THE CAESIUM FOUNTAIN PRIMARY FREQUENCY STANDARD

by National Physical Laboratory

• The caesium second
• Using lasers to make a better clock
• Cooling atoms with light
• A frequency standard using cold atoms
• Frequency shifts
• The NPL caesium fountain

The caesium second

The first caesium atomic clock began operation as long ago as 1955, at the National Physical Laboratory. At that period the motion of the Earth still provided the basis for the world’s time scale, called Universal Time or Greenwich Mean Time. The builders of the NPL caesium clock, Louis Essen and Jack Parry, soon demonstrated that their device could keep time with much greater stability than the Earth itself. In an extensive series of measurements, the output from the caesium clock was compared with time based on the Earth’s rotation. The results of this work provided the basis for a re-definition of the second using the caesium clock signal. This was officially adopted in 1967. The new definition, which remains in force today, states that the second is equal to the duration of exactly 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Almost all caesium clocks constructed over the past 40 years have worked on the same principles. At room temperature, caesium atoms are equally divided between two internal atomic states - the hyperfine levels of the ground state of the atom referred to in the definition of the second - which differ slightly in energy. In caesium, this energy difference is equal to the energy of a photon of microwave radiation with a frequency of about 9.2 GHz. What this means is that atoms in one of these states can be pushed into the other state by microwaves, but only when the microwave frequency is very close to the atomic transition frequency.

In a caesium clock a beam of atoms is produced by heating a small amount of caesium to around 100°C in an oven. The atoms behave like tiny magnets which are oriented differently in the two ground state levels. This property allows those atoms in one of the ground states to be separated from those in the other state and removed from the beam by passing it through a shaped magnetic field. The atoms left in the beam, now all in the desired state, then travel through a microwave cavity. This is a metal enclosure containing microwaves with close to the 9.2 GHz transition frequency. The atoms will interact with the microwaves and a proportion, dependent on the microwave frequency, will transfer to the other state. These atoms which have changed state are selected by a second magnet and counted. As the microwave frequency is changed this signal increases and decreases in a characteristic pattern known as Ramsey fringes. The largest, central fringe is observed when the frequency is tuned as accurately as possible onto the atomic transition frequency. When the device is operating continuously as a clock the microwave frequency is adjusted automatically to keep the signal at the maximum value. This frequency is then known precisely, since it is stated in the definition of the second. Sophisticated electronic methods can be used to divide it down to more useful values, such as 5 MHz or 1 pulse per second, which can be counted to keep track of the passage of time.

Since the time of Essen and Parry, enormous improvements have been made to the performance of caesium clocks and their accuracy has increased by a factor of 10 000. The second is realised, or measured, with greatest accuracy by a small number of large, complex primary frequency standards¹ located in national standards laboratories around the world. It is these primary standards which provide steering corrections to the world’s atomic timescale, UTC, to keep the duration of the scale interval as close as possible to the defined value for the second. The best of these standards, named CS1 and located at the German national standards laboratory (PTB) in Brunswick, achieves an accuracy of 7 parts in 1015. This is equivalent to gaining or losing a second in 4.5 million years.

¹These devices are described as frequency standards rather than clocks because they generally are run for short periods at a time, to provide a correction to other slightly less accurate clocks, rather than continuously recording the passage of time. The term "primary" indicates that these standards are realising the internationally-accepted definition of the second at the highest level of accuracy.

Using lasers to make a better clock

During the 1980s reliable laser diodes operating in the near infra-red began to be produced. When the frequency of the light emitted by one of these lasers is tuned onto a transition frequency in caesium atoms, such as one of those around 852 nm, the laser beam can be used to manipulate the internal states of the atoms. For instance all of the atoms in a beam can be "optically pumped" into one of the ground state levels. As a result it is possible to replace the state selection magnet in a beam standard with a laser beam stabilised on an appropriate transition frequency. Similarly, another beam can be used to count the number of atoms which have changed state after interacting with the microwaves by stimulating the atoms in that state to fluoresce, or emit light.

