CaKFe4As4, superconductors, with diffraction -limited spatial resolution using variable -temperature confocal system. Magnetic induction profiles across the crystal edges were measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all superconductors show nearly perfect screening of magnetic fields applied after cooling to temperatures well below the superconducting transition, Tc, a range of very different behaviors was observed for Meissner expulsion upon cooling in static magnetic field from above Tc. Substantial conventional Meissner expulsion is found in LuNi2B2C, paramagnetic Meissner effect (PME) is found in Nb, and virtually no expulsion is observed in iron-based superconductors. In all cases, good correlation with macroscopic measurements of total magnetic moment is found. Our measurements of the spatial distribution of magnetic induction provide insight into microscopic physics of the Meissner effect.
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