Quantum corrections to Dilute Bose Liquids

P.F. Bedaque (LBL), A. Bulgac and G. Rupak (LBL)

In a recent Letter [72] it was show that in the limit when the two-body scattering length $a$ is negative and much larger than the effective two-body interaction radius the contribution to the ground state energy of a dilute boson system due to the three-body correlations is given by the Efimov effect. The magnitude and sign of the atom-atom scattering length can be relatively easily controlled by means of an applied external magnetic field and the physics of this is routinely denoted as a Feshbach resonance. For particular values of the diluteness parameter $\rho \vert a\vert^3$ the three-body contribution can become the dominant term of the energy density functional. Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion ``designer nuclei'' of various sizes and densities could in principle be manufactured. We have extended the previous mean-field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose-Einstein condensate and by estimating higher order corrections as well [73]. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n\vert a\vert^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.