An Algorithm to Estimate the Power Spectral Density From Allan Deviation.

Complex architectures for wireless communications, digital electronics, and space-based navigation interlink several oscillator-based devices such as clocks, transponders, and synthesizers. Estimators characterizing their stability are critical for addressing the impact of random fluctuations (noise) on the overall system performance. Manufacturers typically specify this as an Allan/Hadamard Variance (AVAR/HVAR) profile in the time domain. However, stochastic processes constituting the noise are more thoroughly described in the frequency domain by the power spectral density function (PSD). Both are second-moment measures of the time series, but it is only possible to translate unambiguously from the PSD to the AVAR/HVAR, not vice versa, except in the case of a single noise type, a rather unrealistic case. This note presents an analytical method to generate an approximated PSD expressed as a set of power-laws defined in specific intervals in the frequency domain, starting from an AVAR/HVAR expressed as a set of power-laws in the time domain. The proposed algorithm is straightforward to implement, applicable to all noise types (and combinations thereof), and can be self-validated by reconstructing the corresponding AVAR/HVAR by direct computation. Coupling with well-established algorithms relying on the PSD for power-law noise generation, the ensuing method encompasses the capability for generating multicolored noise in end-to-end simulations, as demonstrated hereby for NASA's deep space atomic clock. We also report on the limitations of the algorithm and analytical expressions of the continuous version of the algorithm.

Allan Deviation of Atomic Clock Frequency Corrections: A New Diagnostic Tool for Characterizing Clock Disturbances.

As atomic clocks and frequency standards are increasingly operated in situations where they are exposed to environmental disturbances, it becomes more necessary to understand how variations of each clock component impact the clock output, in particular the local oscillator (LO). Most microwave atomic clocks in operation today use quartz crystal LOs with excellent short-term noise variation but large unwanted long-term drift. Fortunately, this slow drift is mitigated by repeatedly comparing the atomic reference frequency to the LO and applying corrections each iteration through a control algorithm. This article focuses on the shot-to-shot corrections themselves. To optimize clock performance, it is important to determine whether disturbances on the output are due to variations of the LO that the control loop failed to remove or variations of the reference frequency itself. Some of this can be diagnosed using the output frequency's Allan deviation (ADEV), the traditional measure of clock performance. However, the ADEV of the corrections reveals somewhat different information, specifically more direct information about all disturbances that the measurement system detects and compensates for, from the LO or elsewhere. In this article: we 1) derive the baseline shot-noise-limited noise floor for this ADEV, 2) validate and adjust for the complexities of our control loop with a computer model, and 3) examine model results and laboratory data that lie on or diverge from the noise floor to understand what divergences reveal about LO and/or clock behavior. Ultimately, we show how to use this corrections-ADEV as a diagnostic to help identify the source of disturbances and drift observed on the clock output.

Using the Deep Space Atomic Clock for Navigation and Science.

Routine use of one-way radiometric tracking for deep space navigation and radio science is not possible today because spacecraft frequency and time references that use state-of-the-art ultrastable oscillators introduce errors from their intrinsic drift and instability on timescales past 100 s. The Deep Space Atomic Clock (DSAC), currently under development as a NASA Technology Demonstration Mission, is an advanced prototype of a space-flight suitable, mercury-ion atomic clock that can provide an unprecedented frequency and time stability in a space-qualified clock. Indeed, the ground-based results of the DSAC space demonstration unit have already achieved an Allan deviation of at one day; space performance on this order will enable the use of one-way radiometric signals for deep space navigation and radio science.

JPL Ultrastable Trapped Ion Atomic Frequency Standards.

Recently, room temperature trapped ion atomic clock development at the Jet Propulsion Laboratory (JPL) has focused on three directions: 1) ultrastable atomic clocks, usually for terrestrial applications emphasizing ultimate stability performance and autonomous timekeeping; 2) new atomic clock technology for space flight applications that require strict adherence to size, weight, and power requirements; and 3) miniature clocks. In this paper, we concentrate on the first direction and present a design and the initial results from a new ultrastable clock referred to as L10 that achieves a short-term stability of 4.5 ×10(-14)/τ(1/2) and an initial measurement of no significant drift with an uncertainty of 2.4 ×10(-16) /day over a two-week period.

