Bose-Einstein condensation

Type of physical science: Gases; behavior of, Atomic physics

Field of study: Nonrelativistic quantum mechanics

Bose-Einstein condensation is a phenomenon that occurs in a gas when quantum-mechanical effects extend across macroscopic distances to convert microscopic, isolated atoms, with integer spins, into a single quantum system. Predicted in 1924 by Albert Einstein, the effect occurs at extremely low temperatures, when the quantum wavelengths of the individual atoms extend to cover one another. The atoms then condense from an atomic gas into a giant quantum system analogous, in solids and liquids, to superconductors and superfluids.

Overview

On the level at which humans can view physical events, moving matter is visible as large and small chunks traveling their "natural" paths: cars speeding along highways, baseballs whizzing through the air from pitcher to batter. Matter is substantial, with clearly defined boundaries. The driver can lean against her car before entering it, and the pitcher can heft the baseball in his hand before throwing it.

Cars are quite massive, but baseballs, being smaller, are light. When moving at 60 miles per hour, a car has very large momentum and high motional, or kinetic, energy. A curving baseball, thrown at the same speed, has momentum and kinetic energy also, and a spin with an action that may fool the batter. Because its mass is much smaller, the baseball's momentum and kinetic energy are much less than the car's. The spin determines the angular momentum of the matter, which depends on size as well as mass. In the equations of classical mechanics used to describe macroscopic matter, such as the car and baseball, scientists often consider these clearly defined chunks as particles, with mass, not size, as the prime quantity that determines their momentums and kinetic energies.

It is natural to think of microscopic matter simply as solid chunks that have very small masses. Because of the small size of microscopic chunks, the idea of describing them as particles seems appropriate. This particle description of nature does indeed work quite well until one considers molecular and atomic sizes. In this atomic domain, the wave nature of matter becomes apparent. Clear boundaries to matter disappear, and the ideas of quantum mechanics must be used to describe matter as composed of waves with spins that are multiples of the fundamental Dirac unit. Waves such as light, conversely, take on particle-like properties such as momentum, energy, and spin.

The wavelength of atomic matter decreases with the momentum of the atomic or molecular matter. Since most macroscopic matter has substantial momentum and, therefore, small wavelength, this wave nature of matter is normally hidden in the macroscopic world.

Bose-Einstein Condensation (BEC) is a long-sought phenomenon that allows the quantum-mechanical wave nature of boson atoms in a gas to escape the microscopic domain and appear in the macroscopic world. In a real sense, the gas of atoms becomes a huge molecule, hundreds of thousands of times the size of a single atom. Only quantum waves hold the molecule together, and no atomic attraction is needed to keep the BEC together. In fact, while the atoms in normal molecules are in intimate contact, the individual atoms in the first BEC molecule produced experimentally were separated by several hundred times their own diameters. To explain how such an enlargement in the quantum regime happens, it is necessary first to discuss bosons and fermions.

Fermions are particles with odd multiples of half-integer spin such as electrons, protons, and neutrons, which have spins of +½ or -½. No two fermions are allowed in the same spin and energy state. This simple rule explains much of the chemical behavior of atoms.

As an example, normal hydrogen has one electron held by a single proton as nucleus in the lowest energy state, which has zero atom spin. Helium has two electrons about a nucleus composed of two protons and two neutrons. Helium can have both electrons in the same tightly bound energy state as hydrogen only if the two electrons have opposite spin. The electron spin of helium is thus zero—plus ½ added to -½—in this state. Because these two electrons are very tightly bound, helium is quite inert chemically. Two similar fermions are the maximum number that fit a given energy state, and this fact leads to particular stability in systems, such as helium, that have an even number of fermions.

Lithium has three electrons, but only two electrons can reside in the tightly bound state, while the third goes upstairs to a loosely bound state. Its electron spin is 1/2, and the last electron is released with relative ease, so that lithium is very active chemically. The fermion nature of electrons in atoms explains the basic chemical behavior of atoms throughout the periodic chart.

