Hartree solution for the “bosonic atom”

Jaime Sañudo A, Amalio F. Pacheco

The Hartree solution for the ground state of N >>1 bosons placed within a spherical impenetrable shell is calculated. The bosons are assumed to interact through Coulomb repulsive forces and therefore occupy a thin volume adjacent to the shell wall. The resulting density profile is compared with its parallel Thomas-Fermi solution for fermions.

Luca Salasnich

Yeongjin Gwak, Oleksandr V. Marchukov, Uwe R. Fischer

We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method, and the statement that it is numerically exact, with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, and underestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

David E. Laird

Manuel C. Membrado, Amalio F. Pacheco, Jaime Sañudo A

The ground state of an N-boson assembly interacting through two-body attractive Yukawa forces is analyzed in the Hartree approximation. The solution, which is not universal, can be adequately characterized by a unique parameter \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} proportional to \ensuremath{\mu}${N}^{\mathrm{\ensuremath{-}}1}$, where ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}1}$ is the range of the force. It is found that for \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} larger than a critical value, there is no bound solution for the system. Our solutions are shown to rigorously fulfill the virial theorem.

George P. Flessas