Size-Induced Highly Selective Synthesis of Organometallic Rectangular Macrocycles and Heterometallic Cage Based on Half-Sandwich Rhodium Building Block.

The controlled synthesis of organometallic supramolecular macrocycles cages remains interesting and challenging work in the field of supramolecular chemistry. Here, two tetranuclear rectangular macrocycles and an octuclear cage were designed and synthesized utilizing a rigid and functionalized pillar linker, 2,6-bis(pyridin-4-yl)-1,7-dihydrobenzo [1,2-d:4,5-d']diimidazole (BBI4PY) based on three half-sandwich rhodium building blocks bearing different sizes. X-ray crystallography in combination with 1H NMR spectroscopy elucidated that the two building blocks with shorter spacers only result in rectangular macrocycles. However, the building block of bulkier size to avoid the π-π stacking interactions between two ligands BBI4PY led to the formation of an octuclear cage complex. The latter cage contains two types of metal ions, namely Rh3+ and Cu2+, showing significant characteristics of heterogeneous metal-assembling compounds. In addition, the cage accommodates two free isopropyl ether solvent molecules, thus displaying host-guest behavior.

Two-dimensional Bose gases near resonance: competing two-body and three-body effects.

We report in this Letter the results of our investigation of 2D Bose gases beyond the dilute limit emphasizing the role played by three-body scattering events. We demonstrate that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of 2D Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied here are universal, fully characterized by the effective 2D scattering length a(2D) (or the size of the 2D bound states) and are, in comparison to the 3D case, independent of three-body ultraviolet physics. We find, within our approach, the ratios of the contribution to the chemical potential due to three-body interactions to the one due to two-body to be 0.27 near the maximum of the chemical potential and 0.73 in the vicinity of the onset instability.

Fermi-Bose mixtures near broad interspecies Feshbach resonances.

In this Letter we study dressed bound states in Fermi-Bose mixtures near broad interspecies resonances, and implications on many-body correlations. We present the evidence for a first order phase transition between a mixture of Fermi gas and condensate, and a fully paired mixture where extended fermionic molecules occupy a single pairing channel instead of forming a molecular Fermi surface. We further investigate the effect of Fermi surface dynamics and pair fluctuations and discuss the validity of our results.

Ground state properties of cold bosonic atoms at large scattering lengths.

In this Letter, we study bosonic atoms at large scattering lengths using a variational method where the condensate amplitude is a variational parameter. We further examine momentum distribution functions, chemical potentials, the speed of sound, and spatial density profiles of cold bosonic atoms in a trap in this limit. The latter two properties turn out to bear similarities to those of Fermi gases. The estimates obtained here are applicable near Feshbach resonances, particularly when the fraction of atoms forming three-body structures is small and can be tested in future cold atom experiments.

Dynamical creation of fractionalized vortices and vortex lattices.

We investigate the dynamic creation of fractionalized half-quantum vortices in Bose-Einstein condensates of sodium atoms. Our simulations show that both individual half-quantum vortices and vortex lattices can be created in rotating optical traps when additional pulsed magnetic trapping potentials are applied. We also find that a distinct periodically modulated spin-density-wave spatial structure is always embedded in square half-quantum vortex lattices. This structure can be conveniently probed by taking absorption images of ballistically expanding cold atoms in a Stern-Gerlach field.

Uniaxial and biaxial spin nematic phases induced by quantum fluctuations.

It is shown that zero point quantum fluctuations completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin-2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry Dih4. There is a novel first-order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of 87Rb atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.