Bosons have even multiples of half-integer spin. The photon has unit spin and is the most common boson in nature. Bosons love to occupy the same energy and spin state, and this fact is at the core of how lasers operate. In a laser, the energy-spin state spans the entire laser and is often referred to as a "mode." A weak single-mode helium-neon laser, such as is used in scanning machines at store checkout counters, may have a million billion photons occupying one macroscopic mode, filling the laser. This enormous number of photons rides a single pencil of light, accounting for the extraordinary directionality of a laser. The laser is the prime boson condensate.

Other boson condensates use bosonic particles in solids or liquids with startling results. An example of a solid boson condensate is a superconductor. In conventional superconductors, two electrons in a metal pair together at low temperature to form a zero-spin boson referred to as a "Cooper pair." The electrons of the solid superconductor form Cooper bosons and settle into the lowest energy state possible. Normal metals have resistance because their moving electrons can lose energy, but the moving electrons of the superconductor have no way to end up lower in energy; thus the resistance of the superconductor is zero. Helium forms a liquid boson condensate called a "superfluid." The nucleus of normal helium (He-4) is composed of two protons and two neutrons, and this particular nucleus, the alpha particular, is a very stable system. The overall electron, atomic, and nuclear spin of He-4 is zero, giving this helium atom boson characteristics. He-4 forms a liquid at very low temperatures, and below 2.19 Kelvins, the bosonic liquid effectively loses viscosity, flows freely, and becomes superfluid.

BEC is a boson condensate of bosonic atoms in a gas. The condensate forms when the quantum wavelength of the atoms of the gas is large enough to overlap with neighboring atoms. In particular, the density of the atoms must be greater than 2.612 divided by the cube of the atomic wavelength. On average, this places one atom about 0.7 of a quantum wavelength from the next atom. For a true BEC to form, the atoms must be very far apart compared to the range of their chemical forces. At these low gas densities, the atom wavelength is quite large, and this requires extremely low temperatures to produce the BEC.

How low is the BEC temperature? The temperature of the gas is proportional to the square of the momentum of the average atom divided by the atom mass, while the momentum varies as the inverse of the atom wavelength. These two facts cause atom temperature to depend on the inverse of the square of the atom wavelength, which needs to be large to cause BEC. The first observation of a BEC was reported in a gas of rubidium-87 atoms in June of 1995 by the Joint Institute for Laboratory Astrophysics (JILA) of the University of Colorado and the National Institute of Standards and Technology. The condensate appeared in a sample of about two thousand rubidium-87 atoms held in a magnetic trap at a density of about 2.5 million million atoms per cubic centimeter (this density is less than one ten-millionth of the density of the atmosphere) when the temperature of the sample was driven below 170 billionths of a Kelvin.

The extremely low temperatures needed to achieve BEC stalled the discovery until new technologies developed to refrigerate the boson gases to such heroic lows. In addition, novel methods were needed to hold the gases without the strong interaction caused by container walls. Techniques developed to place atoms within a confining magnetic field by the use of laser-optical "tweezers." Novel methods originated to cool such atom swarms, first by laser light to slow the atoms down and then by evaporation to allow the "hotter" atoms to evaporate from the trapped swarm, producing the ultimate temperature.

The JILA experiment started with a very low pressure of rubidium-87 atoms at room temperature (about 300 Kelvin) within a 2.5-centimeter-square by 12-centimeter-long glass cell. Six crossed laser beams pierced the six sides of the evacuated glass cell. The beams collected rubidium atoms from an enclosed source over about 300 seconds, cooled them, and placed them between the poles of a complex magnet that lay idle. The atoms occupied a space about 1/100 of a millimeter across. By this time, the temperature had dropped to 20 millionths of a degree.

