Bose–Einstein Condensation of Atoms
Lasers cool rubidium atoms to tens of microkelvin; a magnetic trap lets the hottest go. In June 1995, near 170 nanokelvin, the rest fell into one quantum state, as Einstein, building on Bose, predicted in 1925.
Scroll
A Ten-Millionth of a Degree
In 1995 a group at JILA in Colorado cooled rubidium-87 atoms to about 170 nanokelvin, less than two ten-millionths of a degree above absolute zero. Out of about 20,000 atoms, a small cloud appeared that was all in the same lowest quantum state.
Cooled further, a pure condensate of about 2,000 atoms remained and lasted more than 15 seconds in its trap. Four months later a group at MIT made far larger ones from sodium, up to 500,000 atoms, with a transition near 2 microkelvin.
Room about 300 K · cosmic background 2.7 K · Doppler limit 146 µK · condensate about 170 nK
The Peak in the Picture
The atoms are too cold and too few for a thermometer. Their temperature comes from a picture: the trap is switched off and the cloud flies apart (JILA let it fly for 60 ms), then a beam of resonant light casts its shadow on a camera. The size of the shadow is the spread of the atoms’ velocities.
When the gas is warm, the shadow is a broad round bump, like the speeds of molecules in a gas. Below a certain temperature a narrow peak rises in the middle: atoms that hardly move. Colder still, the peak grows and the broad part shrinks. This is the two-layered distribution in the 1995 picture.
Velocity distributions above, near and below the transition (computed by this page)
Light Head-On
An atom that absorbs a photon gets a push from the light; it sends the photon out again in a random direction, which on average pushes nowhere. So a beam of light can push atoms along.
Tune a laser slightly below the atoms’ resonance and shine it from both sides. An atom running towards one beam sees that beam’s frequency raised by the Doppler effect, closer to resonance; it absorbs more and is pushed back harder. Whichever way it runs, it is held back, as if walking through syrup. Six beams along three axes make an “optical molasses”. Steven Chu’s group made one with sodium atoms at Bell Labs in 1985.
The force of two beams detuned by −Γ/2 on one atom (computed by this page)
The Doppler Limit
The photons kick one by one, in random directions, so the atom keeps jittering. Where the cooling and this jitter balance, the temperature stops falling: the Doppler limit. It depends only on the lifetime of the atom’s excited state: about 146 µK for rubidium 87, about 240 µK for sodium.
In 1988 William Phillips’s group measured sodium atoms at about 40 µK, far below that limit. Jean Dalibard and Claude Cohen-Tannoudji in Paris, and Chu’s group at Stanford, soon explained it: where the beams overlap, the polarisation differs from place to place, and an atom climbs hills like Sisyphus, losing a little energy to the light at each top. Rubidium molasses has been measured at 6 µK.
Rubidium 87: k_B·T_D = ħΓ/2, about 146 µK (computed by this page)
The Magneto-Optical Trap
Molasses slows atoms down but does not gather them. Add a pair of coils with opposite currents: the field is zero in the middle and grows outwards. It shifts the atoms’ levels with position, and the six beams carry opposite circular polarisations, so the farther an atom strays, the closer to resonance the beam pushing it back.
This is the magneto-optical trap, first built in 1987. JILA’s caught atoms straight from the very thin rubidium vapour in its glass cell, about ten million in five minutes, in a cloud a millimetre or two across that glows in the infrared. A strontium MOT is on the plate “Optical Lattice Clock”.
Levels shift with position; red-detuned light comes into resonance only off centre
Evaporation
Laser cooling stops at some tens of microkelvin, far from a condensate. So the lasers go off, a magnetic field alone holds the atoms, and the gas is cooled like a cup of tea: the hottest atoms are let go. In 1995 JILA started from about 4 million atoms at 90 µK.
An antenna sends out radio waves. Where their frequency matches, an atom’s magnetic moment is flipped and the trap pushes it out instead of holding it. That place is an ellipsoid round the cloud that only the most energetic atoms reach, so this “knife” shaves them off. The rest collide, share their energy again and end up colder. As the radio frequency is lowered, the knife closes in; at JILA this step took 70 seconds.
The energy distribution and the cut: atoms above it leave (computed by this page)
Waves Overlap
In quantum mechanics each atom is a wave packet about one thermal de Broglie wavelength wide, wider the colder it is. At room temperature it is smaller than the atom; at 170 nanokelvin it is about 0.45 micrometres, close to the distance between the atoms.
Then bosons crowd together into the lowest state. In a uniform gas this happens when the density times the wavelength cubed reaches about 2.612. Einstein predicted it in 1924–25, building on Bose’s counting of photons.
n·λ³ ≈ 2.612 · λ = h / √(2π m k_B T)
Cut Open: the Cell
In the middle is a glass cell pumped to ultra-high vacuum. The one drawn here is 30 mm square and about 10 cm long, a common size; JILA’s 1995 cell was 2.5 cm square and 12 cm long. One end is flat glass; the other is a round neck that passes through a seal of glass bands, each of a slightly different glass, to metal and a stainless flange.
