快猫短视频

IN HIS lab in Boulder, Colorado, Bob Drullinger has a timekeeping pyramid. At the base is the rough and ready wristwatch. Each higher level has a more sophisticated timekeeper, a means of testing the accuracy of the ones below. At the top sits a small band of scientists who dispense wisdom like so many Himalyan mystics. Drullinger himself is one of this band. His job at the US National Institute of Standards and Technology (NIST) is to measure the second with all the accuracy he can muster-he is a custodian of the definition of time.

For centuries, the second was defined as a fraction of a day or year. But in 1967, an international gathering of scientists decided that the Solar System鈥檚 clocks vary too much for the strict needs of modern humans. To find a more stable timekeeper, they turned instead to the quantum realm, and redefined the second in terms of the frequency of microwave radiation that excites a caesium-133 atom. Ever since, there has been intense competition around the globe to measure this frequency with the smallest possible error.

The results are astonishing. Drullinger鈥檚 second is good to 3.5 parts in 10¹⁵. If his machine had been set running 100 million years ago when dinosaurs tramped the Earth, it would still be correct today to within 1 second. And Drullinger鈥檚 setup is no longer the best. In the past couple of years, it鈥檚 been beaten by a French-designed 鈥渁tomic fountain鈥�. Another team of researchers, who are holding ions in minuscule traps, reckon they should be able to define the second to 1 part in 10¹⁷. If they succeed, their level of error will be about 1 second in 10 billion years-almost the lifetime of the Universe.

Heart of the second

All these devices exploit the fact that atoms will flip between energy states if they鈥檙e hit with radiation of the right frequency-the resonant frequency. In caesium, the nucleus and outermost electron spin like tiny tops and so generate minuscule magnetic fields. The spin of the electron and nucleus can be parallel, in which case the fields repel each other, or anti-parallel, so they attract. The jump between these two spin states, called a hyperfine transition, is at the heart of the definition of the second. It has a resonant frequency in the microwave band at about 9 192 631 770 hertz. Back in 1967, the second was defined as exactly 9 192 631 770 oscillations of this radiation.

Defining the second is one thing. Measuring caesium鈥檚 resonant frequency has proved quite another. Machines that carry out this task are called primary frequency standards. They鈥檙e similar in design to caesium clocks, but ultra-accurate. They work by tuning a microwave source so that it flips the highest possible number of caesium atoms between hyperfine states. The closer the microwaves are to the resonant frequency, the more atoms flip.

Most of these devices employ a beam of caesium atoms that emerge from a hole in the side of an oven (see Diagram). 鈥淵ou get atoms coming out just like steam out of a kettle,鈥� says Drullinger. Only atoms in one hyperfine state are wanted, but those emerging from the oven are split about half and half between the two states. A strategically placed magnet solves this problem by deflecting atoms in one state into oblivion. Atoms in the other state are sent into a microwave cavity, where they are flipped.

To find out how many atoms have successfully made the hyperfine transition, a second magnet deflects them onto a hot filament, where they lose an electron and produce an electric current. (Once again, the magnet sends any atoms that haven鈥檛 flipped into the wild blue yonder.) If the current from the detector falls, it means the microwave oscillator has wandered away from caesium鈥檚 resonant frequency. So this current drives a feedback loop that makes the oscillator dither back and forth until the current is a maximum once more.

The final component for a primary frequency standard is a way to continually count 9 192 631 770 oscillations of the microwave radiation. A clock must also lay each second on top of the last.

This all sounds straightforward. But it is not. Atoms, for example, will flip between hyperfine levels even if the radiation is not bang on the resonant frequency. Look at an atom鈥檚 absorption spectrum, with intensity up the side and frequency along the bottom, and you see a rounded peak-or 鈥渓ine鈥�, as physicists call it-centred on the resonant frequency.

Smearing the line

But things get worse. The machines needed to measure the line tend to make it broader. Temperature, the velocity of caesium atoms and any electric or magnetic fields can 鈥渟hift鈥� the resonant frequency, smearing the line and reducing the machines鈥� resolution. All caesium clocks suffer to a lesser or greater extent, and their accuracy is limited.

