Colloquium: Quantum limits to the energy resolution of magnetic field sensors

The energy resolution per bandwidth E-R is a figure of merit that combines the field resolution, bandwidth or duration of the measurement, and size of the sensed region. Several different dc magnetometer technologies approach E-R = h, while to date none have surpassed this level. This suggests a technology-spanning quantum limit, a suggestion that is strengthened by model-based calculations for nitrogen-vacancy centers in diamond, for superconducting quantum interference device sensors, and for some optically pumped alkali-vapor magnetometers, all of which predict a quantum limit close to E-R = h. This Colloquium reviews what is known about energy resolution limits, with the aim of understanding when and how E-R is limited by quantum effects. A survey of reported sensitivity versus size of the sensed region for more than 20 magnetometer technologies is included, the known model-based quantum limits are reviewed, and possible sources for a technology-spanning limit are critically assessed, including zero-point fluctuations, magnetic self-interaction, and quantum speed limits. Finally, sensing approaches are described that appear to be unconstrained by any of the known limits, thus making them candidates to surpass E-R = h.