Local Oscillator Induced Instabilities in Trapped Ion Frequency Standards*

The trapped ion frequency source is one of a class of passive atomic frequency standards that necessarily use an ancillary frequency source to interrogate the atomic transition. For passive atomic sources such as Rubidium standards, ultimate long term performance of the source is not dependent on this local oscillator, except to the extent limited by feedback gain. For the trapped ion source this immunity to local oscillator phase noise is lost. In contrast to the Rubidium source, a sequential measurement procedure is used in which the signal from the local oscillator is sensed only some of the time. Since the local oscillator is only periodically sampled, certain short term fluctuations in the local oscillator frequency will give rise to long term fluctuations in the difference between the stabilized local oscillator frequency and that of the atomic absorption. We have performed calculations of the influence of such phase noise fluctuations in the reference oscillator on the performance of the standard as a function of duty cycle for a local oscillator with frequency fluctuations showing a llf spectral density, as is typically shown by crystal Quartz oscillators for long measuring times (1-100 seconds). Expressions are generated for the limiting trapped ion 7-'12 variance due to the local oscillator for various values for the duty factor d. Explicitly treated are the cases d << 1, d = 1 6, (6 << 1) and d = 112. It is seen that for a duty factor < 90%, local oscillator performance equal to that of the ion standard (for a measuring time T equal to the period td of the sampling cycle) will significantly degrade the characteristic r-'I2 passive atomic standard performance. For d near 1, (6 = (1 d) << 1) an approximately linear dependence of this degradation on 6 is found.