A Clock More Perfect Than Time

In a lab in Boulder, one physicist is building a clock that will not gain or lose a second for 300 million years. Next door, a colleague is putting together one accurate for 30 billion years. And when they've finished those, they'll start working on better ones.

By Gary Taubes|Sunday, December 01, 1996
Before Robert Drullinger created his latest atomic clock, he went through what might be called his dismantling phase. Drullinger, who works for the National Institute of Standards and Technology (NIST) in Boulder, Colorado, had recognized the potential of optical pumping, a Nobel Prize- winning technology invented in 1950 by French physicist Alfred Kastler. Optical pumping uses a light beam to manipulate atoms, which, Drullinger realized, could act as timekeepers in an atomic clock. First, though, he needed the right light beam.

Lamps weren’t strong enough for what he had in mind. Only lasers would do. And not just any lasers, says Drullinger, but ones that could be run on the scale of a clock, that will operate when your back is turned, day and night, for months and years. The first to fit the bill were microscopic devices called diode lasers, which began appearing commercially in compact disc players in the early 1980s. And so when cd players hit the market, Drullinger and his collaborators drove down to the local stereo store, bought one, dismantled it, removed the diode laser, tossed the rest, and put the laser to use in their incipient atomic clock. We had to do that for a few years, he says, until you could buy the lasers directly.’’

The ultimate expression of this journey from Kastler’s genius into the guts of home stereo technology is a clock known as NIST-7, which is one of the two most accurate timekeepers in the world. The clock--a marvelous ten-foot-long silver cannon--sits in a NIST laboratory nestled at the foot of the Rocky Mountains, and is aligned due west. That way the sun moves across the sky parallel to the clock itself, and even the interaction of the solar radiation on Earth’s magnetic field does not disturb the clock’s accuracy. Indeed, it is so nearly perfect that, at least for the moment, NIST-7 is beyond the realm of the measurable.

NIST-7 can be compared, says Drullinger, only to some unreachable ideal goal of truth, some mythological truth, to which it will remain accurate to the fourteenth decimal place of a second. In other words, when NIST-7 records the passage of a second, it is not counting a second give or take a millionth, as a good quartz wristwatch might. NIST- 7’s seconds are true to at least one hundredth of a trillionth of an ideal second. Should NIST-7 run so long, it would gain or lose only a single second over 3 million years.

NIST-7 is also a dinosaur, the last of its kind. It’s an exceptionally good clock, but as Drullinger will tell you, there is little reason to build another one like it. The next generation of clocks has to be more accurate still. Drullinger is working on an atomic clock that may be accurate to the sixteenth decimal place of the ideal second (thus losing or gaining a second only every 300 million years); a team of researchers led by David Wineland, who works in a laboratory next door, is working on a next next generation atomic clock, which he hopes will keep accurate time to the eighteenth decimal place of a second. That means 30 billion years would pass before it strayed by as much as a second from ideal truth.

It’s tempting to think that with Wineland’s next next generation clock, the clockmakers of NIST will have the demand for chronometric accuracy covered, but that’s not likely to happen. Since NIST scientists started building clocks in the 1950s (when the institute was known as the National Bureau of Standards, or nbs), the accuracy of their timepieces has improved steadily by a factor of ten every seven years or so (from nbs’s first atomic clocks, which were accurate to .0000001 second per second, to NIST-7, which keeps true to .00000000000001 second per second). It takes the researchers a decade at least to develop a new clock, but whatever they make tends to find commercial applications fairly quickly. When they started building NIST-7, for example, the clockmakers could see no obvious or immediate need for a clock that marked ideal seconds to 14 decimal places. However, by 1993, when the the clock was completed, commercial clockmakers were already selling atomic clocks for a mere $50,000 or so that would stay accurate to the twelfth decimal place, and those clocks needed a clock with better accuracy still--that is, NIST-7--by which to set them.

Now the clockmakers of NIST work on the assumption that the long- term demand for chronometric accuracy is effectively insatiable. That need is initially driven by science, but commercial users are not far behind. Drullinger calls it a hierarchy of users. The most demanding, he says, are rather esoteric: astrophysicists, who are timing the phenomenally punctual pulsations of stars known as millisecond pulsars, and nasa, which needs the clocks to time the navigation commands it sends off to deep-space probes. Then comes a slightly less stringent community: people who work with telecommunications, the global positioning system, security, and defense, all of whom want to send or receive signals with billionth-of-a-second accuracy.

