Physics of dilute neutral-atom gases in the nK-μK temperature regime. Laser-cooling (Hansch-Schawlow 1975 proposal, Chu-Cohen-Tannoudji-Phillips 1997 Nobel) down to the Doppler limit T_D = ℏΓ/(2 k_B); sub-Doppler (Sisyphus,…
ultracold-atoms
BEC order parameter Ψ(r,t): macroscopic occupation of the ground state
Bogoliubov / Penrose-Onsager criterion for Bose-Einstein condensation: a one-body density matrix ρ_1(r, r') = ⟨Ψ̂†(r')Ψ̂(r)⟩ has a single…
Doppler cooling limit: T_D = ℏΓ/(2 k_B) (Hansch-Schawlow 1975)
Hansch-Schawlow 1975 / Wineland-Itano 1979 proposal; Chu 1985 experimental demonstration of optical molasses: six red-detuned…
Forced evaporative cooling: truncate the Boltzmann tail to cool the remainder
Hess 1986 proposal; Masuhara-Doyle-Luiten 1988 demonstration in hydrogen; Davis-Petrich-Ketterle 1995 in sodium. After laser cooling has…
BEC critical temperature: k_B T_c = (2πℏ²/m) · (n/ζ(3/2))^(2/3)
Einstein 1925: for a non-interacting ideal Bose gas of N indistinguishable bosons with mass m in a uniform volume V, the thermal de Broglie…
GP healing length: ξ = 1/√(8π n a_s) (kinetic ≡ interaction)
Healing length ξ is the lengthscale at which the kinetic energy ℏ²/(2mξ²) of a condensate density modulation equals the mean-field…
Feshbach resonance: a(B) = a_bg(1 − Δ/(B − B_0)) — tunable interactions
Feshbach 1958 (nuclear scattering); Tiesinga-Verhaar-Stoof 1993 (ultracold atoms); Inouye et al 1998 (observation in ²³Na condensate). …