Bose-Einstein Condensation and Superfluidity

Atomic gases enjoy extraordinary cleanness and control at the microscopic level, permitting quantitative comparison with ab initio theoretical calculations.

“atomic gases enjoy an extraordinary level of cleanness and control at the microscopic level, which permits a quantitative comparison with ab initio theoretical calculations.”

The Hamiltonian for the quantum fluid of light in the lowest q=1 branch exactly corresponds to the Hamiltonian of a bosonic gas of material particles, in particular ultracold atoms.

“All together, it is immediate to recognize this Hamiltonian exactly corresponds to the one of a bosonic gas of material particles, in particular of ultracold atoms [1].”

For three-dimensional dilute Bose-Einstein condensates, the mean-field approach is valid when the diluteness parameter n_3d a_sc^3 is much less than 1.

“for three-dimensional gases, the condition can be expressed in terms of a diluteness condition n 3d a 3 sc ≪ 1, where n 3d is the three-dimensional density and a sc is the atom-atom collisional scattering length”

In low-dimensional geometries, a general condition for mean-field validity is that the characteristic kinetic energy exceeds the interaction energy, ε_kin ≫ ε_int, equivalently n ξ^d ≫ 1.

“a quite general formulation involves the characteristic kinetic and interaction energies, ε kin = ħ 2 n 2/d /2m ≫ ε int = g nl n or, equivalently, the number of particles per healing length, nξ d ≫ 1”

A naive application of the Landau criterion would predict that an impurity moving across the fluid experiences significant friction for any flow speed v, with no specific feature at the equilibrium speed of sound c_s = sqrt(g_nl |ψ|^2 / m).

“A naive application of the Landau criterion for superfluidity [1,105] would then predict that an impurity moving across a fluid will experience a significant friction force for any value of the flow speed v, with no specific feature at the (equilibrium) speed of sound c s = g nl |ψ| 2 /m.”

In a spatially uniform geometry, condensation is typically associated with the appearance of a sharp and macroscopic k = 0 peak in the momentum distribution n(k) = ⟨Ψ†(k)Ψ(k)⟩.

“condensation in a spatially uniform geometry is typically associated [1,107] to the appearance of a sharp and macroscopic k = 0 peak in the momentum distribution n(k) = Ψ † (k) Ψ(k)”