Bose–Einstein condensate

• 1. Introduction

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  A Bose-Einstein condensate is a state of matter so strange that it forces physicists to reckon with quantum mechanics not as an invisible rule governing the very small, but as a visible, measurable reality at human scales. In 1924, Satyendra Nath Bose sent Albert Einstein a paper about the quantum statistics of light. Einstein was so impressed that he translated it himself from English into German and submitted it on Bose's behalf to the Zeitschrift fur Physik, which published it that year. What followed was a prediction so audacious it would take seventy more years to prove: that at temperatures just above absolute zero, particles of a certain kind would stop behaving as individuals and collapse together into a single quantum state. The questions that prediction opened are still being answered today. How cold does matter actually need to be? What happens when an entire cloud of atoms shares one wavefunction? And what can this ghostly fifth state of matter tell us about dark matter, superconductors, and even the behavior of light itself?

• 2. The Prediction

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  Satyendra Nath Bose's 1924 paper derived Planck's quantum radiation law without relying on any concepts from classical physics. That alone was a significant break. Einstein saw in it the foundation for something broader. He extended Bose's ideas to matter in two further papers, developing what became known as Bose-Einstein statistics: a mathematical description of how identical particles with integer spin distribute themselves across energy states. Particles obeying these rules are now called bosons. They include photons, polaritons, magnons, and certain atoms and molecules, including helium-4, lithium-7, and rubidium-87.

  The key property that sets bosons apart is that they are allowed to share a quantum state. Classical particles, and the fermions that make up most ordinary matter, cannot occupy the same state simultaneously. Bosons can, and at sufficiently low temperatures, Einstein predicted that enormous numbers of them would all fall into the lowest possible energy state at once. The result would not merely be very cold matter but a qualitatively new form of matter altogether.

  Einstein's manuscript laying out this prediction was once thought lost. It was found in a library at Leiden University in 2005.

• 3. The Long Wait for Proof

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  A 1976 paper by two program directors at the National Science Foundation, William Stwalley and Lewis Nosanow, restarted the experimental chase. They proposed using spin-polarized atomic hydrogen to produce a gaseous Bose-Einstein condensate. Four independent research groups immediately took up the idea: teams led by Isaac Silvera at the University of Amsterdam, Walter Hardy at the University of British Columbia, Thomas Greytak at the Massachusetts Institute of Technology, and David Lee at Cornell University.

  Atomic hydrogen, however, turned out to be technically brutal to cool. Condensation of atomic hydrogen was not realized until 1998. The breakthrough came from a different direction. Alkali atoms like rubidium could be pre-cooled with laser cooling, a technique that won its inventors Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips the 1997 Nobel Prize in Physics. That head start made it possible to perform the final forced evaporative cooling needed to cross the condensation threshold.

  On the 5th of June 1995, Eric Cornell and Carl Wieman at the University of Colorado at Boulder cooled a dilute vapor of approximately two thousand rubidium-87 atoms to 170 nanokelvins, creating the first gaseous Bose-Einstein condensate. About four months later, Wolfgang Ketterle at MIT condensed sodium-23 into a condensate with roughly a hundred times more atoms, which allowed him to observe quantum mechanical interference between two separate condensates.

• 4. The Nobel and Its Science

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  Cornell, Wieman, and Ketterle shared the 2001 Nobel Prize in Physics for their achievements, cited specifically for Bose-Einstein condensation in dilute gases of alkali atoms and for early fundamental studies of the properties of those condensates.

  A group led by Randall Hulet at Rice University announced a condensate of lithium atoms just one month after the original JILA work. Lithium presented an immediate complication: it has attractive interactions between atoms, which made the condensate unstable. It would collapse for all but a handful of atoms. Hulet's team subsequently showed the condensate could be stabilized by confinement quantum pressure for up to about 1,000 atoms.

