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Proving Einstein

Print edition : Oct 27, 2001 T+T-

Three scientists win the Nobel Prize for Physics for producing a new state of matter in which a cluster of atoms behaved like one "superatom" and thus proving a prediction of Albert Einstein.

IN June 1995, a research group in Boulder, Colorado, United States, created a very cold and minuscule, but spectacular, droplet. It was a droplet of rubidium (Rb) atoms, an alkali metal, but was totally unlike droplets (of fluids) one is familiar with. It was an extraordinarily cohesive assembly or packet of atoms cooled down to less than 100 billionths of a degree above absolute zero, or 100 nanokelvin (100 nK). The scientists, led by Eric A. Cornell of the National Institute of Standards and Technology (NIST) and Carl E. Wieman of the University of Colorado, working at JILA (formerly known as Joint Institute for Laboratory Astrophysics), a centre run jointly by the two institutions, had succeeded in cooling a very dilute gas of about 2,000 Rb atoms to the lowest temperature ever making them lose their individual identity for a full 10 seconds and collectively behave as a "superatom". The atoms' properties, such as their velocities, became identical instead of a spread in values which is characteristic of a collection of atoms at room temperature (300 K) or even at subzero temperatures.

About four months later, a group at the Massachusetts Institute of Technology (MIT), U.S., led by Wolfgang Ketterle, was able to drive the gas of another alkali metal, sodium (Na), into this state of "identity crisis" but with two orders of magnitude more atoms. The two teams had achieved what had eluded scientists for 70 years since Albert Einstein predicted such behaviour. Einstein had shown that if a gas of identical non-interacting atoms was cooled to sufficiently low temperatures, the atoms would "condense" to the same lowest energy state. His work was an offshoot of the work by the Indian scientist Satyendra Nath Bose in his classic paper of 1924, which he sent to Einstein to get published. Bose had shown through statistical arguments how a collection of photons, massless light particles, would be distributed among various energy states at a given temperature. Einstein extended the argument to particles with mass, like atoms, and found that they should all accumulate in the ground state at very low temperatures. The phenomenon is called Bose-Einstein Condensation (BEC).

This year's Nobel Prize in Physics was awarded to the three scientists who led the JILA and MIT research teams that produced Bose-Einstein Condensates of rubidium and sodium respectively. What they achieved was a verification of Einstein's prediction. The Nobel citation says: "For the achievement of Bose-Einstein Condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of condensates."

The condensation Einstein found is based on the fact that the total number of states at vanishing energy becomes exceedingly small, leaving not enough room for all the particles, and the system can accommodate all the particles only by letting them settle in the lowest energy or ground state. Einstein's discovery, in 1925, was received with scepticism. The hypothesis was considered at best curious, given the fact that such extreme low temperatures were impossible to attain at that time. Also, there was no known physical system that could display the phenomenon.

In the intervening decades, however, physicists began to realise that explanations for phenomena like "superfluidity" and "superconductivity" could lie in the concept of BEC. Superfluidity is a phenomenon in which a fluid, below a certain subzero critical temperature (Tc) characteristic of the material, flows without any resistance and possesses very high thermal conductivity. Superconductivity is a similar property by which certain substances, when cooled to below their characteristic Tcs, lose their electric resistivity. But these phenomena, in which constituent atoms evidently participate collectively, are at best manifestations of BEC and not direct evidence of the ideal case of a non-interacting gas of identical particles that Einstein had described.

BEC is essentially macroscopic manifestation D a collection of tens of thousands of atoms would be the size of a human hair D of quantum principles, which every atom in the microscopic domain obeys. All particles in the atomic domain D elementary (like electrons, protons and neutrons) or composite (like atoms and molecules) D can be divided into two basic classes called bosons and fermions. This stems from the intrinsic quantum mechanical property of spin D which can be imagined as a rotation about the particle axis D of all elementary particles. The value of this "spin" is either integral or half-integral multiple of some basic unit. Particles with integral spin are called bosons and those with half-integral spin are called fermions. Quantum mechanics permits more than one boson to be in the same state while only one fermion can occupy a given state. Only bosons, therefore, can settle into the condensate phase.

A large proportion of atoms are bosons. Alkali atoms D like rubidium and sodium D are bosons and this is one of the reasons for choosing alkali atoms to study BEC. Besides, the repulsive forces between the atoms of these species are weak. The fact that superfluidity is seen only in helium-4 (a boson) and not in helium-3 (a fermion) is evidence of the fact that the physics underlying the phenomenon is indeed BEC. In recent years, other evidence for this has emerged.

Besides proving Einstein's prediction, the interest in BEC stems from the fact that the condensate offers a macroscopic system to study the mysterious world of quantum mechanics. One of the quantum mechanical properties is that matter behaves both as a particle and as a wave. Louis de Broglie postulated in 1924 that every particle has a wavelength that is inversely proportional to its momentum. At room temperature, the atoms of a gas in a container move about at high speeds and bounce off its walls. The momenta of the particles are large and the corresponding wavelengths small, typically about 10,000 times smaller than the average spacing between the atoms. But with sufficiently low temperatures, the wavelength becomes comparable to the distance between the atoms and the wave of one atom begins to overlap with that of the neighbouring atom causing them to lose their identity.

