Bose-Einstein Condensate: The Fifth State of Matter

Bosons, de Broglie wavelengths, and the condensation transition

Bosons — particles of integer spin like photons and rubidium-87 atoms — have no exclusion principle, and thermodynamically prefer to occupy the same quantum state. Every particle has a thermal de Broglie wavelength, the spatial extent of its quantum wavepacket:

λ_dB = √(2πℏ² / m·k_B·T)

Room temperature: λ_dB ≪ inter-atom spacing → atoms behave classically
At ~100 nK: λ_dB ~ 1 μm ≈ inter-atom spacing → wavefunctions OVERLAP

T_c = (2πℏ²/m·k_B) · (n/ζ(3/2))^(2/3)   (critical temperature, ideal Bose gas)

Below the critical temperature T_c, a macroscopic fraction of atoms collapses into the same single-particle ground state, losing their individual identities — the cloud is described by a single complex wavefunction Ψ(r,t), the order parameter, a genuine phase transition in the quantum sense.

Making a BEC and the Gross-Pitaevskii equation

Creating a BEC requires laser cooling to ~50 μK in milliseconds, loading into a magnetic trap, then evaporative cooling — slowly lowering the trap depth so the hottest atoms escape and the rest re-thermalise colder, like blowing on hot coffee — until the sample reaches ~100 nK. Eric Cornell and Carl Wieman created the first BEC this way in rubidium-87 on 5 June 1995 at JILA; Wolfgang Ketterle created one independently in sodium weeks later, and all three shared the 2001 Nobel Prize in Physics. A weakly-interacting BEC at zero temperature obeys the Gross-Pitaevskii equation, a nonlinear Schrödinger equation for the macroscopic wavefunction:

iℏ ∂Ψ/∂t = [−ℏ²∇²/2m + V_ext(r) + g|Ψ|²] Ψ
g = 4πℏ²a_s/m   (a_s = s-wave scattering length)

Superfluidity and quantum vortices

The condensate wavefunction Ψ = √n·e^iθ has a phase θ(r), and the superfluid velocity is proportional to its gradient — a remarkable consequence is that flow is irrotational everywhere except at isolated singular points called quantum vortices, each carrying a fixed, quantised unit of circulation. Stir a BEC above a critical rotation rate and a lattice of these vortices appears; they are topologically protected, unable to be removed without unwinding the phase around a loop — a property that makes them candidates for topological quantum computing. Beyond the lab, BEC atom interferometers now measure gravity and rotation with extreme precision for next-generation navigation, and one speculative cosmology model proposes dark matter itself forms a superfluid BEC in galactic halos.

Frequently asked questions

Try it live

Everything above runs in your browser — open Bose-Einstein Condensate and cool bosons toward absolute zero, watching a macroscopic fraction condense into the ground state below T_c.