The Bose Einstein Condensate for Hydrogen

Satyendranath Bose, 1924 • Albert Einstein, 1925 • Eric A. Cornell and Carl E. Wieman, 1995 • Daniel Kleppner and Tom Greytak, 1998

When Thomas Greytak and Daniel Kleppner at MIT started out 22 years ago to form a Bose-Einstein condensate by cooling and compressing a gas of hydrogen atoms, they did not realize just how arduous the journey would be.

There are various ways that fame comes to a scientist. For Satyen-dranath Bose it was asking Albert Einstein to run interference for him. Eventually his name was linked with Einstein's in both a statistical method of dealing with quantum particles, called Bose-Einstein statistics, as well as the peculiar state of matter known as the Bose-Einstein condensate. In addition, Bose had a class of particles named after him: the boson. As this example illustrates, Einstein's scientific influence was telling.

In late 1923, Bose, an Indian physicist from Dacca University in East Bengal, submitted a paper to the British journal Philosophical Magazine. Six months later, the editors informed Bose that his paper had been rejected. Bose did not give up. In a letter dated June 4, 1924, Bose wrote to Einstein and included a copy of his manuscript. Bose asked for Einstein's opinion of the paper and whether Einstein would "arrange for its publication in the

German journal, Zeitschrift für Physik. . . . Though a complete stranger to you," Bose continued, "I do not hesitate in making such a request. Because we are all your pupils though profiting only from your teachings through your writings." Einstein responded decisively. He translated the paper from English into German and submitted it to Zeitschrift.1 The paper was published with a note by Einstein in which he promised to work out the paper's implications in detail.2

The details were significant. In July 1924 Einstein read a paper before the Prussian Academy in which he applied the Bose statistical method to an ideal gas and drew an analogy between a quantum gas and a molecular gas. Over the following few months, Einstein wrote what Martin Klein has called "another of his masterful works,"3 which was published in January 1925.4 In this paper, Einstein predicted that the particles of an ideal quantum gas could collect together in the lowest energy state and form what is now called a Bose-Einstein condensate. At the time, physicists regarded Einstein's prediction as a curiosity with little or no physical significance.

Einstein never failed to acknowledge Bose as the initiator of quantum statistics. (Two years later, in 1926, quantum statistics was extended independently by Paul Dirac and Enrico Fermi in what is now called Fermi-Dirac statistics.)5 But Bose was unable to extract from his work the physical significance that Einstein was able to bring to it. With both Bose-Einstein and Fermi-Dirac statistics on the table, it took a few months for physicists to recognize their applications.

The particles that make up the material world all belong to one of two groups: bosons, the social particles that can come together in the same quantum state, and fermions, the antisocial particles, each of which demands a quantum state for itself. The former obey Bose-Einstein statistics and the latter Fermi-Dirac statistics.

There is another distinction between the two types: All bosons have integral spin—1, 2, and so on—whereas all fermions have half-integral spin—12, 32, 52, and so forth.

Every chemical element displayed in the Periodic Table has distinctive chemical properties because atoms are made up of protons, neutrons, and electrons, which are fermions. The Pauli exclusion principle requires that no two electrons, like all antisocial fermions, can occupy the same quantum state. Thus, electrons bound to nuclei making up atoms exist in an array of shells that allow all the electrons to exist in their own individual quantum state. The shell structures differ from atom to atom, giving each atom its unique chemical and physical properties.

Quarks, electrons, and nitrogen atoms are fermions; photons, alpha particles, and nitrogen molecules are bosons. Bosons are not restricted by the Pauli exclusion principle and many bosons can occupy the same quantum state; in fact, bosons rather like to come together and populate one quantum state. Lasers are possible because photons are bosons.

