The time according to atoms

The construction and marketing of high-performance hydrogen maser atomic clocks remains the privilege of the Americans and the Russians. The Swiss also market this type of clock, but with a Russian heart. Europe would like to become completely autonomous in this sector, in particular to meet the needs of its Galileo navigation system. Professor Thierry Bastin’s atomic physics unit took up the challenge with the Liège-based company Gillam-FEi within the framework of the Walloon “Marshall Plan”. The first prototype has just been completed. The aim of the next step is to divide the weight of these devices by ten so that they can be put on board the satellites at a low cost. This would be a world first for this type of maser.

The history of measuring time is probably as long as that of humanity. Or, to be more precise, the history of measuring time intervals because that is what we have always measured. As a result, Man turned naturally towards phenomena that showed great regularity such as the earth’s rotation on its axis or that of the moon around the earth. He then attempted to create instruments capable of objectivising these observations and measuring such intervals: sun dials or sandglasses for instance. Following Galileo’s work on the pendulum, the 17th century was to experience a decisive advance: the development of the pendulum clock. “Ultimately, what’s a clock?” asks Professor Thierry Bastin, director of the Atomic Spectroscopy and Cold Atom Physics Department at the University of Liège. "A system that oscillates regularly over time. Never mind what it is that oscillates, providing that it is as regular as possible.” In mechanical clocks, the period of oscillation depends on the length of the pendulum and the acceleration of gravity.  In other words, if the length of the pendulum changes (because of the temperature, for instance), the clock will lose its accuracy; the same is true if the acceleration of gravity changes (for example, by gaining altitude). Clockmakers thus continued to successfully perfect their systems: as early as 1759, John Harrison had made a clock whose precision was a tenth of a second per day! But it wasn’t until 1918 – at least in terms of the principle; the actual clock wouldn’t appear until the 1930s – that a new scientific breakthrough occurred:  the quartz system. This time, it was no longer a mechanical system that was oscillating but electrical tension. The mechanical vibration of the crystal induces an electrical field that oscillates at a precise frequency and, in particular, a much higher one than that of pendulums (several million times per second). The greater the number of oscillations within a given time interval, the more precise the measurement is likely to be. Hence, it isn’t difficult to imagine that these quartz clocks, as they were called, had a degree of precision and invariability that was more than sufficient for everyday applications. But while physicists could explain what happened in everyday life, they also had to distance themselves from it. The search for greater precision and reliability thus led them towards the development of atomic clocks.

Atomic clocks

“An atomic clock is known as such because the way it works is based on the individual properties of atoms”, Thierry Bastin explains. "A pendulum clock is based on the properties of the pendulum but not on the individual properties of the atoms comprising the pendulum. The same is true of quartz clocks based on the oscillation of a quartz crystal, thus on the whole crystal and not on the atoms comprising it. However, in an atomic clock, we use the atoms’ properties individually, even if we use a large number of atoms (1).”

How do these clocks work?  They are actually improved quartz systems. They do indeed involve a quartz... but one that could be said to be placed under surveillance! By compressing a quartz crystal, oscillating electrical charges appear on its surface; this is how we obtain an electric oscillator (a clock) at a very stable frequency... as long as the dimensions of the quartz crystal don’t change. As we have seen, these possible deformations are of no importance in the majority of applications. But we know that in the long term, a quartz crystal will undergo modifications that won’t be detected. The clock will therefore drift without the user realising it. Atomic clocks allow this defect to be – almost – eliminated since they detect the slightest variations in the quartz’s frequency in real time: we can therefore “recalibrate” it and constantly maintain it at the desired value.

How can atoms play this role? We know that they can emit or absorb electromagnetic radiation. But only some of the radiation’s frequencies will be absorbed (or emitted) by the atoms. And, of course, each type of atom emits (absorbs) in its own particular frequencies: hydrogen and caesium atoms don't behave in the same way in this respect... but all hydrogen (and caesium) atoms behave identically among themselves. Clearly, this is of great value because a caesium atom in Liège is absolutely identical to a caesium atom anywhere else in the world, thus ensuring perfect replication of the phenomena. When atoms emit (or absorb) radiation, their state changes (for instance, they become excited) and it is possible to know, at any given moment, the probability of an atom being in such or such a state. If the frequency of the radiation that causes this change of state varies slightly, the probability of the atom changing state decreases. And if we subject a cloud of atoms, rather than one atom, to radiation at a precise frequency, we can therefore count how many atoms change state in real time. The number reaches a maximum at the optimal frequency; once we start to move away from this frequency, the number of atoms changing state decreases. Therefore, we have the means to constantly readjust a frequency, an oscillation... in this case, that of the quartz which is part of the atomic clock. “Since atoms are highly sensitive to the frequency of the radiation to which they are subjected", Thierry Bastin explains, “they are capable of measuring this frequency with extraordinary accuracy. As soon as the slightest variation is detected, the servo-control system corrects the frequency of the quartz’s oscillation. We thus have an oscillating system – a clock – of phenomenal regularity!"

One second in 30 million years!