One great advantage of using a laser for state selection is that all of the atoms can be prepared in one state before they enter the microwave cavity, rather than using a magnet to throw away all of the atoms that are not in the desired state, so a better signal to noise ratio is obtained. In addition, the atoms are very sensitive to magnetic fields while passing through the microwave cavity, and the difficulty of providing effective screening of the fields from the state selection magnets in conventional beam standards is a significant limitation to their performance. There is at present one optically pumped caesium primary standard in operation which uses lasers in this way: NIST-7 at the US National Institute of Standards and Technology (NIST) in Boulder, Colorado. This standard has an accuracy similar to that of CS1.

However, optically pumped clocks suffer from the same fundamental limit to their performance as any other standard based on an atomic beam. The width of the central peak of the Ramsey fringes is determined according to the rules of quantum mechanics by the time that the atoms spend interacting with the microwaves: the longer the interaction time then the narrower the resonance peak. In practice it is difficult to find the centre of this peak to better than around one millionth of its width, and there are practical limits to the length of the microwave cavity and the minimum speed of the beam which limit the interaction time to no more than a few tens of milliseconds. This principle therefore imposes a basic limit to the accuracy which can be achieved by any standard using a thermal beam of atoms, and the best beam standards such as CS1 and NIST-7 are now very close to this limit.

Cooling atoms with light

By the mid-1970s it was realised that lasers can do far more than select atomic states; they can for instance be used to cool down and manipulate clusters of atoms. The simplest laser cooling process makes use of the Doppler effect. Atoms illuminated by a laser beam will absorb photons of light provided that the light frequency is tuned to an atomic transition. If the frequency of the laser light is detuned to a slightly lower value than the transition, most atoms in the beam will no longer readily absorb photons. The exception is those atoms which are moving towards the light source, which see the light Doppler-shifted to a higher frequency and therefore closer to resonance. As these atoms absorb photons from the beam the momentum of the photons is transferred to the atoms, slowing them down. Of course, after each absorption an atom will be left in an excited state and it must reradiate a photon in a random direction before it can absorb the next slowing photon from the beam. Each absorbed photon only slows the atom by a tiny amount, reducing its speed by 3.5 mm per second. However, the lifetime of the excited state is so short that the cycle of absorption and re-emission can occur more than 10 million times a second, and the atom experiences a deceleration over 10 000 times that of gravity on an object thrown upwards. There is, though, a minimum temperature that can be attained by this simple Doppler cooling mechanism, which is around 125 microkelvin for caesium.

One cycle of absorption and emission:

Fortunately, experiments have shown that temperatures lower than this theoretical limit can be achieved. It was realised that additional cooling mechanisms were at work. When an atom is illuminated from both sides by a pair of overlapping laser beams it sees a periodically changing polarisation of the light, and this varying polarisation changes the atom’s potential energy. The atom tends to absorb photons when its energy is at a minimum and radiate when near a maximum, so that there is a net loss of energy and therefore an additional cooling mechanism. Much lower temperatures can be attained by this effect, which is known as polarisation gradient cooling. Even this mechanism has a limit, though, which is due to the recoil which an atom experiences when it emits a single photon. The recoil limit for caesium is about 2 microkelvin, and the practical cooling limit is several times this value (although other processes have been discovered which can cool even below the recoil limit). The 1997 Nobel Prize in Physics was awarded to three researchers, Steven Chu who is now at Stanford University in California, Claude Cohen-Tannoudji of the École Normale Supérieure in Paris, and Bill Phillips at NIST, Gaithersburg, Maryland, who developed and explained many of these atom-cooling techniques.

A single laser beam can only cool atoms in one direction. But with three pairs of opposing beams at right angles to each other, atoms which drift from the surrounding low-pressure vapour into the region where the beams intersect will be cooled whichever way they move, producing a cloud of slowly-moving atoms. This technique has been named ‘optical molasses’ because the atoms behave as though they are moving through a viscous fluid. The atoms in a molasses are slowed down considerably, typically to speeds of a few centimetres per second which correspond to temperatures of a few microkelvin. They are not trapped, though, and there is a continuous flux of atoms entering and leaving the molasses. It is, however, possible to form a very effective trap in which atoms can be kept confined for much longer periods. This is done using six laser beams as for molasses, with the addition of a pair of coils above and below the interaction region to generate a magnetic field which has a minimum where the light beams converge. This configuration is known as a magneto-optical trap, or MOT, and can confine atoms at a higher density than molasses.

