Local oscillator requirements for timekeeping in the 10-14 τ-1/2 era

A method of using current local oscillators for timekeeping standards based on Ramsey interrogation of large ensembles of ions or atoms, such as a linear ion trap or a pulsed atomic fountain, is proposed and analyzed. The time domain is used to analyze these systems. The atomic ensemble is regarded as the reference oscillator to measure the local oscillator´s accumulation of the phase error during the time interval between the two Ramsey interactions. Thus, the local oscillator´s degradation of timekeeping can be largely limited to the accumulation of local oscillator phase error during the dead time between Ramsey interrogation cycles. The degradation is studied and presented for different local oscillators in the context of a pulsed atomic fountain. For timekeeping, current quartz local oscillators could be used in a pulsed cesium fountain frequency standard to approach the σ_y(τ) regime of 10^-14τ^-1/2, and with improved local oscillators could be spectacularly better