The short-term instability in the frequency of a linear-ion-trap frequency standard (LITS) can be reduced by modifying two cycles involved in its operation: (1) the bimodal (bright/dim) cycle of a plasma discharge lamp used for state preparation and detection and (2) a microwave-interrogation cycle. The purpose and effect of the modifications is to enable an increase in the microwave-interrogation cycle time, motivated by the general principle that the short-term uncertainty or instability decreases with increasing microwave-interrogation time. Stated from a slightly different perspective, the effect of modifications is to enable the averaged LITS readings to settle to their long-term stability over a shorter total observation time.
The basic principles of a LITS were discussed in several NASA Tech Briefs articles. Here are recapitulated only those items of background information necessary to place the present modifications in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of a ground-state hyperfine transition of 199Hg+ ions. In a LITS of the type to which the modifications apply, the comparison involves a combination of optical and microwave excitation and interrogation of the ions in two collinear ion traps: a quadrupole trap wherein the optical excitation used for state preparation and detection takes place, and a multipole (e.g., 12-pole) trap wherein the microwave interrogation of the “clock” transition takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. This concludes the background information.
One source of systematic frequency error is an AC Stark shift caused by light present during microwave interrogation. To minimize this source of error, most stray light is suppressed by design, and heretofore, the microwave-interrogation time has been limited to the dim portion of the bimodal lamp cycle. It has now been learned that it is not necessary to limit the microwave interrogation to the dim portion of the lamp cycle because the separation of the two collinear ion traps is such that very little light from the lamp reaches the multi-pole trap wherein the microwave interrogation takes place. Indeed, the lamplight-attenuation factor associated with the separation of the collinear ion traps is greater than the ratio between the bright and dim lamp intensities. The abandonment of this limitation creates an option to operate the lamp at an optimum duty cycle and to perform the microwave interrogation for a longer time, as described next.
The equilibrium temperature of the lamp depends on the ambient temperature and the lamp duty cycle. For each lamp, it is possible to empirically determine an equilibrium temperature (and, hence, a duty cycle) that is optimum in the sense that it maximizes the signal-to-noise ratio (SNR) during microwave interrogation. Hence, one of the modifications is to set the bimodal lamp operating cycle to the optimum duty cycle. The other modification is to increase the microwave-interrogation time to a desired integer multiple of the lamp cycle time. (The multiple must have an integer value because it is still necessary to synchronize the optical and microwave operating cycles.) The size of the integer multiple is subject to an overall limit determined by the quantum-coherence time of the 199Hg+ ions and the characteristic stability time of the microwave source.
The following results have been reported from experiments performed on a LITS to demonstrate these modifications: The best short-term fractional frequency instability achieved with a typical microwave-interrogation time of 6 s in the unmodified bimodal lamp cycle was between 7 and 10 × 10–14τ–1/2, where τ is the averaging (observation) time in seconds. The use of the modified lamp mode and a microwave-interrogation time of 30 s resulted in a short-term fractional instability of 5 and 10 × 10–14τ–1/2. To put these numbers in perspective, it was calculated that the time for the LITS to settle to a fractional frequency instability of 10–16 would be about 8.4 days without the modifications or 2.9 days with the modifications.