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30th European Frequency and Time Forum

Abstracts for tutorial lectures

Krzysztof Szymaniec - Cs Primary frequency standard

In 2015, the metrology community celebrated 60 years of the atomic clock. Seminal works of Rabi, Ramsey, Essen and others initiated a disruptive change in timekeeping and led to a new definition of the second based on atomic rather than astronomical phenomena. Decades of subsequent development improved the accuracy of atomic clocks and frequency standards by orders of magnitude with measurement uncertainties currently left at the sixteenth decimal place. In particular, the introduction of laser cooling and construction of atomic fountains have boosted these improvements. Nowadays, more than two decades after its first demonstration, fountain technology appears quite mature and calibrations of the global timescale TAI/UTC rely almost entirely on the fountain standards. In addition, atomic fountains are often used to discipline clocks forming local timescales. A cold atom clock similar to a fountain, but designed to operate in a microgravity environment, will soon be launched and installed on board of the International Space Station for stringent tests of general relativity. On the ground, atomic fountains give important input into the search for a possible time variation of fundamental constants of nature. These devices are also invaluable tools in the development of optical clocks, the anticipated next generation of primary frequency standards.

In this tutorial, I will begin with presenting the basic principle of an atomic clock and a description of a generic atomic fountain set-up. The focus of the lecture will then be on discussing the noise effects limiting short-term stability and systematic effects affecting the accuracy of atomic fountain clocks. The presentation will be given from a 'practitioner' point of view and will conclude with discussing applications of the fountain standards and prospects for further development.


Salvatore Micalizio - Vapor cell frequency standards

Since their first realization in the 1960s, vapour-cell frequency standards have been considered extremely attractive devices in all those applications where good frequency stability performances joined with small sizes, reliability, reduced power consumption and costs are required. These applications include telecommunication, defence, energy, space and radio-navigation. The passive rubidium frequency standard with state selection performed by the incoherent light of a lamp is still nowadays widely adopted in many measurement systems, as well as in advanced technological sectors, such as GPS and GALILEO.

The development of single mode semiconductor laser diodes in the 1980s opened new perspectives in the field of gas cell frequency standards, thanks to the replacement of the discharge lamp with a coherent optical source. In terms of frequency stability, the expected performance improvement was theoretically estimated to be 2-3 orders of magnitude, predicting a white frequency noise limit in the 10-14 τ-1/2 region, τ being the integration time. However, laser noise transferred to the clock signal via the light-shift effect prevented this result from being reached. In the last twenty years, innovative schemes have been considered with the aim of approaching the expected theoretical limit and new concept laser-pumped frequency standards have been developed. These clocks are the object of this tutorial.

After resuming the main features of the traditional lamp-pumped Rb clock, the tutorial will focus on several interesting approaches that have been envisaged not only to get close to the fundamental stability limit, but also to reduce at the same time the requirements on the laser noise. These techniques include coherent population trapping, light-shift compensated schemes and pulsed optical pumping. The tutorial will describe these proposals, their main advantages and limitations and the most significant results obtained by various research groups.


Ekkehard Peik - Optical clocks

Optical clocks based on laser cooled and trapped atoms (in optical lattices at the 'magic' wavelength) and ions (in radiofrequency Paul traps) have made fast progress in recent years, with the most advanced systems now reaching an instability of 10-16 in only 10 s of averaging time and a systematic uncertainty in the low 10-18 range. This lecture will discuss the principles, experimental requirements and methods that have enabled these performances. Emphasis will be placed on the different atomic systems and types of 'forbidden' reference transitions, and on the spectroscopic methods that provide the required control of systematic frequency shifts, especially those associated with the interaction with external electric and magnetic fields. I will also discuss the conceivable future directions for the reliable evaluation and for scientific applications of atomic frequency standards with an uncertainty below that of Cs clocks.


Stephen Webster - Lasers for optical frequency standards

Over the past 50 years, atomic clocks have been based on microwave frequencies and primary standards have demonstrated uncertainties at the level of a few parts in 1016. Optical clocks are a new generation of atomic clock, in which the frequency of light is the signal used for timing. They are based on 'forbidden' atomic transitions for which light is absorbed over a very narrow range of frequencies. Depending on the particular atomic species and transition used, the ratio of the frequency to the frequency width (Q-factor) ranges from 1014-1023, thus, these transitions constitute very precise frequency references. They are also insensitive to external electromagnetic fields and can be highly reproducible with uncertainties at the level of parts in 1018. Further, given that the frequency of light is ~100,000 times higher than that of microwaves, the same level of precision as a microwave atomic clock may be reached in a much shorter time. As optical clocks come of age and prove the stability and reproducibility predicted of them, the prospect will open up for a redefinition of the second in terms of an optical frequency.

The atomic absorber in an optical clock takes one of two forms: it is either a single ion confined in an electro-dynamic trap (Paul trap), or an ensemble of neutral atoms held in an electric dipole force trap (optical lattice). The atomic absorbers are laser cooled so that they are nearly at rest and, to first order, do not experience a Doppler shift on interaction with the light used to probe the atomic transition. To make use of the high-Q of the atomic transition, the probe light must also have a very narrow frequency width and this is achieved by stabilizing a laser to a secondary reference, a high-finesse Fabry-Pérot etalon. A mode-locked femtosecond-pulsed laser (femtosecond comb) converts the very rapid oscillations of the light from some 100s of THz down to a radio frequency so that the output of the optical clock can be counted by commercial electronics and compared to the SI second and the outputs of other optical clocks.

