Look closely enough at a grain of sand and you can see that it is made up of tiny crystals. These in turn are made up of atoms – billions of billions of them in a single grain. Chemical bonds hold each atom at precise distances from its neighbours, forming a recurring pattern called a lattice. Every crystal found in nature, from diamonds to salt grains, is held together in this way.
Now physicists have found another way to organise atoms in a regular lattice: they have succeeded in holding tens of millions of atoms in place using laser light. In this way physicists have the chance to explore the esoteric world of low temperatures and the interplay between atoms and light. More practically, they could also build better atomic clocks and squeeze more finely etched electronic circuits onto a chip.
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These atomic arrays are formed by bathing the atoms of a gas in a fixed pattern of light called an optical lattice. In energy terms, the atoms are trapped in hollows – rather like a ping pong ball in an egg box. But the spaces for atoms in these patterns are hundreds of times farther apart than atoms in a grain of sand, and even in the latest experiments, atoms occupy at most 1 in 10 possible locations, making optical lattices at least a billion times less dense than ordinary crystals.
The idea of trapping electrically neutral atoms in a light field was suggested more than 25 years ago by the Soviet physicist Vladilen Letokhov. Light consists of oscillating electric and magnetic fields. The electric field causes a slight separation of charge in the atom, called a dipole, which can also be thought of as a tiny electric field. This in turn interacts with the light’s electric field.
ENERGY LANDSCAPE
The energy associated with this interaction varies because the light’s electric field varies in direction and strength in a regular way across the light pattern. The result, as Letokhov suggested, is that the atoms find themselves in an energy landscape of ridges and valleys. Just as a ball on a hill settles naturally to the bottom of a valley, so the atom tries to minimise the energy associated with the dipole-electric field interaction, by moving towards the points at which it has the lowest energy.
The problem is that at room temperature atoms whiz around at high speed, and the electric field of light is too weak to trap atoms with this much kinetic energy. The speed at which atoms of a gas move, and hence their kinetic energy, depends on their temperature. So for atoms to settle into the energy valleys in the light pattern they have to be made very cold.
Physicists got the idea of how to cool them from a proposal in 1975 by Arthur Schawlow and Theodor Hansch, two physicists at Stanford University in California. They suggested that neutral atoms could be cooled to temperatures near absolute zero by a stream of laser light. To understand how this works, think of light as a stream of moving particles (photons) which transfer momentum to any object they strike. In the Stanford physicists’ model, a stream of photons could slow down atoms in much the same way that a stream of ping pong balls would gradually slow down an oncoming football. They reasoned that this should work best if the light is tuned to a frequency which promotes one of the atom’s electrons to a higher energy level. It is at such frequencies that the atom absorbs the maximum number of photons.
But they also recognised that there would be a Doppler effect: because the atoms are moving they will ‘see’ the laser light at a slightly shifted frequency. By tuning the lasers to slightly below the critical frequency, they argued, atoms moving towards the laser would see the light shifted up to the frequency it absorbed best, and would be slowed down most efficiently. By shining laser light from all sides – up, down, left, right, front and back – atoms could be made very cold indeed.
Letokhov and his Soviet colleagues took up their idea in 1977. They proposed that the lasers could produce a fixed pattern of light waves that would trap neutral atoms in a regular lattice like that of a crystal. But it was 1985 before anyone demonstrated the Stanford physicists’ proposal in the laboratory. Researchers led by Steven Chu at AT&T Bell laboratories in the US cooled vaporised sodium atoms to 240 microkelvin – 240 millionths of a degree above absolute zero. Sodium has a straightforward atomic structure, with only one outer electron, and can be cooled by using a simple diode laser like those used in CD players. For atoms with more complex atomic structures, more expensive laser setups are required. In Chu’s experiment, the laser fields slowed down the atoms, but they were not brought to a complete standstill. Chu called the multi-laser arrangement ‘optical molasses’, because the atoms could still move rather like pebbles in a thick syrup.
