Time, frequency and atomic clocks

Gaetano Mileti, Laboratoire Temps – Fréquence, Université de Neuchâtel

This article summarises the invited lecture given at the SPS annual meeting held in Geneva on March 27, 2008 (a pdf file of the presentation can be found below). The talk first presented a few fundamentals on frequency standards and on the means to produce and characterise high performance oscillators displaying fractional frequency instabilities ranging from 10^-10 to 10^-17. Then, the various types of existing atomic clocks were explained as well as their applications on ground and in space. Finally, after the description of several contributions of Switzerland (such as the atomic clocks for the European satellite navigation system GALILEO), the main trends of the domain and the current on-going research to improve them were highlighted. In summary, the general effort consists in exploiting: (1) the latest development in photonics (laser diodes and optical combs); (2) the atom-photon manipulation (optical pumping, laser cooling, etc.); (3) the extreme miniaturisation of key components.

Introduction on frequency standards

Two essential components of a clock are the "oscillator" and the "counter". The "oscillator" provides a signal of period T (or frequency f = 1/T), which is supposedly known (or accurate) and stable. Examples of "oscillators" are a pendulum, a spring, a quartz crystal, etc. The "counter" has the function to provide a direct link between those oscillations and an output needed by the user of the clock: the exact time display, a stable 5 or 10 MHz signal, etc. Examples of "counter" components are an escapement, a gear, a dial, hands, an electronic frequency counter, etc. A third important element is the "reference", which may be used to reduce instabilities of the oscillator frequency by adjusting it so as it matches the reference frequency.

For millennia, our time "reference" has been the earth rotation. As knowledge and science have progressed in a variety of fields (astronomy, mathematics, optics, mechanics, materials, etc.), mankind has on one hand developed tools to observe, understand and measure accurately the earth rotation period and on the other hand realised ingenious and sometime beautiful oscillators, counters and clocks. The progress in this truly interdisciplinary domain may be seen as a unique combination of "fundamental" and "applied" research symbolised for example by the quest for a reliable method to determine the longitude on sea and which led – after decades of unsuccessful attempts – to the realisation of the first marine chronometer, capable to keep the exact time within a few seconds per day during months of operation in an harsh environment. Thanks to marine chronometers, navigation on sea became safer and maps more accurate. Marine chronometers became also crucial for military purposes and for explorers such as J. Cook or J.-F. de Lapérouse.

Since the middle of last century, a new category of electronic oscillators exploiting the piezoelectric effect in quartz crystals appeared and replaced the other ones in most of the precise timing applications. In parallel, magnetic resonance on atomic samples have become our basic time (or frequency) reference. In 1967, the SI second was defined by the energy difference of a microwave transition between two hyperfine states of energy E₁ and E₂ in caesium (Cs) atoms, using the following basic formula with ħ = 1:

ħω₀ = |E₁-E₂| = 9'192'631'770 Hz (1)

An atomic frequency standard is made of all the above-described basic components of a clock, with the difference that the reference is intrinsically more stable and more accurate than any other and is actually part of the device. Depending on the type of atomic clock (see below for specific examples), this reference – usually referred to as "atomic resonator" - may be a beam or a vapour of either near-room-temperature or laser-cooled atoms; it also may consist of laser-cooled atoms or ions in a trap.

The instability of atomic clocks is usually expressed as fractional frequency fluctuations. It is typically non stationary and described with its Allan deviation. The Allan deviation of a clock characterises its behaviour on various time scales and is an image of the noise processes limiting the clock stability. It may range between 10^-10 to 10^-17 depending on the standard and on the averaging time. These performances are determined on a short-term scale (1 to 1000 s) by various intrinsic properties of each specific atomic clock and on the medium and long-term by their aging and sensitivity towards external perturbations. The “Quality factor” Q=ω₀ /Δω (where ω₀ and Δω are respectively the frequency centre and the width of the magnetic resonance signal) and the “signal-to-noise ratio” (SNR = amplitude of the reference signal / detection noise) of the magnetic resonance have a direct impact on the clock short and medium term instability. In first approximation, the best fractional instability one may reach with a given SNR and a given Q is (at an averaging time of typically 1 second):

δf/f ∝ (Q⋅SNR)^-1 (2)

Remembering that the magnetic resonance width Δω is inversely proportional to its duration τ (Heisenberg uncertainty principle), this formula becomes:

δf/f ∝ (ω₀⋅τ⋅SNR)^-1 (3)

One may (very roughly) summarise the research in the domain of atomic clocks by a constant effort to improve the three basic parameters given in equations (2) or (3). As shown in the two examples below:

the SNR has been and is still being increased in several atomic clocks, for instance by replacing discharge lamps or magnetic selectors by tunable laser sources such as semiconductor laser diodes;
τ has been and is still being increased by slowing down atoms through laser cooling;
Q has been and is still being decreased by increasing ω₀ using optical transitions.