Next in line of demand is a huge community of commercial users for whom it is crucial to keep the right time or the right frequency. (Frequency, after all, is just the number of occurrences of some regular phenomenon per second or hour or whatever, such as the cycles per second, or hertz, that are used to describe the electromagnetic signals sent by radio stations and received by your car radio.) Television and radio stations, for example, have to broadcast at a specific assigned frequency on the electromagnetic spectrum--say 102.5 megahertz, which is 102.5 million cycles per second--and so they have to know the length of a second with extremely high accuracy. Similarly, for two computers to communicate, they have to know when to start listening and when to stop listening and start sending. If they are transmitting data at a rate of 14 million cycles per second (14 megahertz), the speed of a moderately fast modem in a desktop computer, then they’d better be able to synchronize their sending to within a millionth of a second. In fact, anyone who has a clock and the need to know what time it is, or two clocks and the need to synchronize them, needs a better clock by which to set them and keep them accurate. And by now the fabric of modern society is knit together by electronic technology that regularly sends and receives signals synchronized to a billionth of a second.

Our insatiable need for extraordinarily accurate timepieces is problematic, however, because no universal second exists to which clocks can be compared. The length of a second is a human convention. In the 1820s the French defined it as 1/86,400 of the mean solar day, 86,400 being what you get when you multiply 24 (hours) by 60 (minutes) by 60 (seconds). That definition might have remained useful had the mean solar day been a rigid concept. But, as Drullinger says, Earth is not a very stable rotator; it jiggles and jerks and wobbles. It’s also gradually slowing down by a few tenths of a billionth of a second each year, all of which means that Earth’s rotation is not a good clock by modern standards.

A clock, any clock, is just a device that keeps track of some periodic event; it can be broken down into something that oscillates or resonates--the pendulum in a grandfather clock, for instance--and something else, the clockwork, that counts the oscillations and moves the hands around. An ideal clock, then, requires an ideal oscillator, one that oscillates with perfect precision and perfect stability and will keep doing so for however long you want your clock to run. Moreover, this oscillator should also be perfectly reproducible from clock to clock, which is not the case with the pendulums in grandfather clocks or even the quartz crystals in wristwatches. Quartz crystals will vibrate at a certain preferred frequency when tingled by an electric current. This vibration serves as the oscillator of the clock, but its frequency--the number of times the crystal oscillates per second--will depend on the thickness of the quartz. So two quartz clocks will keep identical time only to the extent that the clockmakers can cut their crystals to the identical thickness. As for grandfather clocks, says Drullinger, my pendulum might be a different length from yours, which means his grandfather clock might run faster or slower than yours.

Atoms are considerably more dependable, because the frequencies at which they can emit and absorb electromagnetic energy are fixed by the laws of quantum mechanics. For this reason, since 1967, the officially sanctioned length of a second has been defined by atomic standards: a second is equal to 9,192,631,770 oscillations of the radiation emitted or absorbed by atoms of cesium 133 when they undergo what’s known as a hyperfine transition. If treated properly, any cesium 133 atom will emit or absorb energy of this frequency, just as a tuning fork will vibrate at its chosen frequency--say, the 440 cycles per second of the A above middle C-- and emit a sound wave with a corresponding frequency. Anyone who has access to cesium and the technological ability to put together an atomic clock can do so and know that the clock will march to the very same quantum drumbeat as every other cesium atomic clock.

As Wineland notes, there was nothing magical about cesium--it was chosen as the standard out of a half dozen equally good candidates mostly because it was relatively easy to work with. Drullinger is still using cesium for his next generation clock. Wineland, meanwhile, has moved on to mercury for the next next generation.

Both Drullinger and Wineland are effectively using the same clock-making strategy, which is to account systematically for every conceivable outside influence that could disturb an atom while it resonates. The quantum nature of the atom provides an oscillator as near to reproducibly perfect as the known universe is likely to offer. It’s when the world outside the atom enters the equation that the accuracy begins to go downhill. Atoms may collide with one another, for instance, or they may be hit by stray electromagnetic radiation, magnetic fields, and the like, all of which will jounce their internal timekeeping apparatus. Even the motion of the atoms will change the apparent frequency of the microwaves they emit, an effect known as the Doppler shift, which is more commonly recognized when it happens to train whistles. The frequency will be pushed higher if the atom (or train) is moving toward you, and lower if it’s moving away.

So atomic clockmakers try to remove the sundry disturbances, one at a time if necessary. There’s a whole laundry list of things we have to go through, says Wineland. With each item on the list, they push the accuracy of their atomic clocks toward the next decimal point. Although, Drullinger notes, the list grows as you move the decimal point over, meaning, of course, that they can never get to the end of it.