Einstein predicted a particular behavior of bosons, the Bose-Einstein condensate, in 1925. A Bose-Einstein condensate has great fascination for physicists not only because it is a unique state of matter, but also because it provides a macroscopic view of quantum behavior. Ordinarily atoms are regarded as particles. However, as quantum theory revealed, atoms have both particle and wave properties. As an atom is cooled, its wavelength increases. If these atoms are bosons and if they can be cooled to the point where their wavelengths begin to overlap, they merge their individual identities, enter a single quantum state, become indistinguishable from each other, and "dance in perfect unison."6 The collection of atoms becomes, in essence, a single atom that can be directly observed: a macroscopic quantum system.

For many years Einstein's prediction was considered as having only theoretical significance. It was not until 1995, seventy years after the prediction, that Eric Cornell and Carl Wieman first produced this curious state of matter with rubidium atoms.7 For reasons described below, it was long expected that hydrogen atoms would be the first to yield to the exacting conditions required to achieve Bose-Einstein condensation; however, hydrogen proved to be exceedingly stubborn. So it was not hydrogen, but 2,000 rubidium atoms that huddled together at a temperature of 0.0000001K, 100 billionths of a degree above absolute zero, in the first Bose-Einstein condensate. Nonetheless, it was the experience gained with earlier attempts to condense hydrogen that prepared the way for success with rubidium. So, it is still accurate to say that the hydrogen atom led the way.

Daniel Kleppner became interested in the hydrogen atom early. In fact, one might say that hydrogen is in his academic genes. Kleppner was a student of Norman Ramsey, who was a student of 1.1. Rabi. Rabi spent much of the 1930s measuring basic properties of hydrogen and Ramsey, who joined Rabi's group in 1937, was an active contributor in the most important work that came out of Rabi's laboratory. In 1960, Ramsey and his graduate student Kleppner developed the hydrogen maser. With that heritage behind him, Kleppner's interest in the simple hydrogen atom was preordained; thus, it is not surprising when Kleppner says, "For me, hydrogen holds an almost mystical attraction."8

Sometime in the mid-1970s, Kleppner and Tom Greytak began to think about creating a Bose-Einstein condensate of hydrogen atoms. To accomplish this feat, a gaseous sample of atoms would have to cool to temperatures edging near absolute zero, yet remain a gas. In other words, the sample of gas could neither liquefy nor solidify. It was this requirement that made hydrogen a prime candidate for the elusive Bose-Einstein condensate.

Both the proton and the electron of hydrogen are fermions with a spin of Y2. When they combine to form a hydrogen atom, the atom becomes a boson with a spin of 0 (the electron and pro ton spins opposing each other) or a spin of 1 (the two spins parallel to each other). When two atoms of hydrogen come together, a hydrogen molecule is formed if the two electron spins are antiparallel. By contrast, if the electron spins of the two hydrogen atoms are parallel, the two atoms cannot combine to form the hydrogen molecule. A group of such hydrogen atoms—called spin-polarized when their electron spins are parallel—can be cooled to absolute zero without forming either a liquid or a solid. The atoms of spin-polarized hydrogen behave as an ideal gas even at the lowest temperatures possible. This was one characteristic of hydrogen that made it such a seductive target for achieving a Bose-Einstein condensate.9

Other properties of hydrogen also made it a prime candidate for Bose-Einstein condensation, such as its low mass. The smaller the mass of a particle, the longer its de Broglie wavelength. It was reasoned that hydrogen atoms would not have to be cooled as much as more massive atoms to achieve significant overlapping of their associated wavelengths. It also appeared that methods to cool hydrogen were available and understood.

But hydrogen did not yield easily. Kleppner, Greytak, and their students began work in 1978. They developed methods to trap hydrogen atoms by means of magnetic fields and to cool them by means of evaporation. In evaporation, the faster atoms are allowed to escape the trapping container carrying with them excess energy and leaving behind the cooler atoms. The experimental methods were demanding and intricate. Although these methods were conceived and executed well, they did not succeed with hydrogen. These same methods, however, were the starting point for Cornell and Wieman in 1989 when they decided to apply them to one of the alkali metals, rubidium. With rubidium they successfully created the first Bose-Einstein condensate in 1995.

