Bose–Einstein condensates in magnetic waveguides

In this article, we describe an experimental system for generating Bose–Einstein condensates and controlling the shape and motion of a condensate by using miniaturised magnetic potentials. In particular, we describe the magnetic trap setup, the vacuum system, the use of dispenser sources for loading a high number of atoms into the magneto-optical trap, the magnetic transfer of atoms into the microtrap, and the experimental cycle for generating Bose–Einstein condensates. We present first results on outcoupling of condensates into a magnetic waveguide and discuss influences of the trap surface on the ultra-cold ensembles. Received: 21 August 2002 / Revised version: 10 December 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-7071/295-829, E-mail: fortagh@pit.uni-tuebingen.de     

Fluctuations of the Maximal Particle Energy of the Quantum Ideal Gas and Random Partitions

We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so-called generalized Bose–Einstein statistics) this distribution is the well-known Gumbel distribution which usually appears in the context of indepedent random variables. In particular, it means that the (properly rescaled) maximal energy of an individual particle in the grand canonical ensemble of the d-dimensional quantum ideal gas has the Gumbel distribution in the limit. We also apply our result to find the fluctuations of the height of a random 3D Young diagram (plane partition) and investigate the order statistics of random partitions under generalized Bose–Einstein statistics.     

The Equilibrium States for a Model with Two Kinds of Bose Condensation

We study the equilibrium Gibbs states for a Boson gas model, defined by Bru and Zagrebnov, which has two phase transitions of the Bose condensation type. The two phase transitions correspond to two distinct mechanisms by which these condensations can occur. The first (non-conventional) Bose condensation is mediated by a zero-mode interaction term in the Hamiltonian. The second is a transition due to saturation quite similar to the conventional Bose–Einstein (BE) condensation in the ideal Bose gas. Due to repulsive interaction in non-zero modes the model manifests a generalized type III; i.e., non-extensive BE condensation. Our main result is that, as in the ideal Bose gas, the conventional condensation is accompanied by a loss of strong equivalence of the canonical and grand canonical ensembles whereas the non-conventional one, due to the interaction, does not break the equivalence of ensembles, at least not on the level of the gauge invariant states. It is also interesting to note that the type of (generalized) condensate, I, II, or III (in the terminology of van den Berg, Lewis, and Pulé), has no effect on the equivalence of ensembles. These results are proved by computing the generating functional of the cyclic representation of the Canonical Commutation Relation (CCR) for the corresponding equilibrium Gibbs states.     

Analogue model for an expanding universe

Over the last few years numerous papers concerning analogue models of (and for) gravity have been published. It has been shown that the dynamical equations for several condensed matter systems, (e.g., simple fluids, superfluids, Bose–Einstein condensates with a sink or a vortex) permit perturbations that are governed by the same type of wave equation as light in a curved spacetime—the curved-space d'Alembertian equation. More recently, several papers have been released which use analogue models to simulate the expanding universe. In this article the de Sitter universe will be simulated using a freely expanding three-dimensional Bose–Einstein condensate with spherical symmetry. Initially the condensate is in a harmonic trap, which is then suddenly switched off. At the same time a small perturbation is injected in the center of the condensate cloud. The motion of this perturbation in the expanding condensate will be discussed, and (after some transformations) the similarity of this system to an expanding universe will be exhibited. Finally, we briefly discuss questions of experimental observability of these effects. Presented at the 4th Australasian conference on General Relativity and Cosmology, Monash University, Melbourne, 7–9 January 2004     

Bose–Einstein condensation in the three-sphere and in the infinite slab: Analytical results

We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit.     

Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.     

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schr?dinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions. Received: 24 November 1999 / Published online: 17 March 2000     

Magnetic resonance imaging of Bose–Einstein condensates

As a new method for measuring the spatial distribution of Bose–Einstein condensates, the magnetic resonance imaging (MRI) method is proposed and studied in detail. The basic concepts, the resolution limit and the formalism of the MRI method are presented. It is expected that a resolution higher than that in optical imaging methods can be obtained by using the MRI method. Results of simulation of expected MRI signals for Bose–Einstein condensates containing dark solitons are also presented. Received: 27 September 2001 / Revised version: 24 October 2001 / Published online: 17 January 2002     

Phonon Superfluids in Sets of Trapped Ions

We show that transverse phonons in a set of trapped ions under the action of lasers are described by an interacting boson model whose parameters can be externally adjusted. If the radial trapping frequency is large enough, the system is described by a Bose–Hubbard model, in which hopping of the phonons between different ions is provided by the Coulomb interaction. On the other hand, the non-linear terms in the interaction of the ions with a standing-wave provide us with the phonon–phonon interaction. We investigate the possibility of observing several quantum many—body phenomena, including (quasi)Bose–Einstein Condensation as well as a superfluid-Mott insulator quantum phase transition.     