Despite Chu’s success, phy-sicists had long abandoned the idea of trapping atoms in light patterns. Calculations in the late 1970s had showed that laser cooling could never rob atoms of enough kinetic energy for them to settle in their light traps. Then in 1988, William Phillips and his colleagues at the National Institute of Standards and Technology (NIST) in the US discovered that atoms could be cooled to temperatures lower than anyone had expected. By tuning the lasers to frequencies much lower than those believed to be optimal for laser cooling, Phillips succeeded in cooling sodium atoms to 43 microkelvin, more than five times lower than anticipated. Using the same method, Christophe Salomon and his colleagues at the Ecole Normale Superieure (ENS) in Paris cooled atoms of sodium’s near relation, caesium, to just 2.5 microkelvin – fifty times lower than had been predicted. Might it be possible after all to trap atoms in light fields?
In 1989, two groups of physicists, one led by Claude Cohen-Tannoudji at the ENS and the other by Chu, independently worked out how these low temperatures were being achieved. Previously, the atoms in the laser fields had been assumed to have only two internal quantum states: a low-energy ‘ground’ state and a high-energy ‘excited’ state. Cohen-Tannoudji and Chu recognised that the lower-than-expected temperatures resulted from multiple ground states. In the absence of a light field, these ground states all have the same energy, but a light field splits them into slightly different energies.
SISYPHUS SYNDROME
Cohen-Tannoudji and his colleague Jean Dalibard pictured it like this. An atom in a particular ground state might be moving up a hill, from a point in the light field where its energy is low to one of higher energy. As the atom climbs the hill, it loses velocity. As a result, the energy associated with its motion – its kinetic energy – is converted into ground state energy. When the atom reaches the top of the hill, it is still in the same ground state, albeit at a higher energy than before. But at this relatively high energy the atom has a high probability of emitting a photon. Once it does this, the atom drops to the valley floor of a different ground state – one that tends to be lower in energy than the one it came from. The atom is rather like Sisyphus in the Greek myth, doomed forever to push a heavy stone up a hill, only to find himself at the bottom of the hill again. As the atom goes through this ‘Sisyphus cooling’ process again and again, it loses more and more kinetic energy. And if it goes through this process enough times, the atom does not merely become very cold – it becomes trapped in a valley. Instead of climbing to the top of the hill, it rolls back and forth between two hills.
Meanwhile, experimental physicists found intriguing evidence that atoms at these ultra-low temperatures were indeed being trapped in laser light fields, but did not know exactly what the atoms were doing. To find out, they needed to detect the oscillations of atoms in their valleys. On the microscopic scale of these vibrating atoms, quantum mechanics comes into play. Quantum mechanically, the trapped atoms exist as a wave function that spans the region around the bottom of the valley, and they jump up and down between vibrational energy levels (states); the higher vibrational states spread the atoms over a larger range of positions and momentum values.
In 1992, Phillipe Verkerk and his colleagues at the ENS announced that they had detected the telltale oscillations in caesium atoms. They did so by creating a repeating one-dimensional light pattern using laser light with a wavelength of 852 nanometres, in the near infrared. Poul Jessen and his colleagues at the NIST also detected oscillations, in atoms of rubidium, another relation of sodium, using 780-nanometre laser light. Because of the way the pattern is set up, the traps for the atoms come at quarter-wavelengths of the light (see Figure 1). These experiments involved a device called a magneto-optic trap, a combination of Chu’s optical molasses and magnetic fields, which traps and cools atoms to tens of microkelvin. The device holds atoms as a gaseous ball at the centre of the trap, at a density of more than 10 billion (1010) atoms per cubic centimetre. Then the magnetic field is turned off and the optical molasses cools the atoms further, to temperatures of 5 to 10 microkelvin. Finally the molasses is turned off and a pair of laser beams is turned on to create the one-dimensional light pattern.FIG-mg19104501.jpg
ON THE CREST OF A WAVE
To understand how such patterns are made, think of light as a wave with crests and troughs. A single laser beam can be thought of as a moving wave. But a pair of such waves moving towards each other can combine to create a stationary pattern called a standing wave, the same pattern that can be made in a guitar string. Plucking the string creates a wave that travels down to the end and reflects back. These two waves combine at every point. At some points (nodes), the two waves cancel out; at some points between the nodes (antinodes) the string vibrates up and down at maximum height. When two light waves travel towards each other their electric fields combine in the same way. In the simplest case, when the two light waves travelling towards each other are identical, the nodes correspond to dark spots and antinodes to bright spots.