The accuracy and stability of atomic clocks exceed all other oscillation systems. The typical stability of an atomic clock is 10^-15 sec per sec. Hence, in the space of a second, we expect a maximum time fluctuation of a millionth of a billionth of a second. In the space of one day, this means that there will be a maximum fluctuation of 10^{-10 sec}, i.e. a tenth of a billionth of a second (a tenth of a nanosecond). In other words, you would have to wait 30 million years to observe two clocks drifting by one second...  “which would equal less than 3 minutes since the beginning of the earth more than 4 billion years ago”, Thierry Bastin tells us enthusiastically. And these limits are continuously getting shorter: we’re now at 10-^{18 sec} per sec!

Such clocks are useful, and necessary, first of all to check certain physical theories, for instance, special and general relativity. According to these theories, time flows differently depending on whether the subject is moving or not, and depending on how close or far it is from the centre of the earth. To check these theoretical predictions, clocks had to be taken on board planes then rockets. But, of course, it was necessary to have clocks with guaranteed total stability for the duration of the experiments.  Another question has been niggling physicists for decades:  are physical constants... constant? For instance, has the speed of light always been what measurements show it to be today? The experimental protocols set up to answer these types of questions require time measurements of physical processes with a level of precision only atomic clocks can provide. Another example: to increase the power of telescopes, they have to be linked. Therefore, it is necessary to co-ordinate the arrival of the signals from the different telescopes with the utmost precision.

But atomic clocks also have a use in everyday life. In global positioning systems (GPS), the positioning of an object on the ground is based on signal transmission time measurements; any inaccuracy in the measurement of signal propagation has an effect on the accuracy on the ground. Only atomic clocks, taken on board satellites, can provide the accuracy and stability required for useable geolocation. The final example and perhaps the most important is the telecommunications sector. The signals bombarding us must be sampled in time at regular intervals upon emission but also upon reception using the same measurement. If the emitter and the receiver aren’t synchronised, this will cause problems. The greater the synchronisation, the higher the transmission flow; the quicker the sampling, the more information per unit of time can be transmitted. High-speed internet is only possible thanks to the existence of atomic clocks. 

But what’s a second?

Atomic clocks have another use: as timekeepers. Or, to be more precise, to provide the definition of the second as a unit of time.
Up until 1960, the second was defined as being the 3,600th of a 24^th of an average day, i.e., the average time it takes the earth to rotate on its axis with the sun as its reference. But over time, the earth turns more and more slowly! Obviously, this is minimal: in 100 years, the earth will take approximately 2 milliseconds more than today to accomplish a complete rotation. Our planet rotated on its axis in approximately 23 hours 200 million years ago and it will complete a rotation in 25 hours in 200 million years. Moreover, regardless of this general slowing down in the long term, there are also irregularities and seasonal variations. In other words, every day is different. To understand this, think of an ice-skater: when he spins around with his arms outstretched and then lowers them by his sides, he increases the speed of rotation. The same is true of the earth whose speed of rotation changes according to the distribution of its constitutive masses; this happens, for instance, when there is an earthquake.  Owing to these two effects, it is difficult to base a precise definition of a second on the rotation of the earth. That is, if we want the time interval known as a second to remain constant over the centuries and even the millenniums. Therefore, in 1960, the decision was taken to base the definition of the second on the revolution of the earth around the sun, a more stable phenomenon than its rotation. From this moment on, the second was defined as the duration of this revolution divided by the exact number of days it requires (slightly more than 365), then by 24 and finally by 3600, i.e., 1/31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time. Its duration is equivalent to that of the second based on the rotation of the earth such as it was on average at the end of the 19th century. This new definition of the second only lasted until 1967, when time became atomic and no long astronomical. The accuracy of atomic clocks is such that they exceed all other time measurement systems. Hence, they were awarded the “honour” of serving as the standard for the definition of the second. That is why the second is currently defined as being the time it takes for a certain electromagnetic wave emitted by a caesium atom to oscillate 9192631770 times.

An extra second in 2012 

With this atomic definition of time, we are faced with two times: we still have astronomical time, the one we experience every day if you like, which is the legacy of the definition based on the rotation of the earth. And then there is atomic time, which is completely independent of this rotation. We therefore have what is known as universal time (UT), based on the rotation of the earth, and international atomic time (TAI), provided by the average of a set of several hundred atomic clocks distributed worldwide. This average is calculated by the International Bureau of Weights and Measures in the suburbs of Paris. The two times will drift over time since the first one is based on a phenomenon that slows down on average while the second one is far more stable and regular. If we measure exactly 24 hours on an atomic clock, you will note that during this lapse of time, the earth hasn’t quite completed its rotation. This is the reason why a ‘leap’ second has to be added from time to time (or removed if, for instance, the distribution of masses on the surface of the earth were to momentarily accelerate its rotation!). This is what will happen this year, in 2012: the last minute of the last day in June will have an extra second: after 23:59:59, 30 June, GMT, it will be 23:59:60, and only 00:00:00, 1 July, one second later. Here, the difference between the two time scales will once again fall below a 0.9 second. Since 1972, 24 leap seconds have been added to maintain the coincidence between the two types of time. The correct TAI time is thus called Coordinated Universal Time (UTC). It has the dual advantage of having the accuracy of TAI while remaining synchronised with the earth’s rotation, i.e., with UT.

