Charged bosons in a random potential

It is shown that the interaction of bosons in a random potential in certain cases provides extended states.     

Condensation of N interacting bosons: a hybrid approach to condensate fluctuations

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.     

Two interacting particles in a random potential

We study the scaling of the localization length of two interacting bosons in a one-dimensional random lattice with the single particle localization length. We consider the short-range interaction assuming that the particles interact when located both on the same site. We discuss several regimes, among them one interesting weak Fock space disorder regime. In this regime we obtain a weak logarithmic scaling law. Numerical benchmark data support the absence of any strong enhancement of the two particle localization length.     

Inelastic multiple scattering of interacting bosons in weak random potentials

We develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. We show how collisional energy transfer between the bosons induces the thermalization of the inelastic single-particle current which, after only a few collision events, dominates over the elastic contribution described by the Gross-Pitaevskii ansatz.     

Superfluid-insulator transition in a moving system of interacting bosons

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.     

Self-consistent Green's function theory for interacting electrons in a random potential

A new set of self-consistent equations is proposed for the calculation of the disorder and Coulomb contributions to the electron self-energy and the electron-hole interaction in a many-electron system in the presence of a site-diagonal random potential. The treatment of the disorder is along the lines of the coherent-potential approximation. An explicit expression for the Coulomb self-energy is derived within the time-dependent screened Hartree-Fock approximation. Some possible applications of the formalism to the formation of a Coulomb gap in a doped semiconductor and to electron-hole interaction effects in the optical spectra of alloy semiconductor systems are discussed.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Polarization of interacting bosons with spin

We prove that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized. Generally, this state is degenerate with other states, but one can specify the exact degeneracy. For T>0, the magnetization and zero-field susceptibility exceed that of a pure paramagnet. The results are relevant to experimental work on triplet superconductivity and condensation of atoms with spin. They eliminate the possibility, raised in some theoretical speculations, that the ground state or positive temperature state might be antiferromagnetic.     

Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential

We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with an amplitude that is small compared to the typical energy per atom, dominated by the interaction energy. Numerical calculations reproduce our observations well. We propose a scenario for disorder-induced trapping of the condensate in agreement with our findings.     

Shell model description of interacting bosons

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.     

Ground-state and quenched-state properties of a one-dimensional interacting lattice gas in a random potential

We determine the zero-temperature properties of a one-dimensional lattice gas of particles that interact via a nearest neighbor exclusion potential and are subject to a random external field. The model is a special limiting case of the random field Ising chain. We calculate (1) the energy and density of the ground state as well as the local energy-density correlation and (2) the pair correlation function. The latter calculation gives access to all higher order correlations. The structure factor is shown to be a squared Lorentzian. We also compare the ground state to the quenched state obtained by sequentially filling the lowest available energy levels.     

Mixtures of strongly interacting bosons in optical lattices

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of 41K induces a significant loss of coherence in 87Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.     

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter g, we construct a large, explicit family of quantum states with energies of the form $E_0+g{E}_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. Any superposition of these states evolves periodically with a period of $8\pi /g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.     

Entanglement of two interacting bosons in a two-dimensional isotropic harmonic trap

We compute the pair entanglement between two interacting bosons in a two-dimensional (2D) isotropic harmonic trap. The interaction potential is modelled by a 2D regularized pseudopotential. By analytically decomposing the wave function into the single particle basis, we show the dependency of the pair entanglement on the scattering length. Our results turn out to be in good agreements with earlier results using a quasi-2D geometry.     

An intrinsic spin for interacting bosons

The addition, to the usual set of T=1 bosons, of s and d bosons with T=0 and an intrinsic spin of S=1 leads to a version of the IBM which incorporates the Wigner supermultiplet symmetry.