Another trend of the research concerns the improvement of properties of the clocks other than frequency instability. Those are in particular: price, volume, consumption, weight, reliability, etc.

Example 1: Laser cooling and the Swiss primary frequency standard

Primary standards employ a Cs beam in vacuum which goes through a microwave Ramsey Cavity in which takes place the magnetic resonance. The obtained discriminator signal is used to measure and correct any frequency fluctuation of a quartz oscillator, providing thus a stable and accurate reference. From approximately 1960 to 1990, primary standards were based on thermal beams (average velocity of 200 m/s) providing a reference signal linewidth of typically 100 Hz, depending on the length of the cavity. With laser cooling, the atoms velocity could be significantly reduced and nowadays primary Cs standards (fountains) supply a 1 Hz wide reference signal, limited only by the earth gravitation. Such standards have now reached an accuracy below 10^-15 and a short-term frequency stability (@ 1s) of 10^-13 or below. Figure 1 shows the METAS Swiss Primary Frequency Standard developed by P. Thomann and his team at UNINE-LTF, formerly Observatoire Cantonal de Neuchâtel (ON). This device is unique since it uses a continuous – instead of a pulsed - Cs beam of cold atoms which reduces the effect of atomic collisions and of the phase noise of the microwave signal probing the atoms in the cavity. Note that cold atomic beams find many other applications than clocks including precision instruments such as atom interferometer gyroscopes and accelerometers.

Fig. 1 Swiss primary continuous atomic fountain (LTF-METAS): CAD drawing (left) and view of the microwave cavity, magnetic shields and lower vacuum vessel

Fig. 2 Laser-pumped Rb clocks: ESA prototype for GALILEO (up) and micro-fabricated vapour cell (10x10x1.5 mm)

Example 2: GALILEO and the new vapour cell and miniature atomic clocks

In a large number of applications, extreme accuracy and long-term stability are not required while consumption, volume, weight or price play a crucial role. Vapour-cell atomic clocks (often referred to as “Rubidium clocks”) offer excellent short medium term performances (10^-12 to 10^-11 at 1 s, 10^-11 to 10^-14 at 20’000 s) even though their volume can be as small as a tennis ball. In this type of standards, the atoms are confined in a 1-2 cm³ glass bulb placed inside a microwave cavity and irradiated by a light beam which creates a microwave-optical double resonance. This category of standards is needed in telecommunication systems as well as in mobile applications such as satellite navigation and positioning. The current research in this area consists in exploiting the properties of lasers to replace the presently used plasma discharge lamps as optical sources. For instance, laser diodes allow the creation of so-called “dark-states” with the Rb atoms, through the Coherent Population Trapping (CPT) effect. Figure 2 shows some atomic resonators developed by G. Mileti and his team at UNINE-LTF (also formerly ON). In particular are shown a laser-pumped Rb clock in view of the “second generation” clocks for the European GALILEO satellite navigation system and a micro-fabricated vapour cell, developed in collaboration with the Institute of Microtechnology (IMT-UNINE). This miniature cell constitutes a first step towards the realisation of chip-scale atomic clocks but may as well serve in future miniature atomic magnetometers, gyroscopes, quantum sensors in general or even quantum computing and quantum communication systems (atom chips).