The laundry list starts with the atom itself. Its frequency of oscillation must be very exact and relatively immune to external influences. While all atoms will emit and absorb signature frequencies of electromagnetic radiation, these frequencies commonly correspond to electrons around the atoms jumping from one orbit to another as allowed by the laws of quantum mechanics. But these transitions, as they’re called, are usually not very precise. The electrons will jump from orbit to orbit quickly, and the quicker they do it, the less precise is their radiation frequency--the energy they emit or absorb is a little blurred, you might say. It all comes down to Heisenberg’s uncertainty principle, says Drullinger. The less time you have to do something, the less you know about it. Since this change happens very quickly, it leaves doubt as to what is happening. The result is a blurry energy signature.

Clockmakers need their energy to be as crisply defined as possible, which means they need the electrons to stay in a new energy level as long as possible. Atoms of cesium 133 happen to have two energy levels known as hyperfine states, which differ only in how the magnetic field of their outermost electron is aligned. The magnetic field of that electron can point either in the same direction as the magnetic field of the atom’s nucleus or in the exact opposite direction, and these two possibilities are known as the hyperfine states. Hyperfine states are not likely to change from one to the other, unless somebody--say a physicist in the laboratory-- makes them change. If you isolate an atom and put it in one of two possible hyperfine states, says Chris Monroe, who works with Wineland, it will stay there for tens of thousands of years.

When the electron does flip from one state to the other, that’s the hyperfine transition. It’s like a little switch in the atom, one that can be switched only with the right frequency of electromagnetic radiation. Cesium will flip hyperfine states only if you zap it with microwaves of very nearly 9,192,631,770 cycles per second--about three times the frequency generated in a microwave oven, says Drullinger. You can think of every cesium atom, he says, as an atomic radio that likes to pick up a single station--the one broadcasting at 9,192,631,770 hertz. And when it hears that station, it flips from one hyperfine state to the other.

Now, the task of the atomic clock is to take a microwave generator--what’s called the laboratory oscillator--and tune it to exactly the frequency of the hyperfine transition in the cesium atom, using the flips from one state to the other as a signal that the oscillator is on the right frequency. Drullinger and his fellow clockmakers talk about probing or interrogating the cesium atoms with the microwaves. It’s as if they’re asking them Is this the right frequency? When the answer is You’re dead on,’’ which is when the microwaves make the cesium atoms flip, then the clock works to keep the microwaves at that frequency and uses it to mark nearly ideal seconds.

The guts of the technology date back 60 years, to the legendary Columbia physicist I. I. Rabi (who won the Nobel Prize in 1944), and to Harvard physicist Norman Ramsey, who refined Rabi’s technology in the 1950s (and won the Nobel Prize in 1989). At the heart of it all is a feedback loop. It starts with a simple device that produces a beam of cesium atoms. These atoms pass through what amounts to a filter (either magnets or, with optical pumping, lasers) that leaves all the atoms in a single hyperfine state. (It doesn’t matter which one of the two, so long as all are in the same state.) These atoms are then zapped by microwaves from the microwave generator. If the frequency of the microwaves is very close to the frequency of the cesium, explains Drullinger, the atoms will flip from the hyperfine state we chose to the state we threw out. The closer the frequency of the microwaves to the ideal 9,192,631,770 cycles per second, the more cesium atoms will tune into it, absorb the microwaves, and flip to the new state. Simple electronics then counts those that flipped. When the number of flipped cesium atoms can’t be increased by fine-tuning the microwave generator further, it means the frequency of the microwave generator is now locked onto the frequency of the cesium--the generator is now tuned to 9,192,631,770 cycles per second. Now the atomic clock will be marking off ideal seconds, or at least ideal seconds to the limits of the technology.

That’s the basic scenario, albeit quite a bit simplified. As you might expect, there are technological elaborations. For instance, as Drullinger goes on to explain, they actually zap the cesium atoms twice with the microwaves--or interrogate them twice, as he puts it. The microwaves are directed into two different zones, which in NIST-7 are five feet apart. This means the cesium atoms get zapped by the microwaves, coast for five feet, then get hit again. By letting the atoms coast for as long as possible between interrogations, the clockmakers force the frequency of the microwaves to be that much more accurately locked onto the hyperfine frequency of the atom.

To understand the logic at work here, imagine that you want to synchronize the speed of your own clock (in this case, the microwave generator) to that of a better clock (the atom). Setting them to the same time once won’t do much good. You want to make sure that they’re not only set to the same time but keep running at the same speed, which means taking some time to synchronize them once and then letting them run for, say, 24 hours and checking your original work to see how well it held up. If your clock is running a little slow or a little fast after 24 hours, you can resynchronize the time, adjust the speed accordingly, and let them go again. The longer the interval between synchronization and check, the better off you are. So the clockmakers separate the two microwave zones as far as they can before they start introducing more problems by having a huge and unwieldy clock.

