Two-body correlations in two-dimensional boson systems

Anna Okopińska, Przemysław Kościk

Barnali Chakrabarti, Arnaldo Gammal, N. D. Chavda +1 more

We study the dynamical fermionization of strongly interacting one-dimensional bosons in Tonks-Girardeau limit by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. We establish that the one-body momentum distribution approaches the ideal Fermi gas distribution at the time of dynamical fermionization. The analysis is further complemented by the measures on the two-body level. The dynamical fermionization in the two-body level should be inferred as the presence of a distinct correlation hole along the diagonal of two-body correlation. Investigation of two-body momentum distribution for the strongly interacting bosons clearly exhibits a pattern along the diagonal which is not extinguished at the time of fermionization. Two-body local and nonlocal correlation also clearly distinguish the fermionized bosons from noninteracting fermions. The magnitude of distinguishablity between the two systems is further discussed employing suitable measures of information theory, i.e., the well-known Kullback-Leibler relative entropy and the Jensen-Shannon divergence entropy. We also observe very rich structure in the higher-body density for strongly correlated bosons, whereas noninteracting fermions do not possess any higher-order correlation beyond two-body.

O. Sørensen, D. V. Fedorov, A. S. Jensen

We formulate a method to study two-body correlations in a system of N identical bosons interacting via central two-body potentials. We use the adiabatic hyperspherical approach and assume a Faddeev-like decomposition of the wave function. For a fixed hyperradius we derive variationally an optimal integro-differential equation for the hyperangular eigenvalue and wave function. This equation reduces substantially by assuming the interaction range much smaller than the size of the N-body system. At most, one-dimensional integrals then remain. We view a Bose-Einstein condensate pictorially as a structure in the landscape of the potential given as a function of the one-dimensional hyperradial coordinate. The quantum states of the condensate can be located in one of the two potential minima. We derive and discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy substantially. The new multibody Efimov states are solutions independent of details of the two-body potential. We compare with mean-field results and available experimental data.

R. F. Bishop

Sangita Bera, Rhombik Roy, Barnali Chakrabarti

Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.

James G. Glimm, Arthur M. Jaffe