Measuring magnetic fields with magnetic field insensitive transitions

Atomic sensing is, at large, based on measuring energy differences. Specifically, magnetometry is typically performed by using a superposition of two quantum states, the energy difference of which depends linearly on the magnetic field due to the Zeeman effect. The magnetic field is then evaluated from repeated measurements of the accumulated dynamic phase between the two Zeeman states. Here we show that atomic clock states, with an energy separation that is independent of the magnetic field, can nevertheless acquire a phase that is magnetic field dependent. We experimentally demonstrate this on an ensemble of optically trapped Rb87 atoms. Finally, we use this effect to propose a magnetic field sensing method for static and time-dependent magnetic fields and analyze its sensitivity, showing it essentially allows for high-sensitivity magnetometery.