Observation Of Bose-Einstein Condensation Research Articles

Bose-Hubbard model on polyhedral graphs

Ever since the first observation of Bose-Einstein condensation in the nineties, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum mechanics. Ultracold bosonic atoms loaded in an optical lattice are usually described by the Bose-Hubbard model or a variant of it. In addition to the common insulating and superfluid phases, other phases (like density waves and supersolids) may show up in the presence of a short-range interparticle repulsion and also depending on the geometry of the lattice. We herein explore this possibility, using the graph of a convex polyhedron as "lattice" and playing with the coordination of nodes to promote the wanted finite-size ordering. To accomplish the job we employ the method of decoupling approximation, whose efficacy is tested in one case against exact diagonalization. We report zero-temperature results for two Catalan solids, the tetrakis hexahedron and the pentakis dodecahedron, for which a thorough ground-state analysis reveals the existence of insulating "phases" with polyhedral order and a widely extended supersolid region. The key to this outcome is the unbalance in coordination between inequivalent nodes of the graph. The predicted phases can be probed in systems of ultracold atoms using programmable holographic optical tweezers.

Quantum liquids

This article is dedicated to Roger A Cowley and his seminal contributions to our understanding of quantum liquids, both liquid 4He and 3He. Roger Cowley’s neutron scattering measurements of the collective and independent particle response of liquid 4He were made at Chalk River Laboratories in 1965–74 chiefly with A D B (Dave) Woods. They measured the phonon–roton (P–R) mode energy, intensity and width with new precision. Particularly, they extended the measurements to higher wave vector and identified both collective and single particle response regimes. They showed that the P–R mode terminated at a finite energy as predicted by Pitaeskii rather than continuing as predicted by Feynman and Feynman and Cohen. They determined both the single P–R mode and multimode contributions to the dynamics. They made direct comparison with theory which Roger understood well. They observed the Bose–Einstein condensate (BEC) fraction in liquid 4He for the first time. This appears to be the first ever observation of BEC in any Bose gas or liquid. Roger Cowley’s pioneering measurements of the density excitations of liquid 3He were made at the Institut Laue Langevin (ILL) in the period 1973–80. Roger, Reinhard Scherm, W G (Bill) Stirling and collaborators showed for the first time that the density response of this highly neutron absorbing liquid could indeed be observed with neutrons. They documented with others the dynamic response as a function of temperature and pressure stimulating extensive theoretical and experimental interest that continues today.

Collapse of the EPR fine structure of a one-dimensional array of weakly interacting binuclear units: A dimensional quantum phase transition

