The quantum chill
Laser cooling removes momentum one photon at a time; evaporative cooling lets the hottest atoms escape a trap, lowering temperature further. When thermal wavelengths overlap, identity matters: bosons love to share states; fermions refuse. This is the doorway to macroscopic quantum matter.
A crude estimate of the critical temperature for an ideal Bose gas at density \(n\) is \[ T_c \approx 0.94\,\frac{\hbar^2}{k_B m}\,n^{2/3}. \] Below \(T_c\) a macroscopic fraction occupies the ground state — a Bose–Einstein condensate (BEC) with a coherent matter wave.
Bose–Einstein condensation
In a BEC, phase coherence extends across the cloud. Release two condensates and they interfere like laser beams — the signature that the many atoms share one macroscopic wavefunction \(\Psi(\mathbf{r})\).
Interactions reshape the density via the Gross–Pitaevskii equation, but the core message survives: cooling bosons reveals order from indistinguishability.
Degenerate Fermi gases
Fermions fill momentum states up to the Fermi energy. Even at zero temperature they exert pressure — Pauli pressure — which keeps the cloud spread out. Pairing can turn fermions superfluid (BCS–BEC crossover), but without pairing they never condense into a single mode.
Interactive • Cooling into order (Bose vs Fermi)
Thousands of “atoms” drift in a trap. Lower the temperature to slow motion. In Bose mode they merge into a bright coherent core; in Fermi mode they stay spread by Pauli pressure. The plot tracks an order parameter: condensed fraction for bosons, degeneracy parameter for fermions.
Coherence, superfluidity, & uses
Ultracold gases provide pristine platforms for analog quantum simulation (Hubbard models), precision metrology (atom interferometers, clocks), and tests of many-body dynamics (quenches, transport, universality). They also serve as clean laboratories for superfluidity, vortices, and sound in quantum fluids.