This is where primary frequency standards come into play. Drullinger and a handful of other researchers around the world have designed their machines so that the uncertainties are minimised or corrected for. At the top of the timekeeping pyramid, they keep a check on how the world鈥檚 caesium clocks are running.

Probably the biggest source of error for both frequency standards and clocks arises from the short time that the atoms have to interact with the microwaves. Atoms in a caesium beam travel at 200 metres per second and pass through the cavity in next to no time. The Nobel prizewinning physicist Norman Ramsey helped to solve this problem in the late 1940s by splitting the cavity into two and drawing on one of quantum theory鈥檚 weirdest effects. The first microwave cavity gives the atoms just enough energy to knock the atoms into a 鈥渟uperposition鈥� of the two hyperfine states. As they leave this cavity they are in a ghostly state that is neither one thing nor the other. Microwaves in the second cavity hit the atoms so as to finish the task of flipping them into the opposite hyperfine state.

For this two-step operation, the micro-waves must be tuned much more accurately than in earlier designs. Drullinger likens what happens to pushing a child on a swing with closed eyes. 鈥淵ou鈥檝e got a pretty good internal timer. You can figure out when that swing is going to come back and touch your hand,鈥� he says. 鈥淏ut suppose you close your eyes and fold your arms and waited for 100 swings and then put your hands out and try to catch it in sync . . . If you got it right, you would know that things were really right: that your internal timer had worked right.鈥� So, the longer the atoms spend between the two cavities, the narrower the linewidth. Using these tricks, NIST鈥檚 previous frequency standard, NBS-6, reached an uncertainty of just 1 part in 10¹³.

Another problem lies with the use of magnets to divert the atoms of the chosen hyperfine state into the cavities. The magnets can make the atoms drift left or right through regions of the cavities where the radiation is not uniform. To overcome this problem, Drullinger鈥檚 present machine, NIST-7, has replaced the magnets with lasers.

Driving atoms

As well as its two hyperfine levels, caesium has a series of short-lived states that are excited by infrared radiation (see Diagram). Hit a caesium atom with laser light tuned to one of these transitions and it jumps into the state and falls back almost immediately, emitting the excess energy as fluorescence. It doesn鈥檛, however, always fall back to the same hyperfine level, and by carefully selecting the laser frequency, Drullinger and his colleagues can drive atoms from one hyperfine state to the other.

With this technique, NIST-7 transfers atoms streaming from its caesium oven into just one hyperfine level before they enter the microwave cavities to be flipped (see Diagram). As the atoms leave the cavities, they are hit by a second, detection laser which is tuned so that only atoms that flipped in the cavities get excited. These atoms absorb the laser鈥檚 light and fluoresce. NIST-7 uses the intensity of this fluorescence to drive the feedback loop to the microwave oscillator.

But adding lasers to a caesium beam machine is like bolting a late 1980s engine into a 1950s Cadillac. It鈥檚 performance will always be limited. So Drullinger is now leading one of several groups building state-of-the-art machines. These refined, late-1990s models are beginning to cruise past NIST-7.

Paradoxically, one of these ultramodern machines is taking shape in the basement of a 17th-century mansion in Teddington, southwest London. Here, at Bushy House, Dale Henderson, Peter Whibberley and Stephen Lea of the National Physical Laboratory (NPL) have raised a shining tower of precision-engineered titanium amid a forest of optical lenses, beam splitters and mirrors. This is a caesium fountain.

The fountain overcomes many of the problems of caesium beam machines at a single stroke-by slowing down the atoms. The high speed of caesium beams is a problem not only because it reduces the amount of time the atoms spend in the cavities; it also introduces errors caused by the Doppler effect. Just as the pitch of an ambulance siren is raised as it races towards you, so fast-moving atoms 鈥渟ee鈥� microwave radiation at their resonant frequency as being higher than it really is. A carefully designed cavity can virtually eliminate this problem. But there is another manifestation of the Doppler effect that won鈥檛 go away-time dilation. Einstein鈥檚 theory of relativity says that a second is longer for a fast-moving object than for one at rest. This, again, makes atoms in a caesium beam see correctly-tuned microwaves as being shifted slightly from resonance.