Mercury Ion Clock for a NASA Technology Demonstration Mission.

There are many different atomic frequency standard technologies but only few meet the demanding performance, reliability, size, mass, and power constraints required for space operation. The Jet Propulsion Laboratory is developing a linear ion-trap-based mercury ion clock, referred to as DSAC (Deep-Space Atomic Clock) under NASA's Technology Demonstration Mission program. This clock is expected to provide a new capability with broad application to space-based navigation and science. A one-year flight demonstration is planned as a hosted payload following an early 2017 launch. This first-generation mercury ion clock for space demonstration has a volume, mass, and power of 17 L, 16 kg, and 47 W, respectively, with further reductions planned for follow-on applications. Clock performance with a signal-to-noise ratio (SNR)*Q limited stability of 1.5E-13/τ(1/2) has been observed and a fractional frequency stability of 2E-15 at one day measured (no drift removed). Such a space-based stability enables autonomous timekeeping of with a technology capable of even higher stability, if desired. To date, the demonstration clock has been successfully subjected to mechanical vibration testing at the 14 grms level, thermal-vacuum operation over a range of 42(°)C, and electromagnetic susceptibility tests.

A new trapped ion atomic clock based on 201Hg+.

High-resolution spectroscopy has been performed on the ground-state hyperfine transitions in trapped (201)Hg+ ions as part of a program to investigate the viability of (201)Hg+ for clock applications. Part of the spectroscopy work was directed at magnetic-field-sensitive hyperfine lines with delta m(F) = 0, which allow accurate Doppler-free measurement of the magnetic field experienced by the trapped ions. Although it is possible to measure Doppler-free magnetic-field-sensitive transitions in the commonly used clock isotope, (199)Hg+, it is more difficult. In this paper, we discuss how this (199)Hg+ feature may be exploited to produce a more stable clock or one requiring less magnetic shielding in environments with magnetic field fluctuations far in excess of what is normally found in the laboratory. We have also determined that in discharge-lamp-based trapped mercury ion clocks, the optical pumping time for (201)Hg+ is about 3 times shorter than that of (199)Hg+ This can be used to reduce dead time in the interrogation cycle for these types of clocks, thereby reducing the impact of local oscillator noise aliasing effects.

A compensated multi-pole linear ion trap mercury frequency standard for ultra-stable timekeeping.

The multi-pole linear ion trap frequency standard (LITS) being developed at the Jet Propulsion Laboratory (JPL) has demonstrated excellent short- and long-term stability. The technology has now demonstrated long-term field operation providing a new capability for timekeeping standards. Recently implemented enhancements have resulted in a record line Q of 5 x 10(12) for a room temperature microwave atomic transition and a short-term fractional frequency stability of 5 x 10(-14)/tau(1/2). A scheme for compensating the second order Doppler shift has led to a reduction of the combined sensitivity to the primary LITS systematic effects below 5 x 10(-17) fractional frequency. Initial comparisons to JPL's cesium fountain clock show a systematic floor of less than 2 x 10(-16). The compensated multi-pole LITS at JPL was operated continuously and unattended for a 9-mo period from October 2006 to July 2007. During that time it was used as the frequency reference for the JPL geodetic receiver known as JPLT, enabling comparisons to any clock used as a reference for an International GNSS Service (IGS) site. Comparisons with the laser-cooled primary frequency standards that reported to the Bureau International des Poids et Mesures (BIPM) over this period show a frequency deviation less than 2.7 x 10(-17)/day. In the capacity of a stand-alone ultra-stable flywheel, such a standard could be invaluable for long-term timekeeping applications in metrology labs while its methodology and robustness make it ideal for space applications as well.

Power dependence of distributed cavity phase-induced frequency biases in atomic fountain frequency standards.

We discuss the implications of using high-power microwave tests in a fountain frequency standard to measure the frequency bias resulting from distributed cavity-phase shifts. We develop a theory which shows that the frequency bias from distributed cavity phase depends on the amplitude of the microwave field within the cavity. The dependence leads to the conclusion that the frequency bias associated with the distributed cavity phase is typically both misestimated and counted twice within the error budget of fountain frequency standards.