  Microscopic studies of superconductors and their vortices play a pivotal role
in our understanding of the mechanisms underlying superconductivity. Local
measurements of penetration depths or magnetic stray-fields enable access to
fundamental aspects of superconductors such as nanoscale variations of
superfluid densities or the symmetry of their order parameter. However,
experimental tools, which offer quantitative, nanoscale magnetometry and
operate over the large range of temperature and magnetic fields relevant to
address many outstanding questions in superconductivity, are still missing.
Here, we demonstrate quantitative, nanoscale magnetic imaging of Pearl vortices
in the cuprate superconductor YBCO, using a scanning quantum sensor in form of
a single Nitrogen-Vacancy (NV) electronic spin in diamond. The sensor-to-sample
distance of ~10nm we achieve allows us to observe striking deviations from the
prevalent monopole approximation in our vortex stray-field images, while we
find excellent quantitative agreement with Pearl's analytic model. Our
experiments yield a non-invasive and unambiguous determination of the system's
local London penetration depth, and are readily extended to higher temperatures
and magnetic fields. These results demonstrate the potential of quantitative
quantum sensors in benchmarking microscopic models of complex electronic
systems and open the door for further exploration of strongly correlated
electron physics using scanning NV magnetometry.