This tutorial will give an overview of the essential elements of an optical clock: the atomic reference, the ultra-stable laser and the femtosecond comb. It will describe how each of these elements is realized in practice and the experimental challenges involved in operating such an apparatus. In particular, a review will be made of the laser sources required for operation of an optical frequency standard, the techniques employed in their stabilisation and the characterization of their noise.


Gesine Grosche - Frequency and time transfer using optical fibers

Ever more accurate clocks and frequency references are being developed in dedicated laboratories around the world, reaching astonishingly low instability and high accuracy, currently near 1 part in 10 to the 18. Making the ultra-stable output of these powerful instruments available beyond the walls of the metrology laboratory, to enable physics experiments, remains a challenge. In the wake of the optical telecommunication revolution, transfer techniques that make use of optical fibre have greatly developed: within one decade, improvements of more than three orders of magnitude in precision have been achieved.

Recently, long-distance frequency transfer with an uncertainty of 2 parts in 10 to the 20, and, for 1 km-scale links, synchronisation at the level of femto-seconds has been reported. Fibre based transfer of frequency has been achieved over distances exceeding 1000 km, which enables international comparisons of clocks and other joint experiments.

In this tutorial I will illustrate advantages and challenges of using optical fibre as a transmission medium for precision metrology. This will cover basic concepts, techniques and limitations, focusing on optical telecommunication fibre (1.55 μm), which is both cheap and optimised for low loss, making it suitable for long-distance transfer. The tutorial will give an overview and comparison of different transfer techniques centred on methods using the optical carrier phase.


Patrizia Tavella - Precise Time Scales and Navigation Systems, the Ultimate Challenge to Time Metrology

Today, atomic clocks enable precision estimates of time and position. Through the use of ultra-precise atomic frequency standards, we can form time scales, such as the international time standard Universal Coordinated Time (UTC), capable of dating events with nanosecond accuracy. Similarly, Global Navigation Satellite Systems (GNSS), provide location all over the world with sub-meter accuracy.

In timekeeping, as well as in navigation systems, the questions may be similar, but the answers are frequently dissimilar, due to different goals, requirements, technology availability and constraints. In both cases precision clocks, measuring systems, and a reference time scale are required; in both cases we need to estimate how often the clocks are to be resynchronized and what is the acceptable time error that a clock may accumulate without compromising system performance. We require a mathematical model to predict clock behaviour in order to maintain agreement with another reference clock or to ensure updated navigation messages. We need to understand the 'normal' behaviour of a clock to be able to quickly identify anomalies which can lead to incorrect estimates.

This lecture presents the needs of precise Timing and Navigation, explaining the current international timekeeping architectures and the timing systems of the current GNSS, giving insight to the most demanding topics that still challenge Time Metrology.


Pascale Defraigne - Global Navigation Satellite Systems

GNSS and Time have a bi-directional relationship. On the one hand, GNSS also relies on time: everything is based on the measurements of the signal travel time between the satellite and the receiver. GNSS therefore needs a reference timescale maintained by the operators and broadcast by the satellites. On the other hand, the satellite navigation systems offer a wonderful tool for time and frequency metrology, as these flying atomic clocks on board the satellites can be used as a reference for the comparison of ground time and frequency standards.

This tutorial will raise both aspects of the link between GNSS and TIME. After showing concretely the need for accurate time scales for the GNSS, the 'GNSS time transfer' technique will be detailed. Code and carrier phase measurements will be presented and the procedure to get a precise and accurate clock comparison will be explained, both from the instrumental point of view and in terms of data analysis. GNSS Common View (or All in View) as well as Precise Point Positioning will be detailed in the presentation. The different error sources on the measurements will be studied and hence an ideal station set-up will be presented.


Craig Nelson - Phase noise metrology

Noise is everywhere. Its ubiquitous nature interferes with or masks desired signals and fundamentally limits all electronic measurements. Noise in the presence of a carrier is experienced as amplitude and phase modulation noise. Modulation noise will be covered from its theory, to its origins and consequences. The effects of signal manipulation such as amplification, frequency translation and multiplication on spectral purity will be examined. Practical techniques for measuring AM and PM noise, from the simple to complex will be discussed. Typical measurement problems, including the cross-spectrum anti-correlation, will also be covered.


Enrico Rubiola - Phase noise and jitter in digital electronics

Digital electronics is progressively replacing analog electronics, even in applications where low noise is critical. When the analog signal cannot be avoided, the world is still going digital, with analog-to-digital and digital-to-analog conversion as the natural complement. The reasons are obvious: simplicity, reproducibility, cost, and no or minimal calibration. Additionally, youngsters are trained to digital, not to analog, and the digital hardware benefits from the Moore law.

Having said that, we go through phase noise in digital electronics and in the analog-digital interface, focusing on frequency applications, synthesis, and measurement. This tutorial will cover the following topics, deriving most of the concepts from examples.

This is a new tutorial, mostly based on material not available in the general literature. The author owes gratitude to P. Y. Bourgeois, C. E. Calosso, J. M. Friedt, G. Goavec-Merou, Y. Gruson, and the Go Digital Working Group at the FEMTO-ST Institute.


Bernd Neubig - Measurement techniques for piezoelectric resonators

This tutorial covers the measurement techniques for piezoelectric resonators in a wide frequency range, from low-frequency (tuning fork) resonators in the kHz range, over AT- and SC-cut resonators in the MHz range to HFF and SAW resonators up to the GHz range. Special emphasis will be given to the relevant IEC standards.

In this tutorial, I will discuss the following measurement techniques with their pros and cons: