Einsteinpedia

Theories · 1924 – 1925

Bose–Einstein Statistics and the Condensate

A letter from an unknown physicist in Dhaka led Einstein to predict a new state of matter, in which atoms cooled almost to absolute zero merge into a single quantum wave.

n‾i=1e(εi−μ)/kBT−1

A Letter From Dhaka

In a letter dated 4 June 1924, Satyendra Nath Bose, who taught physics at the University of Dhaka (then Dacca), sent Einstein a short manuscript. A journal had rejected it. Bose had found a new way to derive Planck's radiation law by counting light quanta as genuinely indistinguishable: swapping two of them does not produce a new arrangement.

Einstein saw at once that it mattered. He translated the paper into German himself and arranged for its publication.

From Light to Atoms

Einstein then applied Bose's way of counting to atoms of an ordinary gas. The result is Bose–Einstein statistics, the rule for how identical particles of a certain kind, now called bosons, distribute themselves over the available energy levels. The equation above gives the average number of particles in a level of energy εi.

Unlike classical particles, bosons prefer company. The more of them already occupy a state, the more likely another is to join. This is the same tendency that underlies stimulated emission.

The Prediction

In his second paper on the subject, in 1925, Einstein noticed something strange in the mathematics. Cool a gas of bosons below a critical temperature and a large fraction of the atoms must suddenly drop into the single lowest energy state, however large the container.

Tc=2πℏ2mkB(nζ(3/2))2/3

Atoms in that state lose their separate identities and behave as one. Einstein was not sure the effect was real. The theory was beautiful, he wrote to a friend, but was there any truth in it?

Seventy Years Later

The temperatures required are extraordinarily low, and the tools to reach them did not exist until laser cooling was developed in the 1980s. In 1995 Eric Cornell and Carl Wieman in Boulder, Colorado, cooled about two thousand rubidium atoms to less than 200 billionths of a degree above absolute zero and saw them condense. Wolfgang Ketterle at MIT produced larger condensates of sodium months later. The three shared the 2001 Nobel Prize in Physics.

Where It Stands

Bose–Einstein condensates are now made routinely in laboratories around the world, and since 2018 aboard the International Space Station. See Bose–Einstein Condensates.

Sources

  1. NASA Jet Propulsion Laboratory — Cold Atom Laboratory
  2. NIST — Cornell and Wieman share 2001 Nobel Prize in Physics
  3. Britannica — Bose–Einstein condensate
  4. Nobel Prize in Physics 2001 — popular information
  5. NIST — physicists create new state of matter at record low temperature (1995)
  6. Nobel Prize in Physics 2001 — press release
  7. Pérez and Sauer — Einstein's quantum theory of the monatomic ideal gas
  8. A. Douglas Stone — Einstein and the Quantum