Ground-state properties of a one-dimensional strongly interacting Bose-Fermi mixture in a double-well potential

We calculate the reduced single-particle density matrix (RSPDM), momentum distribution, natural orbitals and their occupancies, for a strongly repulsive one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. We assume that all particles have the same mass, and fermions are spin polarized. For mesoscopic systems, we find that the ground-state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.

Figure 1

(Color online) Momentum distributions $n_{\mu }\left(k\right)$ for $N_F=6$ (all curves) and $N_B=0,1,2,3,4$; curves are ordered from bottom to top and shifted by a constant for better visibility.

Figure 2

(Color online) Momentum distributions $n_{\mu }\left(k\right)$ for $N_F=7$ (all curves) and $N_B=0,1,2,3$: curves are ordered from bottom to top and shifted by a constant for better visibility.

Figure 3

(Color online) The total momentum distributions $n_{\mu }\left(k\right)+n_{\eta }\left(k\right)$ for $N_F=6$ (all curves) and $N_B=0,1,2,3,4$; curves are ordered from bottom to top and shifted by a constant for better visibility.

Figure 4

(Color online) The total momentum distributions $n_{\mu }\left(k\right)+n_{\eta }\left(k\right)$ for $N_F=7$ (all curves) and $N_B=0,1,2,3$; curves are ordered from bottom to top and shifted by a constant amount for better visibility.

Figure 5

(Color online) Contour plot of the fermionic RSPDM for $N_F=6$ and $N_B=1$.

Figure 6

(Color online) Contour plot of the fermionic RSPDM for $N_F=6$ and $N_B=2$.

Figure 7

(Color online) Contour plot of the fermionic RSPDM for $N_F=7$ and $N_B=1$.

Figure 8

(Color online) Contour plot of the fermionic RSPDM for $N_F=7$ and $N_B=2$.

Figure 9

(Color online) The occupancies of the fermionic RSPDM for the combinations $N_F=6$ and $N_B=1$ (squares), and $N_F=6$ and $N_B=2$ (circles). The lines serve to guide the eyes.

Figure 10

(Color online) The occupancies of the fermionic RSPDM for the combinations $N_F=7$ and $N_B=1$ (squares), and $N_F=7$ and $N_B=2$ (circles). The lines serve to guide the eyes.