The fountain gets round these problems with a range of laser cooling techniques developed over the past two decades. (鈥淎toms caught in a web of light鈥�, 快猫短视频, 29 January 1994, p 32). Chief among these is Doppler cooling, which uses photons at a slightly lower frequency than caesium鈥檚 infrared resonance.

When a fast-moving caesium atom meets one of these photons head-on, the Doppler effect ensures that the atom sees the photon at its resonant frequency. The atom absorbs the photon, jumps to a higher level and then fluoresces, spitting out a photon in a random direction. The end result is a tiny transfer of momentum from the photon to the atom. Bombard the atom with lots of photons and it slows-like stopping a football by firing ping pong balls at it. Now apply beams from front and back, left and right and top and bottom. This configuration slows the atom in all directions, and is called optical molasses.

Last month, the inventor of this technique, Steven Chu of Stanford University, California, won this year鈥檚 physics Nobel (This Week, 快猫短视频, 25 October, p 15). The two men he shared it with, Claude Cohen-Tannoudji of the Ecole Normale Superieure in Paris and William Phillips of NIST, also put their laser cooling skills to work on the caesium fountain鈥檚 design.

The techniques they devised are astonishingly effective. They chill the atoms to a few millionths of a kelvin. But the molasses alone cannot hold enough atoms to give a good signal, so Henderson and his colleagues have added a pair of 鈥渢rapping coils鈥� that increase the payload from 1 million atoms to around 10 million. As in NIST-7, the lasers also shunt the atoms into a single hyperfine level.

With the atoms cold, confined and in the correct state, the coils are switched off and the vertical lasers detuned slightly in opposite senses to launch the atoms upwards at about 3.5 metres per second. They rise through the microwave cavity, where they are pumped into a superposition of the two hyperfine states. At a height of 63 centimetres they begin to fall and on their way down pass through the cavity again. So long as the microwave frequency matches that of the hyperfine transition, all the atoms are nudged into the second hyperfine state. Their number is, once again, detected by fluorescence.

The fountain has some huge potential advantages over caesium beam machines. The extra time the atoms spend between the two microwave pulses gives a big increase in resolution. While NIST-7 hunts for a line that is around 100 hertz wide, the fountain looks at a linewidth of about 1 hertz. Time dilation, while still present, is also much less of a nuisance.

But it鈥檚 not all good news. The metal surrounding the fountain is at room temperature and gives off what physicists call blackbody radiation. This tiny input can be enough to disrupt the delicate superposition of the atoms and shift the resonant frequency. A similar error arises if atoms collide during flight.

This collisional shift is probably the worst of the fountain鈥檚 problems, says Andr茅 Clairon of the Paris Observatory. It鈥檚 his fountain that the groups at the NIST and NPL are hoping to emulate. Clairon and his colleagues got their machine running at the end of 1993 and have since reduced its uncertainties to 2 parts in 10¹⁵. 鈥淚t is still an experimental device,鈥� says Clairon. 鈥淥ur next system will be more reliable.鈥� There is no reason, he believes, why the new model should have errors above a few parts in 10¹⁶.

If the fountain is a late-1990s executive saloon, today鈥檚 concept cars are trapped ion machines. Caesium plays no part in these devices, and if they are ever to become primary frequency standards the second will have to be redefined according to the properties of a different element. The main motivation for switching to ions is to move to a transition with a higher frequency, says David Wineland, who leads the ion trapping group at the NIST. Higher frequencies mean more 鈥渁tomic ticks鈥� in any given unit of time, so precision should increase.

Cold, airless and trapped

The beauty of ions is that their charge makes them easy to confine. This makes it possible to interrogate just one ion and to keep it still. 鈥淵ou鈥檙e probing a single, isolated ion at rest in a vacuum,鈥� says Patrick Gill of the NPL. 鈥淵ou can argue that this is the best arrangement for keeping perturbations out.鈥�

One of the big issues for ion trappers is whether to stay in the microwave band or head for the optical region. The NIST group is playing both sides of the fence. It is working on mercury-199, which has both a microwave transition at 40.5 gigahertz and a transition in the ultraviolet at 1 million gigahertz.

