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Register a new userExact two-body solutions and Quantum defect theory of two dimensional dipolar quantum gas
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In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr{o}dinger equation with isotropic $pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to investigate the scattering properties as well as two-body bound states of ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.
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A halo is an intrinsically quantum object defined as a bound state of a spatial size which extends deeply into the classically forbidden region. Previously, halos have been observed in bound states of two and less frequently of three atoms. Here, we propose a realization of halo states containing as many as six atoms. We report the binding energies, pair correlation functions, spatial distributions, and sizes of few-body clusters composed by bosonic dipolar atoms in a bilayer geometry. We find two very distinct halo structures, for large interlayer separation the halo structure is roughly symmetric and we discover an unusual highly anisotropic shape of halo states close to the unbinding threshold. Our results open avenues of using ultracold gases for the experimental realization of halos with the largest number of atoms ever predicted before.
We present vortex solutions for the homogeneous two-dimensional Bose-Einstein condensate featuring dipolar atomic interactions, mapped out as a function of the dipolar interaction strength (relative to the contact interactions) and polarization direction. Stable vortex solutions arise in the regimes where the fully homogeneous system is stable to the phonon or roton instabilities. Close to these instabilities, the vortex profile differs significantly from that of a vortex in a nondipolar quantum gas, developing, for example, density ripples and an anisotropic core. Meanwhile, the vortex itself generates a mesoscopic dipolar potential which, at distance, scales as 1/r^2 and has an angular dependence which mimics the microscopic dipolar interaction.
Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semi-exactly within the local-density approximation using an empirical fit to Quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to both a one-dimensional stripe phase, and a triangular Wigner crystal. However, we find that there is an instability first to the stripe phase, followed by a transition to the Wigner crystal at higher coupling.
We examine the superfluid and collapse instabilities of a quasi two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipolar interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii--Kosterlitz--Thouless temperature as a function of the dipole angle.
We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.
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