In the one-dimensional experiments, the researchers made a slightly more sophisticated pattern by combining two light waves with perpendicular electric fields. The result is a pattern made up not of light and dark but of changes in polarisation – the manner in which the electric field oscillates. In some places the polarisation is linear – the electric field vibrates in a single plane – and in other places it is circular because the electric field rotates in space. In the one-dimensional pattern, regions of linear polarisation alternate with regions of circular polarisation. It is in the regions of circular polarisation where atoms switch between ground states, lose their kinetic energy and become trapped.
To observe the oscillations, the NIST group studied the light emitted by the atoms trapped in the one – dimensional pattern. Verkerk and his colleagues at ENS shone an additional laser beam on the atoms, and deduced what the atoms were doing from the way this beam was absorbed or amplified. Both teams observed the atoms jumping between vibrational states. The NIST team found that about 60 per cent of the trapped atoms were in the state with least vibrational energy. This implied that, on average, the atoms were confined to regions less than 100 nanometres across – well confined to their traps. These one-dimensional experiments looked promising, and researchers moved very quickly to two and three – dimensional light patterns.
Early last year, Andreas Hemmerich of the University of Munich and Hansch, by then also at Munich, trapped rubidium atoms in a two-dimensional optical lattice. To form the lattice, they aimed two standing waves at right angles to each other. Where the beams crossed, they created a chessboard pattern with two types of circular polarisation – clockwise and anticlockwise. Atoms in the clockwise-polarised region fall into a ground state in which they are magnetised along a certain direction, while atoms in the anticlockwise-polarised region fall into a state of the opposite magnetisation. The result is a pattern of atoms with alternating magnetisation.
To go to three dimensions, the Munich group added a third standing wave perpendicular to the first two. This creates two classes of three-dimensional patterns, depending on the nature of the third standing wave. In one type, the wave essentially cancels out half the traps in the two-dimensional array, trapping the atoms in a state of only one magnetisation. The result is a body-centred cubic (bcc) lattice – the arrangement found in crystals of the metal chromium – in which the atoms can occupy the corners and centres of a cube.
LATTICE TRAP
ENS researchers have succeeded in making two and three – dimensional traps without having to use so many laser beams. Whereas the Munich group used two pairs of laser beams to make patterns in two dimensions, the ENS group used only three lasers, arranged in a triangle, to generate a hexagonal pattern (see Figure 2). Here, too, atoms of alternating magnetisation occupy the traps. Last year the ENS group became the first to make a three-dimensional lattice. For this they used four laser beams converging from the corners of a tetrahedron, producing the same type of bcc lattice as the Munich group later achieved with their setup.FIG-mg19104502.jpg
According to Jessen, three-dimensional structures produced at NIST (Figure 3), using the same technique as the ENS group, are 300 micrometres in diameter, about the size of a small grain of sand. However, the spaces for atoms are at least several hundred nanometres apart, compared with less than a nanometre apart for atoms in a sandgrain.FIG-mg19104503.jpg
As well as demonstrating the marvels of modern physics, optical lattices could have some valuable applications. For example, scientists at NIST are attempting to cool atoms to lower temperatures than have ever been achieved before. The ENS group still hold the record temperature for laser-cooled atoms in three dimensions, at 2.5 microkelvin for caesium. Researchers at NIST speculate that temperatures ten times colder may be possible for caesium atoms. Such supercold atoms could be used to make an exceptionally accurate atomic clock.
The world’s most accurate clock, the NIST-7 in Boulder, Colorado, keeps time to within one second in a million years, which corresponds to less than a ten-thousandth of a second in a human lifetime. This might seem good enough, but accurate clocks are useful for more than telling the time. The Global Positioning System, a navigation system based on a network of satellites, each with its own atomic clock, guided US soldiers through the desert during the Gulf War. More precise clocks would allow positions to be pinpointed with sufficient precision (thousandths or millionths of a metre as opposed to the 10 metres or so currently available) to be useful for locating geological faults, and even for mapping variations in the Earth’s gravitational field. Better clocks would also allow for more precisely synchronised radio telescopes and improved measurements of pulsars.
