Dilute Quantum Droplets

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 due to the three-body correlations is given by the Efimov effect. For particular values of the diluteness parameter $\rho |a{|}^3$ 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 be manufactured.

Figure 1

A typical contour plot of the energy density for an homogeneous Fermi system consisting of two fermion species $\pi$ and $\nu$ [see Eq. (16)] for the case $\mathrm{\hbar }=m=g_3=1$ and $g_2=-5$. Only the negative part of the energy density surface is plotted. The local minimum and the two saddle points are labeled by M and S, respectively. For other sets of parameters there is either only one saddle point or none at all.