Interferencing in Coupled Bose–Einstein Condensates

We consider an exactly soluble model of two Bose–Einstein condensates with a Josephson-type of coupling. Its equilibrium states are explicitly found showing condensation and spontaneously broken gauge symmetry. It is proved that the total number and total phase fluctuation operators, as well as the relative number and relative current fluctuation operators form both a quantum canonical pair. The exact relation between the relative current and phase fluctuation operators is established. Also the dynamics of these operators is solved showing the collapse and revival phenomenon.     

Flat rotation curves in scalar field galaxy halos

We start with a model where the dark matter is of scalar field nature, which condensates and form the dark halos of galaxies. In this work we study Bose–Einstein condensates (BEC) where the scalar field particles are in many different states, and not only in the ground state, as in a realistic BEC. We find that this model is in better agreement with the rotation curves of galaxies than previous models with scalar field dark matter.     

Quantum Entanglement of Many Particles in Spinor Bose–Einstein Condensates

We present a theoretical treatment of the proposal for creating maximally entangled states of many particles in spin-1 Bose–Einstein condensates (BECs) by applying a single atom Raman transition [You. L. (2003). Physical Review Letters 90, 030402]. It is shown that the three-mode model suggested by You can be further reduced to an efficient two-mode one by a simple method. We also suggest a scheme for generating the atom-atom continuous-variable entangled states in this system. PACS number: 03.75.Gg, 03.75.Mn, 05.30.JP, 03.75.Hh     

Bragg spectroscopy and superradiant Rayleigh scattering in a Bose–Einstein condensate

Two sets of studies concerning the interaction of off-resonant light with a sodium Bose–Einstein condensate are described. In the first set, properties of a Bose–Einstein condensate were studied using Bragg spectroscopy. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum distribution of the condensate. Depending on the momentum transfer, both the phonon regime as well as the free-particle regime could be explored. In the second set of studies, the cigar-shaped condensate was exposed to a single off-resonant laser beam and highly directional scattering of light and atoms was observed. This collective light scattering was caused by the long coherence time of the quasi-particles in the condensate and resulted in a new form of matter wave amplification. Received: 26 June 1999 / Revised version: 21 September 1999 / Published online: 10 November 1999     

Soliton complexes and flat-top nonlinear modes in optical lattices

We describe a continuous analog of the quasirectangular flat-top nonlinear modes earlier found for discrete nonlinear models. We show that these novel nonlinear modes can be understood as multi-soliton complexes with either in-phase or out-of-phase neighboring solitons trapped by the periodic potential of the lattice. We demonstrate a link between the flat-top states and the truncated nonlinear Bloch waves, and discuss how these nonlinear localized modes can be monitored experimentally in photonics and Bose–Einstein condensates. PACS 42.65.Tg; 42.65.Jx; 03.75.Lm     

Kinetic Relaxation Models for Energy Transport

Kinetic equations with relaxation collision kernels are considered under the basic assumption of two collision invariants, namely mass and energy. The collision kernels are of BGK-type with a general local Gibbs state, which may be quite different from the Gaussian. By the use of the diffusive length/time scales, energy transport systems consisting of two parabolic equations with the position density and the energy density as unknowns are derived on a formal level. The H theorem for the kinetic model is presented, and the entropy for the energy transport systems, which is inherited from the kinetic model, is derived. The energy transport systems for specific examples of the global Gibbs state, such as a power law with negative exponent, a cut-off power law with positive exponent, the Maxwellian, Bose–Einstein, and Fermi–Dirac distributions, arepresented. MSC classification (2000): Primary: 82C40, 35B40; Secondary: 35K55, 45K05, 82D05, 85A05x     

Optimized loading of an optical dipole trap for the production of chromium BECs

We report on a strategy to maximize the number of chromium atoms transferred from a magneto-optical trap into an optical trap through accumulation in metastable states via strong optical pumping. We analyse how the number of atoms in a chromium Bose–Einstein condensate can be raised by a proper handling of the metastable state populations. Four laser diodes have been implemented to address the four levels that are populated during the MOT phase. The individual importance of each state is specified. To stabilize two of our laser diode, we have developed a simple ultrastable passive reference cavity whose long term stability is better than 1 MHz.     

Pion condensation in a dense neutrino gas

We argue that using an equilibrated gas of neutrinos it is possible to probe the phase diagram of QCD for finite isospin and small baryon chemical potentials. We discuss this region of the phase diagram in detail and demonstrate that for large enough neutrino densities a Bose–Einstein condensate of positively charged pions arises. Moreover, we show that for non-zero neutrino density the degeneracy in the lifetimes and masses of the charged pions is lifted.     

Nonexponential decay of Bose–Einstein condensates: a numerical study based on the complex scaling method

We study the decay dynamics of an interacting Bose–Einstein condensate in the presence of a metastable trapping potential from which the condensate can escape via tunneling through finite barriers. The time-dependent decay process is reproduced by means of the instantaneous decay rates of the condensate at a given population of the quasi-bound state, which are calculated with the method of complex scaling. Both for the case of a double-barrier potential as well as for the case of a tilted periodic potential, we find pronounced deviations from a monoexponential decay behavior, which would generally be expected in the absence of the atom–atom interaction. PACS 03.75.Lm; 03.65.Xp; 03.75.Kk