Limits on Spectral Resolution Measurements by Quantum Probes

The limits of frequency resolution measurements have been discussed extensively in recent years. It is believed that there is a crucial difference between resolution and the precision of a single frequency tracking. Whereas the efficiency of frequency tracking gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific time scale of the probe and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and for some limits both quantities behave in a similar way.