Related papers: 3/2-Body Correlations and Coherence in Bose-Einste…
Few-body correlations often express the distinguishing characteristic features of a many-body system. This thesis studies such correlations within dilute Bose-Einstein condensates in the case of arbitrary negative s-wave scattering length.…
The Bogoliubov theory of weakly interacting bosons is generalized to Bose-Einstein condensates with internal degrees of freedom so that a single effective Hamiltonian produces various many-body ground states or metastable spin domains and…
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
We experimentally and theoretically investigate the lowest-lying axial excitation of an atomic Bose-Einstein condensate in a cylindrical box trap. By tuning the atomic density, we observe how the nature of the mode changes from a…
We describe a model of dynamic Bose-Einstein condensates near a Feshbach resonance that is computationally feasible under assumptions of spherical or cylindrical symmetry. Simulations in spherical symmetry approximate the experimentally…
The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which…
We study the time evolution of weakly interacting Bose gases on a three-dimensional torus of arbitrary volume. The coupling constant is supposed to be inversely proportional to the density, which is considered to be large and independent of…
We propose and demonstrate the appearance of an effective attractive three-body interaction in coherently-driven two-component Bose Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body…
Bose-Einstein condensates with tunable interatomic interactions have been studied intensely in recent experiments. The investigation of the collapse of a condensate following a sudden change in the nature of the interaction from repulsive…
We report on some recent results concerning the dynamics of Bose-Einstein condensates, obtained in a series of joint papers with L. Erdos and H.-T. Yau. Starting from many body quantum dynamics, we present a rigorous derivation of a cubic…
In this Letter, we discuss the effects of $p$-wave attractive interaction in a spin-$1/2$ Bose gas. With a repulsive $s$-wave background interaction, we show that for weak $p$-wave attraction, one obtains a standard Bose-Einstein condensate…
The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a…
This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range…
It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. An asymptotic expansion of this wave function at large interparticle distances is…
We describe interacting bosons at low temperature in spatially correlated random potentials. By a Bogoliubov expansion around the deformed mean-field condensate, the fundamental Hamiltonian for elementary excitations is derived, achieving…
We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the…
We discuss the dynamics of an open two-mode Bose-Hubbard system subject to phase noise and particle dissipation. Starting from the full many-body dynamics described by a master equation the mean-field limit is derived resulting in an…
We introduce a family of correlated trial wave functions for the $N$-particle ground state of an interacting Bose gas in a harmonic trap. For large $N$, the correlations lead to a relative energy decrease of a fraction $3/5N$, compared to…
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the…