Daniele C. E. Bortolotti

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.

Scattering Length Instability in Dipolar Bose-Einstein Condensates

We characterize zero-temperature dipolar Bose gases under external spherical confinement as a function of the dipole strength using the essentially exact many-body diffusion Monte Carlo (DMC) technique. We show that the DMC energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly. Our calculations suggest stability diagrams and collapse mechanisms of dipolar Bose gases that differ significantly from those previously proposed in the literature.

Dipolar Bose-Einstein condensates with dipole-dependent scattering length

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in nonisotropic traps.

Bose-Fermi mixtures near an interspecies Feshbach resonance: testing a non-equilibrium approach

We test a non-equilibrium approach to study the behaviour of a Bose–Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree–Fock–Bogoliubov (HFB) equations of motion for the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose–Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that noncondensed bosons play in the Bose–Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose–Fermi mixtures is driven by three-point and higher-order correlations in the gas.

Stability of fermionic Feshbach molecules in a Bose-Fermi mixture

In the wake of successful experiments in Fermi condensates, experimental attention is broadening to study resonant interactions in degenerate Bose-Fermi mixtures. Here, we consider the properties and stability of the fermionic molecules that can be created in such a mixture near a Feshbach resonance. To do this, we consider the two-body scattering matrix in the many-body environment, and assess its complex poles. The stability properties of these molecules strongly depend on their center-of-mass motion, because they must satisfy Fermi statistics. At low center-of-mass momenta the molecules are more stable than in the absence of the environment due to Pauli-blocking effects , while at high center-of-mass momenta nontrivial many-body effects render them somewhat less stable.

Wave mechanics of a two-wire atomic beam splitter

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to nonadiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three-dimensional structure of the beam splitter, gathering quantitative information about mode mixing, splitting ratios, and reflection and transmission probabilities.

Generalized mean-field approach to a resonant Bose-Fermi mixture

We formulate a generalized mean-field theory of a mixture of fermionic and bosonic atoms, in which the fermion-boson interaction can be controlled by a Feshbach resonance. The theory correctly accounts for molecular binding energies of the molecules in the two-body limit, in contrast to the most straightforward mean-field theory. Using this theory, we discuss the equilibrium properties of fermionic molecules created from atom pairs in the gas. We also address the formation of molecules when the magnetic field is ramped across the resonance, and we present a simple Landau-Zener result for this process.