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arXiv:1111.5977 · Physical Review A

Ground states of dipolar gases in quasi-one-dimensional ring traps

Sascha Zöllner

Published Dec 14, 2011• 18 citations
arXivHTMLPDF

Abstract

We compute the ground state of dipoles in a quasi-one-dimensional ring trap using few-body techniques combined with analytical arguments. The effective interaction between two dipoles depends on their center-of-mass coordinate and can be tuned by varying the angle between dipoles and the plane of the ring. For sufficiently weak interactions, the state resembles a weakly interacting Fermi gas or a (inhomogeneous) Lieb-Liniger gas. A mapping between the Lieb-Liniger--gas parameters and the dipolar-gas parameters in and beyond the Born approximation is established, and we discuss the effect of inhomogeneities based on a local-density approximation. For strongly repulsive interactions, the system exhibits a crystal-like localization of the particles. Their inhomogeneous distribution may be understood in terms of a simple few-body model as well as a local-density approximation. In the case of partially attractive interactions, clustered states form for sufficiently strong coupling, and the dependence of the state on particle number and orientation angle of the dipoles is discussed analytically.

DOI
10.1103/physreva.84.063619

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We compute the ground state of dipoles in a quasi-one-dimensional ring trap using few-body techniques combined with analytical arguments. The effective interaction between two dipoles depends on their center-of-mass coordinate and can be tuned by varying the angle between dipoles and the plane of the ring. For sufficiently weak interactions, the state resembles a weakly interacting Fermi gas or a (inhomogeneous) Lieb-Liniger gas. A mapping between the Lieb-Liniger--gas parameters and the dipolar-gas parameters in and beyond the Born approximation is established, and we discuss the effect of inhomogeneities based on a local-density approximation. For strongly repulsive interactions, the system exhibits a crystal-like localization of the particles. Their inhomogeneous distribution may be understood in terms of a simple few-body model as well as a local-density approximation. In the case of partially attractive interactions, clustered states form for sufficiently strong coupling, and the dependence of the state on particle number and orientation angle of the dipoles is discussed analytically.
Abstract Using the Bose–Fermi mapping method, we obtain the exact ground state wavefunction of one-dimensional (1D) Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit. Its ground state density distributions for both repulsive and attractive dipole interactions are exhibited. It is shown that in the case of the finite dipole interaction the density profiles do not change obviously with the increase of dipole interaction and display the typical shell structure of Tonks–Girardeau gases. As the repulsive dipole interaction is greatly strong, the density decreases at the center of the trap and displays a sunken valley. As the attractive dipole interaction increases, the density displays more oscillations and sharp peaks appear in the strong attraction limit, which mainly originate from the atoms occupying the low single particle levels.
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 $\ensuremath{\delta}$-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 $\ensuremath{\delta}$ 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.
Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree--Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multiatom Schrödinger equation, we discover that such systems can exhibit not only the well-known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multiatom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case.