We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without breaking the spin or any other symmetry. In particular, it shows "bumps" (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly correlated systems. Here, we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation.

In the Appendix of our paper, we derive the effective onedimensional (1D) dipole-dipole interaction (DDI) potential. The derivation and the result are incomplete, since the singularity of the three-dimensional (3D) DDI at zero distance is not properly accounted for. To see this, we introduce a small > 0 in the denominator of the 3D DDI. The first steps of the calculation are analogous to those shown in the Appendix until one arrives at 1with w = ρ/ l ⊥ and u = x/ l ⊥ . This is equal towith v = √ u 2 + 2 andIn the limit → 0, one finally obtainsi.e., apart from the second term in square brackets, which is already given in the paper, there is an additional δ term present in the 1D DDI. This term is missing in Eqs. (2)-(4) of our paper. Let us briefly show that lim →0 ∞ −∞ du δ (u) = 1. One finds thatThe third step follows from the substitution t = (w 2 + 2 )/2, the fourth step from an integration by parts, and the last step from Ei(x) ≈ ln(x) and x 2 ln(x) → 0 for x → 0, where Ei(x) is the exponential integral. It can be seen from Eq. (4) that the strength of the δ interaction depends on the dipole orientation with respect to the weak trap axis (the angle θ ). This is different from the δ contribution, which stems from the point limit of a real (extended) dipole [1], where the strength depends on the relative orientation of the two interacting dipoles. In total there are three δ terms, which originate from the van der Waals interaction, the point limit of a real dipole, and the integration over the transverse directions.In our paper, we study the effect of the 1D DDI without the δ terms and perform a sweep of the interaction strength. Such a sweep can be performed experimentally, when the strength of all δ terms is tuned to zero by means of a Feshbach resonance. Then, the strength of the interaction term in square brackets with respect to the level spacing can be tuned by changing the axial angular frequency, as described at the end of Sec. III.

We study the ground state of few bosons with repulsive dipole-dipole interaction in a quasi-one-dimensional harmonic trap by means of the exact diagonalization method. Up to three interaction regimes are found, depending on the strength of the dipolar interaction and the ratio of transverse to axial oscillator lengths: a regime where the dipolar Bose gas resembles a system of weakly δ-interacting bosons, a second regime where the bosons are fermionized, and a third regime where the bosons form a Wigner crystal. In the first two regimes, the dipole-dipole potential can be replaced by a δ potential. In the crystalline state, the overlap between the localized wave packets is strongly reduced and all the properties of the boson system equal those of its fermionic counterpart. The transition from the Tonks-Girardeau gas to the solidlike state is accompanied by a rapid increase of the interaction energy and a considerable change of the momentum distribution, which we trace back to the different short-range correlations in the two interaction regimes.

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.Recent experimental advances in cold quantum gases have placed focus on atoms or molecules with permanent dipole moments. A Bose-Einstein condensate of 52 Cr atoms has been realized [1,2], and recently Dy atoms were cooled and trapped [3]. These atom species have magnetic dipole moments of several Bohr magnetons. A promising development is the trapping and cooling of diatomic molecules with electric dipole moments [4][5][6]. The realization of a molecular fermionic 40 K 87 Rb gas was a significant breakthrough [7]. Dipolar gases offer access to a broad range of novel few-and many-body physics, in single traps as well as in optical lattices which has spurred intensive theoretical interest (see the recent reviews by Baranov [8] and Lahaye et al. [9]). The attractive part of the dipolar interaction leads to a collapse instability in three dimensions [9]. A remedy is to use traps of reduced dimensionality. For instance, the interaction between dipoles in a 2D plane is predominantly repulsive when they form a sufficiently large angle with respect to the plane (see Fig. 1). This stabilizes the system against collapse [10]. A variety of interesting many-body states for dipoles in 2D has been examined theoretically [10][11][12].Here, we examine a 2D system of this kind in the regime of strong repulsive interactions using exact diagonalization as well as a classical analysis. Contrary to the analogous Wigner states of electrons in metals [14] and quantum dots [15] the anisotropic dipolar interaction is shown to give rise to Wigner states with nontrivial geometries that depend on the alignment angle. This leads to transitions between different geometries that are crucially influenced by quantum statistics. We finally argue that our results are experimentally observable.We consider particles with mass m and a magnetic (electric) dipole moment µ (d) which is aligned by an external field such that it lies in the xz plane, forming an angle Θ with the x axis (see Fig. 1). The interaction between two electric dipoles separated by a vector r iswhere θ rd is the angle between a dipole moment and r. The particles are...

We theoretically investigate the transport properties of cold bosonic atoms in a quasi one-dimensional triple-well potential that consists of two large outer wells, which act as microscopic source and drain reservoirs, and a small inner well, which represents a quantum-dot-like scattering region. Bias and gate "voltages" introduce a timedependent tilt of the triple-well configuration, and are used to shift the energetic level of the inner well with respect to the outer ones. By means of exact diagonalization considering a total number of six atoms in the triple-well potential, we find diamondlike structures for the occurrence of single-atom transport in the parameter space spanned by the bias and gate voltages. We discuss the analogy with Coulomb blockade in electronic quantum dots, and point out how one can infer the interaction energy in the central well from the distance between the diamonds.