Above and below the cell is the quadrupole pair; around it, two pairs of smaller coils. Six laser beams pass through its walls and cross in the middle. The cloud floats at the centre of the cell, touching nothing.
Glass cell 30 × 30 mm (JILA 1995: 25 × 25 mm) · graded seal · layout schematic
A Zero That Turns
The quadrupole’s field is zero in the middle, and near that zero an atom’s magnetic moment can flip and the atom leaks out of the trap. The colder and smaller the cloud, the faster it leaks.
JILA added a bias field that turns in the horizontal plane 7,500 times a second; such a field is usually made by two pairs of coils carrying alternating currents a quarter cycle apart. The zero is pushed off the centre and sweeps round the cloud. The atoms cannot follow so fast a change and feel the average: a smooth bowl whose bottom never reaches zero field. This is the time-averaged orbiting potential, the TOP trap. MIT plugged the zero with a 514 nm laser beam instead.
TOP trap: the zero circles the atoms, which sit in the averaged well
Shadows
The trap is switched off and the cloud spreads. A little later a weak beam resonant with the atoms shines through; where atoms absorb, it darkens, and the camera records the shadow. One picture with atoms, one without; comparing the two gives the optical depth.
In the shadow the thermal atoms spread into a circle. The condensate spreads differently: fastest along the direction in which the trap squeezed it hardest. The contrast between the circle and that ellipse was one of the 1995 signatures. Each picture destroys the cloud; the next one starts over.
Optical depth = −ln(I / I₀) · after 25 ms of flight (computed by this page)
Two Nobel Prizes
The 1997 Nobel Prize in Physics went to Steven Chu, Claude Cohen-Tannoudji and William D. Phillips “for development of methods to cool and trap atoms with laser light”.
The 2001 prize went to Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman “for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates”. Atomic clocks, atom interferometers and quantum simulators build on these cold-atom methods.
1924–25 prediction · 1985 molasses · 1987 MOT · 1995 condensate · 1997 and 2001 prizes
Taken Apart
The cell, the graded seal, the quadrupole coils, the two TOP pairs, the RF antenna, the vacuum cross, the ion pump, the valve, the MOT optics, the probe, the camera, the fibre box and the RF synthesizer, one by one.
Point at a part and it lifts out alone, the rest fading; at rest, every part is named.
Lower the Cut
The lever is the height of the RF cut, in microkelvin. Pull it down and the cut follows the radio frequency down, by at most about a third each second, as an experiment sweeps it. Atoms are shaved off; the rest collide, share their energy and cool.
The chart counts the velocities of atoms drawn one by one from the gas: the bars are the counts, the line the distribution in theory. It starts as a broad Gaussian. With the cut near 1 µK a narrow peak rises in the middle and the condensed share climbs. Push the cut too low and it shaves the condensate itself.
Try thisLower the RF cut slowly from 900 µK to 0.5 µK: at what temperature does the peak appear in the velocity distribution, and how many atoms are left by then?
What the model leaves out
The apparatus follows what the first rubidium condensate experiments have in common: a glass vapour cell, a six-beam MOT, a magnetic trap of a quadrupole pair with a turning bias field, RF evaporation and absorption imaging. Sizes are common ones; the layout is schematic, not any laboratory’s drawings. In a real lab the lasers sit on another optical table and arrive by fibre; the frequencies of the cooling and probe light, the acousto-optic modulators and the shutters are not drawn. Light at 780 nm is barely visible; it is drawn dark red. The cloud is enlarged: the MOT at about its real size (a millimetre or two), the atoms in the magnetic trap on a square-root scale (86 µm drawn as about 6 mm, 4 µm as about 1.3 mm), and each dot stands for many atoms. The evaporation is computed for an ideal Bose gas: each round removes the atoms above the cut and the rest settle at once; the condensate’s interactions follow the Thomas–Fermi approximation; collisions with the background gas take 8.5 % of the atoms per second of the page’s clock (which runs about four times faster than the experiment, so a lifetime of about 50 s in the experiment’s time, a little shorter than the paper’s about 70 s); three-body losses are left out. The start is the 1995 paper’s: 4 million atoms at 90 µK. The trap runs at 98 Hz radially and 277 Hz along its axis; the paper gives no frequencies at the transition, so these are illustrative, chosen so that about 20,000 atoms condense near 170 nK, as in the paper. The page’s clock runs faster than the experiment, whose evaporation took 70 seconds.
Common misreadings
A condensate is not atoms “standing still”: even the lowest state moves a little, with a width set by the trap. Nor is it ordinary condensation: the atoms do not bind into a droplet; they stay some tenths of a micrometre apart, a thousand times farther than molecules in water. What crowds together is their quantum state, not their positions. Laser cooling does not “freeze” atoms with light; it makes an atom running into a beam absorb a little more of it. It has a floor, so the last step is evaporation. Temperature here means how fast the atoms move; a cloud at a few hundred nanokelvin can float in a room-temperature cell because almost no heat gets in: nothing touches them, and they barely absorb the room’s thermal glow. From its measured density the 1995 paper got n·λ³ of about 0.3, below 2.612, and put the gap down mainly to the calibration of the cloud’s size.
Common questions · 4
- How was the first Bose–Einstein condensate made?
