The Condensate Queen: Bose–Einstein Condensate
Quantum Foundations arc, page 8 of 193. Back to The Pixelated Physics Universe
Who they are
Meet The Condensate Queen, who gathers thousands of atoms into a single quantum state. Cool a gas of bosons until each atom's quantum wave is as wide as the gap between atoms, and a large fraction drops into the lowest state together: a Bose-Einstein condensate. In 1995 Eric Cornell and Carl Wieman at JILA did it first in a gas, with rubidium-87 at about 170 nanokelvin, and Wolfgang Ketterle at MIT followed with sodium. The three shared the 2001 Nobel Prize. The Condensate Queen on a pixel-art unisex tee; equations, symbols and sources in the physics panel below."Many atoms, one wave."
The Condensate Queen is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Cool atoms until their quantum waves are as wide as the spaces between them, and thousands of them fall into the same lowest-energy state and act as one. It was first done in a gas in 1995, at about 170 billionths of a degree above absolute zero.
$$ \begin{gathered} \lambda_{\mathrm{dB}} = \frac{h}{\sqrt{2\pi m k_B T}} \\ n\,\lambda_{\mathrm{dB}}^{3} = \zeta(3/2) \approx 2.612 \\ k_B T_c = \frac{2\pi\hbar^{2}}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\quad\text{(uniform gas)} \\ k_B T_c \approx 0.94\,\hbar\bar\omega\,N^{1/3}\quad\text{(harmonic trap)} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\lambda_{\mathrm{dB}}$ | thermal de Broglie wavelength | m |
| $h$ | Planck constant | J·s |
| $\hbar$ | reduced Planck constant, h/2π | J·s |
| $m$ | mass of one atom | kg |
| $k_B$ | Boltzmann constant | J/K |
| $T$ | temperature | K |
| $T_c$ | critical temperature for condensation | K |
| $n$ | number density (peak density in a trap) | m⁻³ |
| $\zeta(3/2)$ | Riemann zeta function at 3/2, ≈ 2.612 | 1 |
| $\bar\omega$ | geometric mean of the trap angular frequencies | rad/s |
| $N$ | number of atoms in the trap | 1 |
Sources
- Anderson, Ensher, Matthews, Wieman & Cornell (1995) Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science 269, 198
- Davis et al. (1995) Bose-Einstein Condensation in a Gas of Sodium Atoms, PRL 75, 3969
- NobelPrize.org — The Nobel Prize in Physics 2001
- NIST CODATA 2022 — Boltzmann constant
- NIST CODATA 2022 — Planck constant
Crossovers
The Condensate Queen meets Exclusor (Pauli Exclusion Principle / Degeneracy Pressure). Exclusor lets no two identical fermions share a state. The Condensate Queen gathers bosons into one state by the thousand. Spin decides which ruler a particle obeys: half-integer spin answers to Exclusor, integer spin to the Queen.
The Condensate Queen meets Molassa (Doppler Cooling Limit). The Condensate Queen needs atoms cold enough that their quantum waves overlap. Molassa's laser cooling gets them close. In the first condensates, evaporative cooling in a magnetic trap made the final step.
The Condensate Queen meets Trimera (Efimov States). Trimera's Efimov trios are studied in ultracold atomic gases, the Condensate Queen's home ground, where magnetic Feshbach resonances can tune the atoms' scattering length. That is how the predicted three-body states were finally seen.
Wear the lore
Concept keywords: Bose–Einstein Condensate, The Condensate Queen, Quantum Foundations, physics lore, Pixelated Physics