Ground state properties of weakly bound few-body systems

Silvano Simula

Arkadiusz Kuroś, Anna Okopińska

S. E. Rasmussen, A. S. Jensen, D. V. Fedorov

Abstract We investigate the two lowest-lying weakly bound states of N ≤ 8 bosons as functions of the strength of two-body Gaussian interactions. We observe the limit for validity of Efimov physics. We calculate energies and second radial moments as functions of scattering length. For identical bosons we find that two ( N − 1 ) -body states appear before the N -body ground states become bound. This pattern ceases to exist for N ≥ 7 where the size of the ground state becomes smaller than the range of the two-body potential. All mean-square-radii for N ≥ 4 remain finite at the threshold of zero binding, where they vary as ( N − 1 ) p with p = − 3 / 2 , − 3 for ground and excited states, respectively. Decreasing the mass of one particle we find stronger binding and smaller radii. The identical particles form a symmetric system, while the lighter particle is further away in the ground states. In the excited states we find the identical bosons either surrounded or surrounding the light particle for few or many bosons, respectively. We demonstrate that the first excited states for all strengths resemble two-body halos of one particle weakly bound to a dense N -body system for N = 3, 4. This structure ceases to exist for N ≥ 5 .

J. I. Abdullaev, Akhmad Miyassarovich Khalkhuzhaev, J. Kh. Boymurodov

Joseph Carlson, Stefano Gandolfi, U. van Kolck +1 more

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this Letter we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- and three-body contacts, and the condensate fraction. We find that uniform matter is more bound than three-body clusters by nearly 2 orders of magnitude, the two-body contact is very large in absolute terms, and yet the condensate fraction is also very large, greater than 90%. Equilibrium properties of these systems may be experimentally accessible through rapid quenching of weakly interacting boson superfluids.

Richard Froese