Timed to perfection

 The fabled Omega Speedmaster is there for good reason; the chronometer, which became the official watch of the US Space Program, has survived every test that Nasa can throw at it and is accurate to within 6 s every 24 hours.

Within days the Apollo 13 astronauts have good reason to be grateful for the Speedmaster’s accuracy. One of the craft’s fuel cells explodes and, as part of the emergency regime to conserve power, onboard clocks are turned off. The watch is all that stands between them and infinity.

Astronaut Jack Swigert has been assigned the task of timing the duration of a ’corridor control burn’ that will realign the spacecraft into a safe landing trajectory. Too little burn and they will skip off the top of the Earth’s atmosphere into space to die a hideous and lonely death of asphyxiation; too much and they will burn up by plunging too deeply and too fast into the Earth’s atmosphere.

Swigert’s Speedmaster does not let him down. The burn is accurate, and the rest as they say is history. The crew of Apollo 13 literally owe their lives to ’split-second’ timing.

The era of atomic clocks had arrived and with it the ability to measure time to 14 decimal places. Think of it in this way: a caesium-based atomic clock will lose 1 s in 30 million years, or fractionally more than 2 s in the time that separates us today from the extinction of the dinosaurs.

Today the science of horology is undergoing another revolution that may well require that the second is once again redefined. The latest generation of atomic clocks will not be based on the energy state of the caesium atom. Instead, the so-called ’optical clocks’ will measure time by locking the oscillation of a laser beam to changes in the energy level of an atom of mercury, ytterbium, strontium, indium or calcium.

In a conventional atomic clock, the oscillator is a group of heated caesium atoms which, when bombarded by microwaves of a specific frequency, ’flip’ their electron shells 9,192,631,770 times a second. To achieve this state, caesium atoms are first boiled off and passed into a vacuum tube where a magnetic field separates atoms of the correct energy state. These atoms then enter an intense microwave energy field, the frequency of which is under the precise control of a crystal oscillator. When a caesium atom receives energy of exactly the right frequency (9,192,631,770 Hz) it changes its energy state. A further magnetic field separates these excited caesium atoms and channels them to a detector.

The output of the detector is proportional to the number of atoms arriving, and peaks when the microwave frequency is exactly correct. This in turn is used to correct the crystal oscillator controlling the microwave field, and the resulting ’locked’ frequency (the ’counter’) is divided by 9,192,631,770 to give a single pulse per second.

This second is the SI (Systeme Internationale) or ’atomic’ second first defined in 1967. A crucial point here is that the reference is self-recalibrated by the microwave oscillator; humans have been removed from the calibration loop.

However, caesium clocks have in-built inaccuracies owing to the laws and tolerances of quantum physics. For example, the optimum possible accuracy of measuring the vibration of a single atom of caesium cannot be achieved. According to Heisenberg’s uncertainty principle, it is not possible to measure precisely the frequency of the single microwave photon emitted when the caesium atom is stimulated.

Similarly, the hot caesium particles crash through the vacuum chamber in a jumble of angles and speeds. Their susceptibility to the crucial frequency of 9,192,631,770 Hz varies because of the Doppler shift. Particles moving at near quantum velocities experience Einsteinian time-dilation effects (or ’warp drive’).

The upshot of all this is that the caesium ’ticks’ are no longer identical and the clock’s accuracy suffers as a result.

A crucial point about atomic clocks is that their accuracy is proportional to the wavelength of the radiation that the clock uses - microwaves in the case of caesium clocks. Moving further up the electromagnetic spectrum - say into the visible and near-infrared portions - should in theory allow us to improve the accuracy of our clock. At these shorter wavelengths, the higher frequencies provide a more sensitive counter. Such differences in oscillator frequencies are key to the accuracy of all time-keeping devices.

Compare, for example, the sundial with an American railroad grade pocket watch, which lost just 30 seconds a week and represented a breakthrough in precision timekeeping in the late 1800s. The balance wheel (oscillator) of the railroad watch vibrates much more rapidly than the motion of the sun in the former. It is this same principle, therefore, that distinguishes optical clocks from their caesium-based cousins.

