Uwe R. Fischer

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation a

We consider quasi-two-dimensional atomic or molecular Bose-Einstein condensates with both contact and dipole-dipole interactions. It is shown that as a consequence of the dimensional reduction, and within mean-field theory, the condensates do not develop unstable excitation spectra, even when the dipole-dipole interaction completely dominates the contact interaction.

Generalizing the one-component case, we demonstrate that the propagation of sound waves in two-component Bose-Einstein condensates can also be described in terms of effective sonic geometries under appropriate conditions. In comparison with the one-component case, the two-component setup offers more flexibility and several advantages. In view of these advantages, we propose an experiment in which the evolution of the inflaton field, and thereby the generation of density fluctuations in the very

The occupation of more than one single-particle state, and hence the emergence of fragmentation, is a many-body phenomenon occurring for systems of spatially confined strongly interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems in single wells. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the "acoustic geometry" that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity Gamma/2pi(cb), where Gamma is the vortex circulation, c the speed o

By means of an adapted mean-field expansion for large fillings $n⪢1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum

We investigate the level population statistics and degree of coherence encoded in the single-particle density matrix of harmonically trapped low-dimensional [quasi-one-dimensional (quasi-1D) or quasi-two-dimensional (quasi-2D)] Bose gases with repulsive contact interactions. Using a variational analysis, we derive fragmentation of the condensate in the weakly confining directions into two (quasi-1D) and three (quasi-2D) mutually incoherent macroscopic pieces, upon increasing a dimensionless inte

We derive an inequality governing "long-range" order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.

We consider ultracold quantum gases of scalar bosons residing in a coupling strength-density regime in which they constitute a twofold fragmented condensate trapped in a single well. It is shown that the corresponding quantum states are, in the appropriate Fock space basis, identical to the photon cat states familiar in quantum optics, which correspond to superpositions of coherent states of the light field with a phase difference of π. In marked distinction to photon cat states, however, the ve

We consider phase coherence collapse and revival in deep optical lattices, and calculate within the Bose-Hubbard model the revival amplitude damping incurred by a finite tunneling coupling of the lattice wells (after sweeping from the superfluid to the Mott phase). Deriving scaling laws for the corresponding decay of first-order coherence revival in terms of filling factor, final lattice depth, and number of tunneling coupling partners, we estimate whether revival damping related to tunneling be

Recent developments in simulating fundamental quantum field theoretical effects in the kinematical context of analogue gravity are reviewed. Specifically, it is argued that a curved spacetime generalization of the Unruh–Davies effect — the Gibbons–Hawking effect in the de Sitter spacetime of inflationary cosmological models — can be implemented and verified in an ultracold gas of bosonic atoms.

The possibility of an atomic detection of gravitational waves on earth is considered. The combination of extremely high lifetimes and resulting small radiative transition probabilities with rapidly growing interaction strength for Rydberg atoms having principal quantum numbers in a region $10^4\ldots 10^5$ might result in transition probabilities which are high enough to open up such a possibility. Transition probabilities and absorption cross sections are calculated as a function of the relevan

We study an atomic quantum dot representing a single hyperfine ``impurity'' atom which is coherently coupled to two well-separated Bose-Einstein condensates, in the limit when the coupling between the dot and the condensates dominates the intercondensate tunneling coupling. It is demonstrated that the quantum dot by itself can induce large-amplitude Josephson-like oscillations of the particle imbalance between the condensates, which display a two-frequency behavior. For noninteracting condensate

We discuss the feasibility of quantum Hall states of vortices in trapped low-density two-dimensional Bose gases with large particle interactions. For interaction strengths larger than a critical dimensionless 2D coupling constant $g_c \approx 0.6$, upon increasing the rotation frequency, the system is shown to spatially separate into vortex lattice and melted vortex lattice (vortex liquid) phases. At a first critical frequency, the lattice melts completely, and strongly correlated vortex and par