Binuclear (also called dimeric) compounds with pairs of antiferromagnetically coupled spins \textonehalf{}, ${\mathbf{S}}_{\mathbf{1}}$ and ${\mathbf{S}}_{\mathbf{2}}$ (${H}_{\mathrm{ex}}$ = \ensuremath{-}${J}_{0}$ ${\mathbf{S}}_{\mathbf{1}}$.S${}_{\mathbf{2}}$, with ${J}_{0}<0$ for antiferromagnets), have been around for \ensuremath{\sim}60 years, providing roots to the field of molecular magnetism. In addition, as reported in recent years, weak interactions between binuclear units in a crystalline network give rise to interesting systems of interacting bosons having an energy gap, which are important in the study of quantum phenomena in many body systems coupled by stochastic distributions of interactions. Binuclear compounds have gained new relevance in the last decade with the observation of Bose-Einstein condensation. In this work, we use electron paramagnetic resonance (EPR) to study the role of weak inter-binuclear exchange couplings J' (|J'| $\ensuremath{\ll}|{J}_{0}|$) in the spectra, elementary excitations, and spin dynamics of a one-dimensional (1-D) array of antiferromagnetic (AFM) binuclear units in the hybrid (organic-inorganic) Cu${}^{\mathit{II}}$ compound [Cu(CH${}_{3}$COO)(phen)(H${}_{2}$O)]${}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}(NO${}_{3}$)${}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}4H${}_{2}$O. In this material, the acetate (CH${}_{3}$COO)${}^{\ensuremath{-}}$ anion supports the intra-binuclear exchange coupling ${J}_{0}$, and the stacking of the (phen) = 1,10-phenanthroline rings of neighbor units supports the inter-binuclear interactions J\ensuremath{'}, giving rise to well-isolated chains. This has advantages over other binuclear compounds studied previously because magnetically equal units are arranged in a 1-D spatial arrangement along the direction of their symmetry axis, simplifying the analysis of the data and allowing a simpler treatment. In addition, single crystals of good quality allow detailed EPR experiments.EPR spectra were collected at \ensuremath{\sim}33.8 and \ensuremath{\sim}9.4--9.8 GHz in oriented single crystals at room temperature and in powder samples at temperatures (T) between 10 and 300 K. By varying the energy levels of the binuclear units with the magnetic field orientation, or changing the population of the excited triplet state with temperature and, consequently, the effective coupling between units, we observe in single-crystal samples sudden merges of the fine structure peaks, accompanied by a large narrowing, when the inter-binuclear coupling becomes larger than the splitting of the triplet state. In addition, and because of this collapse of the fine structure peaks, the spectra of powder samples display a strong and unexpected central peak that decreases in intensity with decreasing temperature, as it occurs with the binuclear signals. We first discuss the dimensional quantum phase transition indicated by the spectral changes using Anderson-Kubo's theory of exchange narrowing. The data allow evaluation of the binuclear exchange coupling ${J}_{0}$ = (\ensuremath{-}74 \ifmmode\pm\else\textpm\fi{} 3) cm${}^{\ensuremath{-}1}$, and the interactions between neighbor binuclear units |J\ensuremath{'}| = (0.04 \ifmmode\pm\else\textpm\fi{} 0.01) cm${}^{\ensuremath{-}1}$. We also consider the magnetic excitations (triplet excitons or triplons) arising from the inter-binuclear couplings, and introduce a model explaining qualitatively the observed collapse and narrowing of the EPR spectra in terms of these excitons. We analyze the role of temperature in the inter-binuclear interactions and the exchange correlation times of the binuclear systems and compare our results with those in binuclear compounds in which Bose-Einstein condensation occurs.

Prediction of Feshbach resonances in collisions of ultracold rubidium atoms

The observation of Bose-Einstein condensation ~BEC! in dilute ultracold gas samples of rubidium @1#, lithium @2#, and sodium atoms @3# has made it possible to study this macroscopic quantum phenomenon in its pure form without complicated modifications due to strong interactions. A variety of experiments has been proposed or already carried out, fascinating examples being the observation of collective shape oscillations and the observation of the relative phase of two Bose-Einstein condensates @4,5#. A rich variety of other experiments would come into reach if one could alter arbitrarily, possibly even in real time, the sign and magnitude of the atom-atom scattering length a. The scattering length occurs as the coefficient of the condensate self-interaction term in the condensate wave equation and has a profound effect on the stability and other properties of the condensate. An opportunity to change this parameter would arise if it were possible to tune the scattering length by means of external fields, i.e., either a static magnetic field @6# or a timedependent optical @7# or rf field @8#.

Renormalization group study of Bose-Einstein condensation

Due to the observation of Bose-Einstein condensation in dilute atomic87Rb,7Li, and23Na vapors last year, there is currently a great interest in the degenerate dilute Bose gas. Existing theoretical approaches using basically non-interacting Bogoliubov quasi-particles do not predict the deviation from the ideal gas critical temperature claimed to be observed in the experiments. Improving the theoretical analysis by including interactions between the Bogoliubov quasi-particles is however not trivial in the degenerate regime due to infrared divergencies showing up in regular perturbation theory. Motivated by these aspects we present a renormalization group study of the weakly-interacting homogeneous Bose gas.