Once the ion is in its super-chilled state another laser is tuned to the specific frequency needed to shift the ion’s outer electron from one energy state to another. When the laser is tuned to this frequency the electron ceases fluorescing - the mercury ion goes dark. As long as the electron stays in this ’dead zone’ the laser is at the correct frequency - and the clock is ticking accurately. If the electron blinks ’on’ then the laser automatically retunes itself to the dead zone.

The laser’s oscillation though is of the order of a quadrillion (10 15 ) cycles a second, much faster than the oscillator in a conventional caesium clock. It is this speed after all (remember the sundial and the pocket watch) that gives the optical clock its superior accuracy.

The problem until recently has been how to measure something that oscillates so fast, way beyond the capabilities of conventional electronics. The answer is a ’frequency comb’. Think of this comb as a gearbox that slows the rapid oscillations of the ’probe’ laser down to something that is measurable.

The frequency comb is a device by which the light from the probe laser, now locked to the frequency of the mercury ion electron’s oscillation, is transmitted via a special fibre optic cable to another laser pulsing ’only’ a billion times a second. This second calibration laser acts as the reducing gear, condensing the probe laser’s quadrillion cycles a second to a countable billion times a second. Pulses of light from this laser last for just a few femtoseconds with intervals of darkness between them.

When passed through a prism and split into its constituent frequencies this light has a perfectly regular spectrum - just like the teeth on a cog. By adjusting a mirror in front of the prism it is possible to bring the probe laser pulses into perfect phase with one of the teeth on this cog and voilà , you have your reducing gear, or in a plainer language, your clockwork. The ’comb’ tag comes from the perfectly regular spacing of the calibration laser’s constituent frequencies.

With the principle of the optical clock established it is becoming clear that mercury may not be the ideal element to use. Mercury is sensitive to minor fluctuations in local magnetic fields for example. However, other elements such as indium, strontium, or calcium do not suffer from this disadvantage. But all optical clocks will begin to suffer from the same problems once their ultimate goal of an accuracy of a second every 30 billion years is realised.

At such accuracies even the relativistic effects of rising and walking to the front door become important. And then there is gravity; the stronger its pull the slower the passage of time. A height difference of only 10 cm will change the rate of a conventional clock by one part in 10 ¹⁷ so it is clear that the new generation of optical clocks will have to be corrected even for what floor in a building they stand on. And then there are fluctuations in the pull of gravity, caused by tides and even variations in local geology, that will need to be taken into account too. Optical clocks will be a nightmare to set up.

The Global Positioning System (GPS) that people increasingly use in cars and other vehicles relies on atomic clocks in a network of satellites and ground stations around the world. The system works by measuring the time taken for signals sent from receivers to travel to and from the orbiting satellites. With the current limitations of atomic clocks, the uncertainty in timing this duration results in an uncertainty on the ground of several metres. With the new generation of optical clocks this uncertainty will shrink to a few centimetres at most. In a world where terrorism is the new menace and satellite surveillance and surgical strikes increasingly likely the advantages of this are obvious.

But distance is important too on the planetary and interstellar scale. As we send spacecraft farther and farther into space we will need to know their position accurately. Once again optical clocks will provide the means to do this.

Finally, there is the problem of the so-called fine structure constant, which is one of the fundamental forces that holds the Universe together. There has recently been speculation that this ’constant’ may not be so at all and, since it influences the resonant frequency of ions, comparing two optical clocks based on different ions will allow this theory to be tested.

From plus-or-minus 30 seconds a week to keep railroad passengers safe, through plus-or-minus six seconds a day to save three men in outer space, to plus-or- minus 1 second in 30 billion years to test whether God has a sense of humour after all; time remains of the essence.

Acknowledgements

Richard Corfield is an isotope geochemist and directs the stable isotope laboratory in the Department of Earth Sciences, Oxford University.