  The JILA team returned to the question of attractive interactions in 2000, this time using rubidium-85, which has a negative atom-atom scattering length. Through a process called Feshbach resonance, they swept a magnetic field to cause spin-flip collisions, lowering the discrete energy levels at which rubidium bonds and temporarily making the atoms repulsive. When they then raised the magnetic field strength further, the condensate suddenly reverted to attraction, imploded, shrank beyond detection, and then exploded, expelling roughly two-thirds of its 10,000 atoms. Carl Wieman noted that under the atomic theory then available, this behavior could not be explained, since the energy state of an atom near absolute zero should not be sufficient to trigger an implosion.

• 5. Superfluid Connections

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  In 1938, Pyotr Kapitsa, John Allen, and Don Misener discovered that helium-4 became a superfluid below 2.17 K, a temperature physicists call the lambda point. Superfluids flow without any dissipating energy and support quantized vortices. Fritz London, also in 1938, proposed that Bose-Einstein condensation was the underlying mechanism for this superfluidity.

  Superfluid helium-4 is a liquid rather than a dilute gas, which means the interactions between its atoms are far stronger than in the condensates Cornell and Wieman produced. The original theoretical framework must be substantially modified to handle it. Near absolute zero, only about 8% of helium-4 atoms are in the condensed fraction, compared to nearly 100% for a weakly interacting atomic BEC. Still, Bose-Einstein condensation remains fundamental to the superfluid properties helium-4 displays.

  Helium-3, which is a fermion rather than a boson, also enters a superfluid phase, but only at a much lower temperature. It does so through the formation of bosonic Cooper pairs of two atoms, a mechanism directly parallel to the Cooper pairs responsible for superconductivity in certain metals.

• 6. Beyond Atoms: Quasiparticles

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  Magnons, which are electron spin waves in a solid, were among the first quasiparticles found to form Bose-Einstein condensates. Because magnons have a mass close to that of an electron and can reach greater densities than dilute atomic gases, their condensation threshold is far higher. Condensation in an antiferromagnet was demonstrated in 1999 at temperatures as high as 14 K. By 2006, condensation in a ferromagnetic yttrium-iron-garnet thin film was observed even at room temperature, achieved through optical pumping.

  Excitons, which are bound electron-hole pairs in semiconductors, were predicted to condense at low temperature and high density as far back as 1961. Bilayer system experiments demonstrated their condensation in 2003 through the disappearance of the Hall voltage.

  Polariton condensation was first detected in a quantum well microcavity held at 5 K. Since then, Bose-Einstein condensation has been achieved at room temperature in microcavity-coupled organic semiconductors and in plasmon-exciton polaritons within periodic arrays of metal nanoparticles coupled to dye molecules. In June 2020, the Cold Atom Laboratory aboard the International Space Station created a BEC of rubidium atoms and observed them for over a second in free fall, with roughly half the atoms forming a magnetically insensitive halo-like cloud around the main body of the condensate.

• 7. Applications and Frontiers

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  In 1999, Danish physicist Lene Hau led a team from Harvard University that slowed a beam of light to about 17 meters per second using a superfluid. Her group subsequently made a group of condensate atoms recoil from a light pulse in a way that recorded the light's phase and amplitude, which were then recovered by a second nearby condensate, a process they called slow-light-mediated atomic matter-wave amplification.

  The first demonstration of a BEC in weightlessness was achieved in 2008 at a drop tower in Bremen, Germany, by a consortium led by Ernst M. Rasel from Leibniz University Hannover. The same team demonstrated in 2017 the first creation of a Bose-Einstein condensate in space, enabling precision atom interferometry experiments that require the extreme quietness of microgravity.

  Continuous BEC production was a major unsolved experimental problem for decades. Evaporative cooling produces condensates in pulses and discards more than 99% of atoms to reach the condensation threshold. Continuous BEC was achieved for the first time in 2022. In the realm of dark matter, P. Sikivie and Q. Yang proposed that cold dark matter axions would form a Bose-Einstein condensate through gravitational self-interactions, and upgrades to the Axion Dark Matter Experiment at the University of Washington were completed in early 2018 to pursue that search. A potential hexaquark particle detected at the Julich Research Center in 2014, named d*(2380), is theorized to have formed Bose-Einstein condensates during the low-temperature conditions of the early universe.