Why seek this coincidence when the difference is so minimal that it wouldn’t be noticed for a very long time? We would indeed have to wait several thousand years for there to be a difference of one hour between the two time scales. There would still be time at this point to carry out a correction in one go... It was actually seamen who asked for synchronisation at the beginning of the 1970s, when atomic time had just been defined. They needed time signals that were as much in line with the earth’s rotation as possible because they were still making many of their measurements using a sextant. This need disappeared with the advent of GPS and eliminating the leap second is looking evermore likely since it is no easy matter to add a second to all the atomic clocks at the same time. “However, the English aren’t keen on this”, Thierry Bastin smiles, “because this would mean that the Greenwich Meridian would lose even more of its importance! Through the misuse of language, Greenwich Mean Time (GMT) is now often used as a synonym for Coordinated Universal Time (UTC), although GMT in the strict sense simply means the average solar time at the Greenwich Meridian and therefore normally corresponds to Universal Time (UT). So, if UTC were to disappear in favour of TAI, Greenwich would be well and truly relegated to history..., at least as far as its special role in establishing the official time scale is concerned.”

The Liège clock

The first atomic clocks were created at the end of the 1940s, but these trials weren’t conclusive. This was to change in the mid-1950s, with the recourse to caesium atoms, or isotope 133 to be exact, which isn't radioactive. “In principle, any kind of atom can be used in atomic clocks”, Thierry Bastin points out, “but when people started making them, they selected atoms (caesium, rubidium and hydrogen) that emitted in a range of well-mastered frequencies, i.e., microwaves.” While caesium atoms were the first to be used and undoubtedly remain the most frequent, hydrogen clocks (called hydrogen masers [Microwave Amplification by Stimulated Emission of Radiation]) appeared at the beginning of the 1960s, offering greater stability. The clock developed by the University of Liège belongs to this category.

The first step consists of selecting the hydrogen atoms in their emitting state. Once this is achieved, a cloud of these atoms is sent to a cavity called a cavity resonator. There, they are subjected to an electromagnetic wave of the appropriate frequency. When the atoms are excited, they emit a signal (very low, approximately a tenth of a picowatt!) which is captured by a detector. But an atom can be easily disturbed by a magnetic field. Therefore, it is necessary to eliminate all the effects due to residual fields (for instance, the earth’s magnetic field), which requires surrounding the system with a magnetic shield. A vacuum must be created so that the hydrogen atoms are isolated in the cavity, hence the presence of vacuum pumps. Since the cavity can only accommodate one wave at a particular frequency, its size depends on the wavelength that excites the atoms, i.e., the one they have chosen. For hydrogen, a cavity of 20 cm in diameter is required (the cavities for rubidium clocks are smaller, but these clocks are less stable). A size that cannot vary in the least, especially under the effect of temperature, otherwise this will influence the frequency and disrupt the system. Therefore, it is necessary to stabilise everything to ten-thousandth of a degree! Not to mention a system that first splits the H2 molecules in the hydrogen gas into H atoms followed by all the signal detection electronics. In short, a hydrogen maser is a relatively voluminous and heavy system, which subsequently increases the size and weight (and therefore the launching cost!) of satellites when they have to be sent into space.

Hence, Thierry Bastin’s and Gillam-FEi’s intention is to miniaturise such a clock. Relatively small hydrogen maser clocks already exist but they perform less well because they function in passive mode.  Liège’s goal is to miniaturise the system without decreasing performance (while maintaining the active nature of the clock). “We submitted a project within the framework of the Marshall Plan in 2008”, Thierry Bastin explains. “Our goal was to create a prototype to be taken on board a satellite. But we were starting from zero, and we therefore chose to begin by building a traditional atomic clock with the help of someone who already had specific experience in this type of clock, Dr. Cipriana Mandache to be exact. This is what we did and the clock now functions to our complete satisfaction. The following stage is miniaturisation. And here, we’re just at the beginning..." While the basic principle of the maser has been well known for decades, actually making one is quite another matter.  And miniaturisation comes up against another problem... size: the size of the cavity matters and is linked to the wavelengths used. Therefore, how can this cavity be reduced without the system really noticing it? “We have to devise another design for the cavity”, Thierry Bastin explains. “But it’s important to realise that we don’t know everything, there isn’t a ready-made formula for such small clocks and the simulations require enormous computer capacities; we still don’t know how to simulate everything and our work sometimes has to be empirical in certain respects when it comes to optimising the components." Let's talk about it again in two or three years time to find out whether they have succeeded!

(1)  Here, it might be useful to remind ourselves that an atomic clock has nothing to do with radioactivity! The chosen atoms aren’t radioactive, there is no phenomenon of disintegration of atoms or emission of particles. Only the size of these clocks and their cost prevents them from being worn on a wrist!