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The energy resolution per bandwidth $E_R$ is a figure of merit that combinesthe field resolution, bandwidth or duration of the measurement, and size of thesensed region. Several different dc magnetometer technologies approach $E_R =\hbar$, while to date none has surpassed this level. This suggests atechnology-spanning quantum limit, a suggestion that is strengthened bymodel-based calculations for nitrogen-vacancy centres in diamond, forsuperconducting quantum interference device (SQUID) sensors, and for someoptically-pumped alkali-vapor magnetometers, all of which predict a quantumlimit close to $E_R = \hbar$. Here we review what is known about energyresolution limits, with the aim to understand when and how $E_R$ is limited byquantum effects. We include a survey of reported sensitivity versus size of thesensed region for more than twenty magnetometer technologies, review the knownmodel-based quantum limits, and critically assess possible sources for atechnology-spanning limit, including zero-point fluctuations, magneticself-interaction, and quantum speed limits. Finally, we describe sensingapproaches that appear to be unconstrained by any of the known limits, and thusare candidates to surpass $E_R = \hbar$.

Quantum limits to the energy resolution of magnetic field sensors