The NIST group has had most success with the microwave transition, using not a single ion but about 10. The mercury ions are cooled with lasers and confined in a 鈥渓inear Paul trap鈥�, a tiny cylindrical device (see Diagram). Four electrodes run end to end, and when an alternating voltage is applied across them they set up an electric field that falls to zero along the axis of the trap. The ions line up or 鈥渃rystallise鈥� along this axis.

As in the fountain, lasers pump the ions into just one hyperfine state. But unlike the fountain, the ions are not launched through a microwave cavity. Instead, the microwaves are brought to the ions. An initial pulse pushes the atoms into a superposition of the hyperfine states. A second pulse completes the transition and laser fluorescence is used once again to measure how many ions have flipped.

鈥淲e can make the interval between the two pulses almost as long as we want,鈥� says Wineland. 鈥淲ith mercury we make it 100 seconds.鈥� This extended interval makes for a very narrow linewidth-about 5 millihertz. The level of uncertainty of this machine is 3.5 parts in 10¹⁵, very close to that of Clairon鈥檚 fountain. 鈥淲e鈥檙e very encouraged,鈥� says Wineland. 鈥淭his is our first try at it. There鈥檚 a lot of chewing gum and beeswax holding this thing together.鈥�

Woollen mittens

The much higher optical frequencies would give even more atomic ticks per second and the NIST group is just beginning experiments in this band. A dozen labs around the world are working on similar devices. Gill and his colleagues are using ytterbium and strontium ions, while others are trying indium and barium.

But the optical frequencies bring their own problems. Many transitions have broad natural linewidths, so will never give good resolution. And even when you find a transition with a narrow linewidth, you then need a laser with a narrow enough linewidth to lock onto it-just as a microwave oscillator locks onto caesium鈥檚 hyperfine frequency. Using a laser with too broad a linewidth is like trying to pick up a pin while wearing woollen mittens. Gill鈥檚 group recently found an optical transition in ytterbium with a natural linewidth counted in nanohertz. No laser is narrow enough to lock onto this yet, says Gill. Even transitions with linewidths around 1 hertz are still a problem.

The other difficulty with optical transitions is how to count a million billion oscillations every second-not an easy thing to do accurately at present. But even with these obstacles, Wineland reckons the future looks rosy for an optical frequency standard. 鈥淲e don鈥檛 see why we can鈥檛 get down well below 1 part in 10¹⁷,鈥� he says.

But this is an uncertainty of about 1 second in 10 billion years. Isn鈥檛 this getting a bit obsessive? The justification, says Drullinger, is historical. 鈥淓very time we鈥檝e made an advance, somebody鈥檚 been right there behind us,鈥� he says. 鈥淎s soon as we got there they said: `Ooh, I know what to do with it鈥�.鈥� Just look at the Global Positioning System, he says. 鈥淚t鈥檚 using everything we鈥檝e got right now.鈥�

There are other advantages. Real clocks, all the way down Drullinger鈥檚 pyramid, improve as the frontier is pushed back. And physicists in other areas benefit. Gill at the NPL, for example, works in length metrology. The metre these days is defined as the distance travelled by light in a vacuum in a fraction of a second. So the better the second can be measured, the more precisely we know the metre. Together with Chris Monroe of NIST, Wineland also heads a quantum computing group which uses trapped ions as logic gates (鈥淚t takes two to tangle鈥�, 快猫短视频, 28 September 1996, p 26). 鈥淭he clock people are at the edge,鈥� says Wineland. 鈥淚f some of the problems of quantum computation are solved, it will be because of their work.鈥�

The final irony, though, is that these clock people aren鈥檛 really interested in clocks. Custodians of the second they may be, but their primary frequency standards don鈥檛 add up the seconds to make minutes or hours and they don鈥檛 tell you if it鈥檚 midnight or teatime. They are simply yardsticks for measuring the second. On Drullinger鈥檚 wall is a clock with the numbers one to 12 scattered at random round the face. In big letters in the middle is written 鈥渨ho cares鈥�.