As is true of many atoms, rubidium atoms act as tiny magnets that can be captured by a magnetic field. The magnetic field was generated by two circular coils that produced a fixed four-pole field, and a rotating field plugged the leak that would normally occur along the coil axis. The laser beams were then switched off, and the magnetic field was turned on rapidly to take over the task of grasping the atoms during the final stage of evaporation cooling. The rubidium atoms moved back and forth, trapped like marbles in a bowl. The "hotter" atoms escaped the sides of the bowl; as the remaining atoms collided with one another, the swarm kept cooling until, finally, the BEC formed near 170 billionths of a Kelvin. The JILA experiment was able to preserve the condensate for about 15 seconds, and seventy years of waiting paid off.

The condensate was viewed by illuminating it with a laser flash and capturing the brief image on a video camera. The condensate was so small in size that a normal view would produce just a smudge, so the trap was opened and the swarm allowed to slowly spring apart. A normal gas would spread uniformly in all directions but at the center a sharp spike remained. This was the relic of the BEC, spreading elliptically as dictated by the uncertainty principle of quantum theory and confirming the quantum nature of the condensate.

Subsequent experiments quickly took place at a number of other laboratories, rapidly improving the properties of the BEC. Researchers at MIT produced a cigar-shaped sodium BEC with upward of half a million atoms. Various laboratories now explore the quantum nature of the condensate and have started work to exploit this unique state of matter.

Applications

The experimental verification of BEC is so recent that a listing of possible applications is quite tentative. Like the laser, superconductors, and superfluids, the physical nature of the BEC eludes a commonsense understanding of how nature works but, like them, gives promise of novel applications. The keys to developing these applications involve understanding the nature of BEC and determining how this nature fits human needs. The understanding will come with diligent experimentation and patience. Lasers, for example, have proved extraordinarily useful, but their applications in communications, medicine, data storage, surveying, and elswhere were scarcely glimpsed at the technology's discovery.

BECs can serve as sources of coherent beams of atomic waves, just as lasers are sources of coherent optical waves. "Coherence" means that the waves are in step, like soldiers in a military march, and not out of step, like people milling in a crowd. Soldiers march in a single column, like a laser beam, while a crowd spreads apart, like incoherent lamp light. Control of optical coherence is the secret behind the laser's widespread and sometimes spectacular applications. Because of its coherence, the laser produces pencil-like beams that can travel to the Moon and back and pulses that last but a millionth of a second, but have the power of all the generating stations in the United States.

BEC promises a source of extremely "bright" and coherent atomic waves. Broadly speaking, this bright atomic wave source should have two sets of applications, fairly immediate scientific ones and, later, commercial ones.

As a scientific study, the BEC is already unique. It comprises the only purely quantum-mechanical phase change that can occur without any atomic forces between the gas particles. More commonly encountered phase changes are the freezing of water into ice and the condensing of steam to water, and these phase changes require forces between the water molecules. The properties of the BEC quantum phase change form a rich area for scientific investigation.

In general, numerous applications will arise from the behavior of groups of atoms possessing one and the same wave. A BEC forces the atomic waves into the same mode, or space pattern, with, ideally, a single quantum frequency. Allowing the BEC to leak out one end of an atomic trap will produce a coherently patterned beam. Manipulating this beam allows control of the BEC output for specialized use.

Since atoms behave as tiny magnets, and since magnets can be moved by magnetic fields that change over distances or time, control of a BEC output beam is possible by external magnetic fields. This control mimics the trapping produced by the magnetic coils used to produce the BEC. Acceleration of the beam changes its momentum and so its wavelength and frequency. Thus, an external magnetic field can tune the BEC output.

Applications of normal atomic beams are constrained because the beam atoms, unlike photons, cannot pass through windows and air. Atoms in a normal atomic beam scatter readily from the atoms in the window or air, strongly reducing the beam transmission. However, there are theoretical predictions that atomic scattering with a BEC beam may be reduced significantly by tuning the exterior magnetic field.

In addition, the long coherence distance of a BEC may lead to enhanced transmission even in the presence of atomic scattering. Witness the fact that photons in light scatter easily from atoms in glass, but the light still passes readily through the glass. The strong interaction of photons with glass is clear because the atoms of normal glass slow the light beam to about two-thirds of the speed of light in a vacuum.