Kleppner and his students were foiled in their early attempts to realize Bose-Einstein condensation with hydrogen because hy drogen atoms were lost through recombination on the walls of the container. In response, they developed a no-wall container with magnetic fields. They successfully cooled the atoms to around 0.00010K by means of evaporation, but then they hit a temperature wall. Fast hydrogen atoms did not evaporate, as expected, and carry the sample temperature lower. They applied an ingenious technique using radio-frequency (RF) electromagnetic waves. By juggling the frequency of the RF and the magnetic fields they were able to target the most energetic atoms and effectively whisk them away from the sample, thereby leaving the remaining residue colder. This brought the remaining hydrogen atoms down to a temperature of about 0.000050K and at this juncture a twenty-year quest ended: a Bose-Einstein condensate consisting of about 1 billion (109) atoms was observed late in the summer of 1998.10 The number of atoms in the hydrogen Bose-Einstein condensate was much larger (1 billion) than the 2,000 that had been achieved with rubidium, making the hydrogen condensate attractive for further study.

As soon as Bose-Einstein condensates were created, physicists recognized that they were going to be a rich object for study. Theodor Hänsch has said, "It is like a door that has opened to a new world."11 The new world portends both practical applications and opportunities to extend theoretical understanding.

For example, atoms in a Bose-Einstein condensate are analogous to photons in a laser. The novel features of a laser are achieved because the photons are optically coherent, which means that every photon has the same frequency and phase. The atom waves in a condensate are also coherent. Wolfgang Ketterle and co-workers at MIT beautifully demonstrated the single-wavelength nature and the coherence of the wave nature of atoms in condensates by merging two clouds of condensate atoms and observing interference fringes in the overlapping region.12 This coherence opened the possibility of atom lasers, which in fact have already been demonstrated,13 although it is not clear whether atom lasers can be manipulated or sharply focused. One difference between photons and atoms is that photons in a laser beam do not interact with each other. Atoms do interact. What consequences will arise from their interactions? Optical lasers are used for lithography. Physicists are imagining lithographic applications where condensates with the proper atoms are finely focused and used to deposit atoms on a surface to form transistors and other practical devices.

Bose-Einstein condensates are unusual in numerous ways. With careful study physicists will gain basic knowledge about the material and quantum worlds. The atoms in a condensate are indistinguishable. All atoms move at the same speed in the same space. One can ask: How can two objects occupy the same place at the same time? A condensate is a macroscopic quantum wave packet and a macroscopic example of Heisenberg's uncertainty principle. Condensates hold the promise of bringing new insights to the strange world between the microscopic quantum and the macroscopic classical domains.

When atoms congeal into a condensate, they form a very dense medium. The speed with which light propagates in a medium is dependent on, among other things, the density. What is the speed of light in a Bose-Einstein condensate? Lene Hau and her co-workers have answered this question for a condensate of sodium atoms. She directed laser light through a condensate and found that in this curious medium the light crawled through it at the unbelievable rate of seventeen meters per second—some 299,792,299 meters per second less than light moves through a vacuum!14

In this dense form of matter, condensates will become an arena where the physics of many-body systems can be tested. As a strange mixture of a fluid and a coherent wave, condensates will bring together the high precision of atomic physics with the theoretical frameworks of many-body physics.

In all of the excitement generated by the creation of Bose-Einstein condensates, hydrogen offers its own customary charm. Precision spectroscopy awaits. The frequency of the 1S-2S transition measured so precisely by Hansch may be measured with even greater precision. With hydrogen, more atoms can be brought together in a condensate than is the case with other atoms. Hydrogen's simplicity allows theory to be applied to its interactions with exactitude.

All this bodes well for hydrogen's role in elucidating the intricacies of this novel state of matter. Kleppner's "mystical attraction" to hydrogen is certainly justified.

For achieving a Bose-Einstein condensate in dilute gases of alkali atoms, Eric A. Cornell and Carl E. Wieman were awarded the 2001 Nobel Prize in Physics. Sharing the prize with Cornell and Wieman was Wolfgang Ketterle for his fundamental studies of condensates.

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