An atomic clock’s accuracy depends on precisely defined energy transitions in the atoms. In most atomic clock designs, instruments are tuned to the frequency at which a particular transition occurs. The colder the atoms are, the less motion they have, and the more precisely the instruments can be tuned to the transition. But for the atoms making the transition to produce a signal strong enough for reliable tuning requires more densely occupied optical lattices than are currently available.
The best that researchers have managed is to put atoms in one-tenth of the positions in the lattice. ‘Most traps are empty,’ says Hansch. One idea for increasing the density of atoms is to start off with better magneto-optic traps. In 1993 David Pritchard and his colleagues at MIT made magnetooptic traps that hold atoms at more than ten times the density achieved previously. No one knows whether this will translate into more densely occupied lattices. But this is not stopping researchers from pursuing low-temperature frontiers.
The idea behind cooling atoms in optical lattices exploits the fact that decreasing the intensity of the light field can reduce the strength of the interaction between the electric field and the atomic dipoles – with the result that the atoms become less confined. In the ‘classical’ picture, the valleys become less deep and each atom rolls over a larger amount of terrain. Quantum mechanically, each atom occupies a larger volume of space – the atoms ‘expand’. But to do this they must do work against their surroundings. In doing so they expend kinetic energy and become colder.
It is a quick, one-shot process similar to the ‘adiabatic cooling’ that occurs when gas escapes from a bicycle tyre. In less than a thousandth of a second, the atoms can be cooled to well below their initial temperature, just as the remaining gas in the tyre cools down because each molecule must do work to expand into the greater volume available to it. In the ‘adiabatic cooling for atoms’, the trapping laser must be turned off after the expansion and cooling process, to prevent light-scattering processes from heating the atoms again.
The converse of this process could have equally interesting applications. Increasing the intensity of the laser field makes the atoms more closely confined, so that they oscillate over a narrower region of their valleys. The result would be atoms localised more precisely in space. Mara Prentiss and her colleagues at Harvard University, working with the NIST group, are planning to make two-dimensional optical lattices in which atoms are highly localised, and use these to deposit the atoms onto a silicon surface. They hope this will open up a route to exceptionally finely etched electronic circuits.
CHIP ETCHINGS
With the best conventional techniques, chips can be etched with circuits as narrow as 250 nanometres. By shooting a beam of chromium atoms through a standing wave of light, Robert Celotta and his colleagues at NIST produced still narrower lines on a silicon surface (Technology, 20 November 1993). In Celotta’s experiments, the light focuses atoms onto the surface: the light wave induces dipoles in the atoms, so they are attracted to certain regions of the standing wave and fall on precisely defined positions on the silicon. With this method, researchers have produced lines as narrow as 65 nanometres. Prentiss estimates that the limits of the ‘light as a lens’ technique are lines between 5 and 10 nanometres wide. But she says that with optical lattices ‘there’s no theoretical limit that I know of’ to the narrowness of features.
Optical lattices could also increase our understanding of how atoms interact with light. Hansch and Hemmerich recently observed atoms in 3D optical lattices jumping between vibrational states through the exchange of 10 photons with the light field, instead of the usual two. It is the first multi-photon process observed in the lattices, and the researchers believe it may lead to new insights into nonlinear optics and spectroscopy.
Other researchers are interested in comparing the arrays made with optical lattices with the behaviour of atoms in real crystals. Calling such arrays ‘optical crystals’ implies that the atoms are self-organised, Phillips says. ‘But in this case, they’re not. They’re organised by the imposed light field.’ For the atoms to be like natural crystals, there has to be what Phillips calls ‘an organisation that occurs because of the forces between the atoms’.
Jessen looks forward to achieving a density high enough for there to be an atom in each potential valley. ‘Then they should be close enough that they interact with each other and you might be able to see some of the same behaviour that you can see in crystals,’ he says. Then a phenomenon such as phonons – the packets of energy that travel from atom to atom in a crystal – might be next on the research agenda. Meanwhile, scientists have their hands full, investigating the ultimate in light and airy crystal structures.
Ben P. Stein works in the Public Information Division of the American Institute of Physics in College Park, Maryland.