A further qualification, Drullinger points out, is that neither microwave zone actually flips the atoms all the way from one hyperfine state to the other. During the first microwave interrogation, the atoms are only sort of flipped into the new state. This is what Drullinger calls one of those quantum mechanical weirdness things, where the atoms are neither in one state nor the other but in what’s called a superposition of both. When they hit the second zone, they get zapped again and pushed much closer to the new state. Not until they hit the second laser filter are they pushed to that final state.

With the microwave frequency locked onto the cesium frequency, and the atomic clock supposedly marking very nearly ideal seconds, Drullinger can ask rhetorically, Is it right? Well, how could it be wrong? Oh, Murphy has a million ways it could be wrong, and our job is to know every way Murphy could sneak in there. Now the laundry list starts. Once the clockmakers figure out how each item on it affects the clock--whether it makes it lose a trillionth of a second every second, or gain a quadrillionth, or whatever--they can add up all these uncertainties and calculate at what decimal point the clock’s time and ideal time go their separate ways.

With NIST-7’s predecessor, nbs-6, for instance, they had a clock that marked ideal seconds to 13 decimal places and then diverged because of the way the magnetic filter chose a single hyperfine state. The filter caused the cesium atoms to travel a very slightly curved trajectory. Faster atoms would take the curve a little farther out than slower atoms, and when the microwaves asked whether they were on the right frequency, they would get slightly different answers if they were asking faster atoms. The result was errors creeping in at the thirteenth decimal place.

So Drullinger and his colleagues spent ten years learning to make a workable clock that replaced the magnets with a laser beam and Kastler’s optical pumping. The resulting clock, NIST-7, was ten times more accurate than nbs-6 and started losing touch with ideal seconds at the fourteenth decimal place.

By the fifteenth decimal place, the limiting factor in atomic clocks seems to be that the cesium atoms are moving at all. The atoms scoot between the two microwave zones in about a hundredth of a second; it’s as though you synchronized your two clocks at midnight and then checked them again a hundredth of a second later. If you could wait a full second (or a day or a month) to recheck, you’d be able to synchronize the clocks that much better. The slower the atoms are moving, the longer the time between the two interrogations with the microwaves, and the better the microwave frequency can lock onto atomic time. To make it beyond the fifteenth decimal place, Drullinger and Wineland must slow the atoms down, or even stop them.

The technology needed to do this, known as laser cooling, is something Wineland and Drullinger first collaborated on back in 1977. It’s a way to bring atoms to a halt by bombarding them with the photons in a laser beam. James Bergquist, who works with Wineland, describes the process as similar to stopping a bowling ball by pelting it with Ping-Pong balls.

Drullinger’s next generation of atomic clocks uses the lasers first to stop the atoms and then to toss them in the air like a tennis ball. You collect a little ball of atoms, says Drullinger, which are stuck in the intersection of six different laser beams. But you can’t actually measure them at that point, because they’re being too highly perturbed by the light. To measure them, you’ve got to let go of them, and just like a tennis ball, they’re going to fall down. But just at the instant you let go of them, you give them a little bit of a push with the lasers. And now the atoms are moving up at a couple of meters per second. Think of a tennis ball in your hand; you toss it up about three feet, and it will come back down to your hand. If you had a stopwatch and timed that, it would take about one second. Now, suppose I toss my atoms up through the microwaves. Then they get to the top, turn around, and come back down and pass through the microwaves again. From the time they first interacted with the microwaves until they interact again, that’s about a second. Because this is 100 times longer than the corresponding interval in NIST-7, it promises to make a clock with 100 times the accuracy of NIST-7.

The technology, for obvious reasons, is called a fountain clock, and it’s another one of those ideas that predated the technology necessary to realize it. One of Rabi’s postdocs, Jerrold Zacharias, thought it up in the 1950s when he was working at mit. With luck, fountain clocks should take the accuracy of atomic clocks to the sixteenth decimal place. French researchers, led by André Clairon, have already built a prototype, which is running at the Paris Observatory. Both the French and the NIST physicists say the French clock is probably now better than NIST-7, and that it certainly will be with time because it has more room for improvement. Clairon and his colleagues are now building a second clock, which Clairon cautiously says should probably make it to the sixteenth decimal place.

Although the French have a five-year head start, Drullinger insists he will soon catch them. André had to suffer through the agony of building the first one, he says, and all the unanticipated things you trip over. We have the benefit of seeing what he’s doing and what he’s already done. The laserology is a nightmare, ten times more complicated than the lasers in NIST-7. But it’s all engineering at this point; there’s very little science left.