Context

The secret of why light photons pass readily, although at a slower pace, through glass and other materials in the presence of scattering is that individual photons maintain their wavelength and frequency coherence over very long distances. When each photon scatters from the dense atoms in a solid, interference effects from the many atoms cancel the scattering that would occur from a single atom over all directions except straight ahead. This allows the photon and its beam to continue forward, but at a reduced speed. It is only necessary to ensure that the light photons do not have a frequency near atom absorption.

Atoms in an atomic beam, however, have waves that stretch only the size of one atom, and the atom beams do not profit from long-range coherence as do photon waves in light. Yet the atomic wave in a BEC beam is coherent and long, rather similar to a photon wave. Tuning the BEC output away from absorption with window and air atoms may allow enhanced transmission through these media and widen the applications of BEC beams.

BEC promises to make unique contributions to the infant fields of atomic optics, extremely small-scale fabrication (nanofabrication) and atomic spectrometry. Lasers improve the performance of certain optical spectrometers by a millionfold, and it is hoped that similar improvements will be possible with BEC beams in comparison to normal atomic beams. In addition, the interaction of coherent atomic BEC beams with coherent laser beams may open new areas of scientific and commercial applications.

Finally, it appears that such manipulation of BEC beams may allow tuning the strength of the weak interaction, which is responsible for neutrino interaction and which is normally studied by nuclear experiments. BEC may thus permit novel investigations of nuclear phenomena, such as spontaneous symmetry-breaking and decay of unstable macroscopic states, using atoms instead of nuclei.

Principal terms

atom: the smallest chemically active unit of matter, composed of negatively charged electrons and a nucleus consisting of positively charged protons and chargeless neutrons

bosons: particles with even multiples of half-integer spin; photons, the particles of light, are bosons, but individual atoms with integer spin also act like bosons

energy: the capacity of matter to do work; quantum mechanics associates a frequency to the total energy of the matter

fermions: particles with odd multiples of half-integer spin; electrons, protons, and neutrons are fermions, and individual atoms with odd multiples of half-spin act like fermions

kinetic energy: the energy of motion of matter; classical mechanics equates kinetic energy to one-half mass times the square of velocity

momentum: in classical physics, the product of mass and velocity of matter; in quantum mechanics, the product of Planck's constant and the inverse of the matter's wavelength

Planck's constant: commonly designated by h and equal to 6.63 × 103⁴ joules per second

quantum mechanics: a branch of physics that assigns both a wave and particle nature to matter, along with spin

temperature: a measure of the random energy of a system of particles or waves

Bibliography

Anderson, M. H., et al. "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor." Science 269 (July 14, 1995): 198-201. The report of the discovery of BEC, with a short review of the experimental history. Technical in spots, but quite understandable. Two excellent illustrations and two graphs enliven the report.

Burnett, Keith. "An Intimate Gathering of Bosons." Science 269 (July 14, 1995): 182-183. One of the "Science Choice" articles that accompany especially important reports in the magazine. Written by an authority, this understandable article sets the perspective for the historic report of Anderson and his colleagues.

Collins, Graham P. "Quantitative BEC Results at DAMOP Meeting." Physics Today 49 (August, 1996): 19-20. In the same issue as Kleppner's article, below, this gives a semitechnical review of the status of BEC.

Cornell, Eric A., and Carl E. Weiman. Physics News in 1995: A Supplement to APS News. Woodbury, N.Y.: American Physical Society, 1995. A short, readable summary of discoveries in BEC by two members of the team that produced the first experimental BEC.

Kleppner, Daniel. "The Fuss About Bose-Einstein Condensation." Physics Today 49 (August, 1996): 11-13. The author, a pioneer in the experimental search for BEC, presents his unique perspective on the theoretical and experimental history of BEC.

Taubes, Gary. "Physicists Create a New State of Matter." Science 269 (July 14, 1995): 152-153. Science commonly presents very readable news reports to help readers understand the context of its technical reports. This article meets the periodical's high standards.