A frequency standard using cold atoms

The method of cooling and trapping atoms using laser beams can form the basis of a new form of caesium frequency standard. The cluster of cold atoms contained in an optical molasses can be thrown vertically upwards by turning off the horizontal laser beams and slightly shifting the frequencies of the vertical beams by equal but opposite amounts. With a microwave cavity positioned above the cooling region, the atoms will rise upwards through holes in the cavity then fall back under gravity along the same path. During each pass through the cavity the atoms interact with the microwaves inside, as in a beam standard. The cooling beams can prepare the atoms in the desired level before launching, by optical pumping, while further laser beams can be used to measure the populations of the ground state levels after the microwave interaction. The fountain therefore operates in a pulsed fashion, with the cycle of cooling, launching, interaction and detection repeating every second or so.

This form of frequency standard is known as a caesium fountain. The fountain has an immediate advantage over caesium beam standards. The total time for the atoms to interact with the microwaves during each cycle is increased to about half a second. This gives a signal width of only 1 Hz, approaching a factor of 100 narrower than in the best thermal beam standards. It is therefore possible to lock the microwave frequency much more precisely onto the narrower resonance observed in a fountain standard. As a result a much greater accuracy can in principle be achieved, and the narrower linewidth also gives rise to better frequency stability.

The first caesium fountain designed to operate as a frequency standard was constructed at the LPTF (Primary Laboratory for Time and Frequency), Paris in 1990. The performance of this fountain has since been studied extensively and on two occasions it has contributed to UTC. The accuracy of the LPTF fountain is now assessed to be 2 parts in 1015, equivalent to a second in 16 million years, and this performance is likely to be improved further. It is at present the most accurate of all primary frequency standards. Following on from the work at LPTF various other standards laboratories have begun to construct their own caesium fountain frequency standards. Apart from the NPL, these include NIST at both Boulder and Gaithersburg, the United States Naval Observatory in Washington, and the national standards laboratories in Germany, Canada, Japan and several other countries.

Frequency shifts

At the phenomenal level of accuracy now being attained by primary frequency standards, there is a wide range of effects which can cause the microwave transition frequency in the atoms to change from the unperturbed value required by the definition of the second. Their effect is to move the frequency produced by the standard very slightly away from the "correct" value. These must be carefully evaluated and corrected in a caesium fountain, as in a beam standard, before it can operate as a primary frequency standard.

As well as the greater accuracy resulting from the narrower linewidth, the fountain configuration substantially reduces several of the causes of frequency uncertainty found in thermal beam standards. Because the atoms in a fountain are moving so slowly, the frequency shifts which arise from their motion, such as the Doppler shift and a relativistic effect, are greatly reduced. In addition, a limiting factor in the performance of a beam standard is the slight difference in the phase of the microwaves between the two arms of the U-shaped microwave cavity (known as a Ramsey cavity). In a fountain a simple cylindrical cavity can be used, through which the atoms pass twice, with the result that the phase difference experienced by the atoms becomes insignificant.

The largest shift in the frequency of any caesium standard is due to the magnetic field in the interaction region. This causes the atomic energy levels to separate into a number of field-dependent sub-levels; a phenomenon known as the Zeeman effect. On a fountain this effect is dealt with by the use of a non-magnetic material, such as titanium or aluminium, for this part of the vacuum chamber, with several layers of magnetic shielding surrounding it to deflect the Earth’s magnetic field from penetrating inside. A solenoid inside the shields generates a uniform magnetic field inside the interaction chamber which will separate the magnetic sublevels of the atoms by a controlled amount. By launching the atoms to different heights it is then possible to map out the small variations in the internal magnetic field so that the frequency correction required can be calculated accurately. The temperature of the interaction chamber is also important, as the thermal background radiation inside the chamber causes a frequency shift. This can be measured and corrected, provided that the temperature of the vacuum chamber is well stabilised and known with sufficient accuracy.

