Ab-initio determination of Bose-Hubbard parameters for two ultracold atoms in an optical lattice using a three-well potential

We calculate numerically the exact energy spectrum of the six dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential which can be adapted to model the behavior of the s-wave scattering length at Feshbach resonances. By adjusting the parameters of the corresponding Bose-Hubbard (BH) Hamiltonian the deviation between the numerical energy spectrum and the BH spectrum is minimized. This defines the optimal BH parameter set which we compare to the standard parameters of the BH model. The range of validity of the BH model with these parameter sets is examined, and an improved analytical prediction of the interaction parameter is introduced. Furthermore, an extended BH model and implications due to the energy dependence of the scattering length and couplings to higher Bloch bands at a Feshbach resonance are discussed.Comment: 14 pages, 11 figures; typos and minor errors corrected, five references added, next-to-nearest neighbor hopping included in extended Bose-Hubbard mode

Influence of a tight isotropic harmonic trap on photoassociation in ultracold homonuclear alkali gases

The influence of a tight isotropic harmonic trap on photoassociation of two ultracold alkali atoms forming a homonuclear diatomic is investigated using realistic atomic interaction potentials. Confinement of the initial atom pair due to the trap leads to a uniform strong enhancement of the photoassociation rate to most, but also to a strongly suppressed rate for some final states. Thus tighter traps do not necessarily enhance the photoassociation rate. A further massive enhancement of the rate is found for strong interatomic interaction potentials. The details of this interaction play a minor role, except for large repulsive interactions for which a sharp window occurs in the photoassociation spectrum as is known from the trap-free case. A comparison with simplified models describing the atomic interaction like the pseudopotential approximation shows that they often provide reasonable estimates for the trap-induced enhancement of the photoassociation rate even if the predicted rates can be completely erroneous.Comment: 19 pages, 17 figure

Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations

A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently to treat any time-dependent external perturbation of the lattice potential up to quadratic order. Example calculations of the experimentally relevant cases of an acceleration of the lattice and the turning-on of an additional harmonic confinement are presented.Comment: 8 pages, 6 figure

Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials

A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles.Comment: 19 pages, 5 figure

Mimicking multi-channel scattering with single-channel approaches

The collision of two atoms is an intrinsic multi-channel (MC) problem as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of the open channel, are often applied in calculations. In this work the complete MC problem is solved numerically for the magnetic Feshbach resonances (MFRs) in collisions between generic ultracold 6Li and 87Rb atoms in the ground state and in the presence of a static magnetic field B. The obtained MC solutions are used to test various existing as well as presently developed SC approaches. It was found that many aspects even at short internuclear distances are qualitatively well reflected. This can be used to investigate molecular processes in the presence of an external trap or in many-body systems that can be feasibly treated only within the framework of the SC approximation. The applicability of various SC approximations is tested for a transition to the absolute vibrational ground state around an MFR. The conformance of the SC approaches is explained by the two-channel approximation for the MFR.Comment: 15 pages, 10 figure

Ultracold collisions in traps

Die ultrakalte Atom- und Molekülephysik, zu welcher man zum Beispiel bei der Bose-Einstein-Kondensation von verdünnten Gasen Zugang hat, wurde untersucht. In solchen Systemen dominieren Zwei-Körper-Stöße und ihre detaillierte Untersuchung ist eines der zentralen Themen dieser Arbeit. Diese wurden durchgeführt unter Berücksichtigung von elementaren chemischen Reaktionen, Photoassoziation und magnetischen Feshbach-Resonanzen. Weiterhin wurden Untersuchungen von Atomen in optischen Gittern durchgeführt. Die Viel-Teilchen-Systeme wurden nicht nur mit dem üblichen mean-field Ansatz behandelt, sondern auch darüber hinausgehend, um die voll korrelierte Bewegung zu simulieren.The ultracold atomic and molecular physics as it is accessible, e.g., in Bose-Einstein condensates of dilute gases was investigated. In such systems two-body collisions are dominant and their detailed study is one of the central topics of this work. They were done considering elementary chemical reactions as photoassociation, and magnetic Feshbach resonances. Additionally, studies of atoms in optical lattice sites were carried out. The many-body systems were not only considered within the usually adopted mean-field approach but also beyond that in order to simulate the fully correlated motion

Search for Scalar Diphoton Resonances in the Mass Range 65−60065-600 GeV with the ATLAS Detector in pppp Collision Data at s\sqrt{s} = 8 TeVTeV

A search for scalar particles decaying via narrow resonances into two photons in the mass range 65–600 GeV is performed using $20.3\text{}\text{}{\mathrm{fb}}^{-1}$ of $\sqrt{s}=8\text{}\text{}\mathrm{TeV}$ $pp$ collision data collected with the ATLAS detector at the Large Hadron Collider. The recently discovered Higgs boson is treated as a background. No significant evidence for an additional signal is observed. The results are presented as limits at the 95% confidence level on the production cross section of a scalar boson times branching ratio into two photons, in a fiducial volume where the reconstruction efficiency is approximately independent of the event topology. The upper limits set extend over a considerably wider mass range than previous searches

Search for Higgs and ZZ Boson Decays to J/ψγJ/\psi\gamma and Υ(nS)γ\Upsilon(nS)\gamma with the ATLAS Detector

A search for the decays of the Higgs and $Z$ bosons to $J/\psi\gamma$ and $\Upsilon(nS)\gamma$ ($n=1,2,3$) is performed with $pp$ collision data samples corresponding to integrated luminosities of up to $20.3\mathrm{fb}^{-1}$ collected at $\sqrt{s}=8\mathrm{TeV}$ with the ATLAS detector at the CERN Large Hadron Collider. No significant excess of events is observed above expected backgrounds and 95% CL upper limits are placed on the branching fractions. In the $J/\psi\gamma$ final state the limits are $1.5\times10^{-3}$ and $2.6\times10^{-6}$ for the Higgs and $Z$ bosons, respectively, while in the $\Upsilon(1S,2S,3S)\,\gamma$ final states the limits are $(1.3,1.9,1.3)\times10^{-3}$ and $(3.4,6.5,5.4)\times10^{-6}$, respectively

Search for Scalar-Charm pair production in pp collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

The results of a dedicated search for pair production of scalar partners of charm quarks are reported. The search is based on an integrated luminosity of 20.3 fb$^{-1}$ of pp collisions at $\sqrt{s}=8$ TeV recorded with the ATLAS detector at the LHC. The search is performed using events with large missing transverse momentum and at least two jets, where the two leading jets are each tagged as originating from c-quarks. Events containing isolated electrons or muons are vetoed. In an R-parity-conserving minimal supersymmetric scenario in which a single scalar-charm state is kinematically accessible, and where it decays exclusively into a charm quark and a neutralino, 95% confidence-level upper limits are obtained in the scalar-charm-neutralino mass plane such that, for neutralino masses below 200 GeV, scalar-charm masses up to 490 GeV are excluded