Other examples and conclusion

Several other types of atomic frequency standards exist and/or are currently being studied. Hydrogen (H) Masers make use of the stimulated emission of H atoms in a Teflon-coated bulb, thus providing an extraordinary stable reference in the medium a short-term range (10-13 at 1 s, 10^-15 or below from 100 to 10’000 s). The main applications of H-Masers are timekeeping and VLBI (Very Long Baseline Interferometry) for radioastronomy. Optical frequency standards constitute also a very active and very successful field of research as optical references allow in principle to gain several orders of magnitude in accuracy and in stability since ω₀ /2π increases from 10⁹ - 10¹⁰ Hz to 10¹⁴-10¹⁵ Hz (see equations 1-2-3). In practice, it proved very difficult to realise the “counter” providing a direct link from the quartz frequency to this reference. However, optical combs are now enabling us to establish this link in a very convenient manner (Nobel prize of Physics in 2005 by T. W. Hänsch and J. L. Hall). Combining this technique with trapped ions or cold atoms in an optical lattice makes realistic to aim at instabilities and inaccuracies as low as 10^-18. Space environment is also stimulating researchers to push the performances of atomic clocks to their limits and to use them for performing fundamental tests of the laws of physics. The ACES (Atomic Clock Ensemble) experiment on the International Space Station (ISS) includes a French laser-cooled Cs clock and a Swiss active H-Maser. Thanks to the micro-gravity environment, the Cs clock displays Ramsey fringes which are only 0.1 Hz wide. ACES will provide a mean for: (1) studying cold atoms in microgravity; (2) a worldwide comparison of ultra-stable clocks (30 ps accuracy and clock synchronisation at the 10^-16 level); (3) improvements of fundamental tests of general relativity (red shift, drift of the fundamental constant α, anisotropy of speed of light, etc.). Space Hydrogen Masers will also serve to increase the baseline and therefore the angular resolution of VLBI for radioastronomy (RADIOASTRON mission).

In conclusion, research on atomic clocks is currently very active for both the everyday applications (telecoms, positioning, timescales, etc.) and the fundamental research (study of light-atoms interaction, tests of fundamental laws, etc.). Experiments are on-going both on ground and in space and their progress also depends on key technological developments, in particular in the field of photonics and microtechnology. Two general trends may be observed: going optical and going miniature.

Acknowledgements

Many activities described in this article and the current research of LTF are funded by the Canton of and the University of Neuchâtel, the Swiss National Science Foundation, the Swiss Federal Office of Metrology (METAS), the Swiss Space office (SER-SSO), the European Space Agency (ESA), the European Union (INTAS, EC-FP7), the Association Suisse pour la Recherche Horlogère (ASRH), the Fondation en faveur d'un Laboratoire de Recherche Horlogère (FLRH). In addition to the members of LTF listed below, the author acknowledges the contributions of many other persons who performed the scientific, technical and administrative work at ON and at UNINE. We also thank the numerous research laboratories and companies who contributed to this research through essential scientific collaborations.

References and bibliography

Articles presenting the activities of LTF (see also www2.unine.ch/ltf ):
G. Mileti, C. Affolderbach, E. Breschi, C. Schori, P. Scherler, P. Thomann, Recherches sur les horloges atomiques miniatures et optiques, Comptes-rendus du Congrès International de Chronométrie, p. 91-95, Colombier, 26-27 septembre, (2007)
G. Mileti, C. Affolderbach, F. Droz, E. Murphy, Navigating more precisely with laser clocks, ESA bulletin, vol. 122 (May), p. 53, (2005)
Specialised Time & Frequency bibliography
J. Vanier, C. Audoin, The Quantum Physics of Atomic Frequency Standards, Bristol: Adam Hilger, 1989
Special issue of Metrologia: Fifty years of atomic time-keeping: 1955 to 2005, Vol. 42, N. 3, June 2005
Bibliography for non-specialists
F. Riehle, Frequency Standards, Basics and Applications, WILEY-VCH, 2004
C. Audoin, B. Guinot, S. Lyle, The Measurement of Time: Time, Frequency and the Atomic Clock, Cambridge, (Original version in french : Masson, 1998)
J. Camparo, The Rubidium atomic clock and basic research, Physics today, p. 33-39, November 2007

Brief presentation of Laboratoire Temps – Fréquence (LTF-UNINE)

LTF-UNINE was created on February 1st 2008, following the transfer of two groups from Observatoire Cantonal led by P. Thomann (laser cooling and primary standards) and G. Mileti (vapour cell clocks and stabilised lasers). The main research lines concern: (1) the study the interaction of atoms and electromagnetic radiation; (2) the development of primary and frequency standards; (3) the development of optical sources and frequency standards. LTF performs also technological developments in particular related to space clocks and to the new standards for the European satellite navigation system GALILEO. The following persons presently form LTF: Prof. P. Thomann, G. Mileti, C. Affolderbach, E. Breschi, G. Di Domenico, A. Joyet, C. Schori, V. Dolgovskiy, G. K. Gulati, R. Roy, D. Miletic, T. Bandi, F. Gruet, P. Scherler

[Released: July 2008]

G. Mileti's talk held at the SPS Annual Meeting in Genève on March 27, 2008