Yet another frequency shift arises from the use of cold atoms. When atoms are cooled their effective size, or collisional cross-section, increases according to the rules of quantum mechanics. The density of the cold atom cluster in a fountain is also much greater than in a thermal beam of atoms. Together these effects result in a much greater rate of collisions between atoms, and this causes the atomic transition frequencies to change slightly. Although potentially a significant limitation, this shift is now understood theoretically and has been studied in the laboratory. As a result it should be possible to apply a correction for it provided that the density and the temperature of the cold atoms is known with sufficient accuracy, although it may still prove to be the ultimate limitation to the precision of caesium fountain standards.

The NPL caesium fountain

Over the past two years an experimental caesium fountain has been assembled at the NPL. It is housed in the basement of Bushy House, the 17th century mansion at the focus of the NPL site. This location provides both reasonable temperature stability and a solid floor which gives good isolation from sources of vibration. A vertical cross-section through the vacuum chamber which forms the core of the fountain is shown in Figure 2. The trapping and cooling region is in the centre, with the interaction region containing the microwave cavity above and the detection region below. The interaction chamber is screened by three layers of magnetic shielding and provided with heating elements (not shown in the figure) to stabilise the temperature. Above and below the cooling region is a pair of coils which can be used to form a magneto-optical trap.

The cooling laser beams are produced by two laser diodes. These are stabilised in frequency by injecting light into them from a master laser which is in turn frequency-locked to a transition observed in a caesium vapour. This is done using a technique called saturated absorption spectroscopy, which removes the Doppler broadening of the absorption line. A fourth laser diode, the re-pumper, is needed to prevent the atoms collecting in the ground state level which is not being used in the laser cooling process. The master and re-pumper lasers also provide the light for counting the number of atoms in each of the two ground state levels after the microwave interaction. As the atoms fall through the detection beams they repeatedly absorb and reemit photons, or fluoresce, and the emitted light is measured using a pair of photodiodes. The sequencing of each cycle of the fountain and the processing of the photodiode signals is carried out by a PC.

Because of the pulsed operation of the fountain, the error signal which keeps the microwave frequency tuned onto the atomic transition frequency is only available intermittently. Some hundreds of seconds of averaging are required to obtain the fountain’s inherent accuracy, and the source of microwaves must therefore be very stable in frequency over this interval. This is achieved by using a low noise microwave source called a dielectric resonant oscillator (DRO) and improving its stability by "locking" to an integer multiple of the frequency from a stable quartz crystal oscillator. The crystal’s frequency is itself controlled by reference to a hydrogen maser (another type of atomic clock). Using a synthesiser it is possible to offset the output frequency of the DRO from the locking value to the caesium transition frequency with millihertz resolution. In this way the frequency of the transition observed in the fountain can be related to that of the hydrogen maser. The maser is central to the production of the national timescale, UTC(NPL), which in turn is related to the world timescale UTC.

This experimental fountain has been used to investigate the cooling and launching of atoms using both molasses and an MOT, and Ramsey fringes have been observed. The experience gained in this work is now being applied to the design of a second caesium fountain, which will ultimately operate as a primary frequency standard at the NPL after its frequency shifts have been evaluated and their uncertainties measured. A hydrogen maser will act as the short-term frequency reference for the fountain primary standard, while the fountain will contribute both longer term frequency stability to the national timescale and improve its accuracy by providing a direct realisation of the SI second at the NPL. In addition, the NPL fountain will contribute directly to the accuracy of the world atomic timescale, UTC, by the regular measurement of its frequency relative to that of UTC.

Contact:

time@npl.co.uk for more information.

© Crown Copyright 2005. Reproduced with the permission of the Controller of HMSO and Queen's Printer for Scotland.

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