The chances of finding more than one atom in the same state thus dramatically increase as the atoms are cooled. Atoms begin to sense one another and coordinate their state. The whole system is now described by a single "macroscopic" wave function, with a well-defined amplitude and phase. It is in this sense that a Bose-Einstein condensate is a "superatom". Indeed, the transition from disordered to coherent matter waves can be compared to the transition to coherent light in the case of laser.

THE fundamental difficulty in obtaining the ideal situation was that before the temperatures required for BEC, around or less than one microkelvin, can be reached, atoms in gases would condense into a liquid or freeze into a solid because of inter-atomic forces. In other words one had to create a supersaturated gas. It was only in the late 1970s that cryogenic technology had advanced to a stage where physicists could conceive of methods that could create Einstein's BEC in a gas.

Efforts to produce a BEC in hydrogen started more than 15 years ago. Since hydrogen atoms resist the clumping necessary for freezing, scientists presumed that it would be easy to produce a supersaturated hydrogen gas. In these experiments hydrogen atoms were first cooled in a dilution refrigerator, then trapped by a magnetic field and cooled by evaporation. This approach came very close to observing BEC in hydrogen but was limited by the tendency of hydrogen atoms to form molecules.

In the 1980s, laser-based techniques such as Doppler cooling, polarisation gradient cooling and magneto-optical trapping (MOT) were developed to cool and trap atoms. Alkali atoms are well-suited to these laser methods because their internal energy structures are favourable to laser excitation. Indeed, in the experimental set-up for BEC, all the equipment is at room temperature D no liquid nitrogen or helium D and the nanokelvin region where BEC occurs is a small glass chamber 2.5 cm across.

However, laser cooling does not make the gas cold enough for BEC. The density of atoms is typically about a million times lower than what is required. What keeps them from getting any colder? The lowest temperature achievable is limited by the energy of a single photon. Laser photons scatter off the atoms randomly in all directions, giving the atoms a residual jitter that cannot be got rid of because of the discrete energy quantum each photon carries.

The successful route to BEC turned out to be a clever combination of MOT and evaporative cooling. The latter had been developed at MIT by D. Kleppner and T. J. Greytak. In evaporative cooling high energy atoms are allowed to escape from the sample so that the average energy of the remaining atoms is reduced. The process is the same as when a cup of tea or coffee cools: the energetic coffee molecules are able to break the surface barrier and escape as steam. The trick makes use of the fact that each atom is a tiny magnet. In an atom trap, the cold atoms are held in place by the force of the surrounding magnets after the lasers have been switched off. This attractive force can be turned into a repulsive force if the atomic magnetic poles are reversed. This can be achieved by using a radio-frequency (RF) field, and the "cup of tea" analogy helps understand this. The magnetic potential well in which atoms are trapped is like a cup, with rapid atoms populating the edge of the well. Since the magnetic field is high at its edge, the strength of the pole conversion force required is also high. A high frequency RF field is, therefore, able to switch the poles of atoms close to the edge and tip them over. By progressively reducing the frequency of the RF field, successive layers of energetic atoms are skimmed off the hot atoms. As the atoms cool down, they occupy smaller and smaller volume because they do not have enough energy to climb up the side of the potential well. This way, the JILA group managed to achieve, for the first time, the BEC limit in rubidium.

There is one more problem to overcome. In the magnetic potential well, there is zero magnetic field at the bottom. This means that there is a finite probability of atom leakage from the centre of the trap because of spontaneous pole switching. The JILA group solved this by rotating the magnetic field sufficiently rapidly over the sample D the so-called time-averaged orbiting potential (TOP) trap D to keep the atoms away from the "hole" and prevent them from pouring out of the trap. The MIT group, on the other hand, "plugged the hole with a repulsive action of a focussed laser beam."

Though the MIT group recorded similar results, it could do a lot more with the condensate because that had a hundred times more atoms to work with. By splitting the condensates into two and allowing them to expand into each other, Ketterle demonstrated the existence of the quantum matter wave associated with the condensate. He obtained clear interference effects, indicating coherence of matter waves and long-range order across the macroscopic size of the condensate. He was also able to make use of the coherence in the atoms to produce an "atom laser" of coherent matter just as a laser light consists of a beam of coherent photons. He switched off parts of the condensate so that they would fall as "BEC drops" in the field of gravity.

Today over 20 groups are engaged in BEC experiments. Of particular interest is the observation of BEC in lithium-7 D whose atoms attract each other as opposed to what happens in rubidium and sodium D by R. G. Hulet's group in Rice University. Theory predicts that BEC should be able to hold only about 1,000 atoms, exactly what Hulet observed. BEC has also been observed in other types of atoms. An Indian physicist C. S. Unnikrishnan of the Tata Institute of Fundamental Research (TIFR), Mumbai, is part of the Paris-based group led by C. Cohen-Tannoudji and M. Leduc, which very recently observed BEC in metastable helium atoms.

BEC is too new a state of matter for its usefulness to be gauged at this point of time and any discussion of practical applications will at best be speculative. What is driving physicists to investigate BEC is the possibility of understanding the quantum principles that can manifest at the macroscopic level, like the condensate's viscosity, vortex formation and so on. It turns out that the condensate is easier to manipulate than scientists had imagined, and therein lies the key to potential applications. What one expects is entirely guided by a striking physical analogy of the BEC to coherence in laser. The "atom laser" is likely to become the most important tool derived from the phenomenon of BEC and should find applications in lithography, holography and nanotechnology D by focussing atoms to a millionth of a metre across D to high precision measurements of fundamental natural phenomena.