By the time atomic fountains push the frontier of timekeeping to the sixteenth decimal place of the second, cesium may be played out as a frequency standard and the world might have to think of moving on. This is where Wineland comes in, with his plans for the next next generation, in which a single atom sits preternaturally still for hours or days on end while being interrogated at leisure by the microwave generator that will lock onto its frequency. For this, Wineland needs not a neutral atom but an ion--in his case, an atom that has one electron fewer than it should, giving it a positive electric charge. A mercury ion, like Drullinger’s cesium atom, can be cooled with laser beams to very near absolute zero. Once it’s cold enough, the ion’s positive charge allows it to be held gently and serenely in place by an electromagnetic field, which means clockmakers can probe its oscillations without needing to find a way to defy gravity, which is essentially what the fountain clock does.

Wineland and his colleagues have been working on the mercury ion clock for a decade and a half now, and they think they can eventually get one to push the accuracy of the second into the eighteenth decimal place. They chose mercury, like cesium before it, not for any magical properties but because it fit many of the criteria they needed to make a clock. For example, it has an even number of electrons, so when it loses one, becoming an ion, a single electron is left in the outer shell to provide a nice hyperfine transition. And as a bonus, that transition is at 40 billion hertz (40 gigahertz), as compared with 9 billion for cesium, which gives four times the precision right there.

You can see, says Bergquist, that if you have a pendulum swinging back and forth at one cycle per second, it’s very difficult to do timing on a billionth of a second. You have to split the cycle into billionths. If on the other hand you have a cesium atom whose internal vibration is 9 gigahertz, you count 9 billion of these to make one second. Now you can do precision timing. And mercury has a much higher frequency-- 40 gigahertz.

Already Wineland and his colleagues have the makings of a mercury clock down in their basement laboratory, which is crisscrossed by laser beams and stacked floor to ceiling with oscilloscopes, computer screens, and esoteric electronics. They have been cooling mercury ions to the point where they’re virtually sitting still, locked into a form known as ionic crystals, which can be used as timepieces, while the clockmakers go through a whole new laundry list of disturbances.

Mercury offers one last treasure of accuracy, although Wineland and company will have to figure out how to extract it. In addition to its hyperfine transition, mercury has another nice, stable energy transition with a frequency of a quadrillion hertz--a million times higher than its 40-billion-hertz hyperfine transition. This quadrillion-hertz frequency, known as an optical transition, could give a mercury clock some additional decimal places of accuracy. Unfortunately, there is no such thing as a quadrillion-hertz oscillator that can lock onto that frequency, as the microwave generator does for cesium clocks. And once Wineland and his colleagues have created one, they’ll have to count its quadrillion ticks per second--which won’t be easy.

We’ll bootstrap our way up, says Wineland, which means that first they’ll find an oscillator that works at the highest possible frequency, say 100 billion cycles per second. Then they’ll run that through some device that doubles the frequency, and doubles it again, and they’ll keep going until they finally have their quadrillion-cycles-per-second oscillator. The basic principle is fairly well established, Wineland says, but obviously it gets pretty difficult to implement. You end up with a room full of lasers to do all this stuff. It’s a brute force kind of approach.

Adding to the trouble, the lasers themselves aren’t perfect; they have slight errors in their frequencies, which at 18 decimal places or so will undo the precision the researchers are getting from the mercury ions. To solve that, Wineland and his colleagues have to run the lasers into optical cavities, which can be thought of as little boxes that lock the laser light onto a frequency that fits perfectly within the physical dimensions of the boxes. Bergquist has built what he calls the trampoline, an optical cavity inside a vacuum system, suspended from the ceiling of the lab by very thick rubber bands. On Bergquist’s trampoline, says Wineland, sit the most stable optical lasers in the world, but they’re still not good enough for the optical transition of mercury. For that, the clockmakers have to build a cavity so that its physical dimensions remain fixed to within one-thousandth the size of the nucleus of a hydrogen atom.

Is that possible?

Well, yes, says Wineland, in principle. But it’s very hard.

Should Wineland and his colleagues do it, NIST will have clocks working at the eighteenth decimal place. While this sounds like a sufficient cushion beyond the needs of modern society, it’s a reasonable bet that the demand for accuracy will still catch up to the clocks, as it always has, and that the clockmakers will have to move on. The question then becomes, how far can they go? Is there any theoretical end point to the accuracy of a timekeeper?

Not that modern science knows, says Drullinger. And we don’t see any limits.
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