In 1995 a group at JILA in Colorado cooled rubidium-87 atoms to about 170 nanokelvin, less than two ten-millionths of a degree above absolute zero.
01A Ten-Millionth of a Degree ↑- How can a laser cool atoms?
An atom running towards one beam sees that beam’s frequency raised by the Doppler effect, closer to resonance; it absorbs more and is pushed back harder.
03Light Head-On ↑- When does a gas form a Bose–Einstein condensate?
In a uniform gas this happens when the density times the wavelength cubed reaches about 2.612.
07Waves Overlap ↑- Did laser cooling win a Nobel Prize?
The 1997 Nobel Prize in Physics went to Steven Chu, Claude Cohen-Tannoudji and William D. Phillips “for development of methods to cool and trap atoms with laser light”.
11Two Nobel Prizes ↑
Sources
- M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell (1995): Observation of Bose–Einstein condensation in a dilute atomic vapor, Science 269, 198 (170 nK, 2.5 × 10¹² cm⁻³, more than 15 s; 2 × 10⁴ atoms at the transition; 4 × 10⁶ atoms at 90 µK before evaporation; 7.5 kHz rotating field; 60 ms of flight)
- K. B. Davis et al. (1995): Bose–Einstein condensation in a gas of sodium atoms, PRL 75, 3969 (up to 5 × 10⁵ atoms, densities above 10¹⁴ cm⁻³, about 2 µK, a 514 nm optical plug)
- Nobel Prize: 1997 physics press release (Chu, Cohen-Tannoudji, Phillips)
- Nobel Prize: 2001 physics press release (Cornell, Ketterle, Wieman)
- Nobel Committee for Physics: 2001 scientific background
- S. Chu et al. (1985): PRL 55, 48 (optical molasses, sodium, about 240 µK)
- E. L. Raab et al. (1987): Trapping of neutral sodium atoms with radiation pressure, PRL 59, 2631 (the MOT)
- P. D. Lett et al. (1988): Observation of atoms laser cooled below the Doppler limit, PRL 61, 169 (sodium, 43 ± 20 µK)
- J. Dalibard, C. Cohen-Tannoudji (1989): Laser cooling below the Doppler limit by polarization gradients, JOSA B 6, 2023
- C. Gerz et al. (1993): The temperature of optical molasses for two different atomic angular momenta, Europhys. Lett. 21, 661 (rubidium, 6 µK)
- W. Petrich, M. H. Anderson, J. R. Ensher, E. A. Cornell (1995): A stable, tightly confining magnetic trap for evaporative cooling of neutral atoms, PRL 74, 3352 (the TOP trap)
- D. A. Steck: Rubidium 87 D Line Data (780.241 nm, Γ = 2π × 6.0666 MHz, Doppler temperature 145.57 µK)
- E. G. M. van Kempen et al. (2002): PRL 88, 093201 (rubidium-87 scattering length 98.98 a₀)
- F. Dalfovo, S. Giorgini, L. P. Pitaevskii, S. Stringari (1999): Theory of Bose–Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (T_c ≈ 0.94 ħω̄N^{1/3}; Thomas–Fermi)
- W. Ketterle, D. S. Durfee, D. M. Stamper-Kurn: Making, probing and understanding Bose–Einstein condensates, arXiv:cond-mat/9904034 (the RF cut)
- Y. Castin, R. Dum (1996): PRL 77, 5315 (how a released condensate expands)
- E. A. Cornell, C. E. Wieman (2002): Nobel lecture, Rev. Mod. Phys. 74, 875 (5 June 1995)
- W. Ketterle (2002): Nobel lecture, Rev. Mod. Phys. 74, 1131
Data
The apparatus follows the layout that the first rubidium condensate experiments share in their published descriptions (a glass vapour cell, a six-beam magneto-optical trap, a quadrupole trap with a rotating bias field, RF evaporation, absorption imaging); it is not drawn from any one laboratory’s plans. The forces, temperatures, the evaporation and the velocity distributions are computed by this page; they are not measured data. Rubidium 87 numbers from D. A. Steck, “Rubidium 87 D Line Data” (rev. 2.3.4). Material presets, parts and the softbox studio of the site’s model kit are ported from AirsupHQ/machine-skill (MIT, © 2026 Air Supply Technologies Inc.).
The text, pictures and models on this page are licensed CC BY-NC 4.0: free to use and adapt for teaching and other non-commercial purposes, with credit to world.lapla.si. Third-party material listed above keeps its own licence.
Cite this plate
Laplace’s Mini World, Plate F27, “Bose–Einstein Condensation of Atoms”, https://world.lapla.si/en/bec/, CC BY-NC 4.0, updated 2026-10-20.
Follow the question
Plate F23The Optical Lattice ClockA laser beam swings about 429 trillion times a second, kept on time by strontium atoms held in a lattice of light. It is good to the eighteenth decimal place: raise the clock by a centimetre and the tiny speed-up can be measured.
Plate 36Where Is the Electron?Textbooks often draw electrons as little balls circling the nucleus. In fact an electron has no orbit. It is more like a cloud: all we can say is where it is likely to be.
