Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose–Einstein Condensation (BEC) in the Infinite-Range-Hopping Bose–Hubbard model with repulsive on-site particle interaction in the presence of an ergodic random single-site external potential with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. We observe new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at certain fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the suppression of BEC at integer densities observed in Bru and Dorlas (J. Stat. Phys. 113:177–195, 2003) in the absence of a random potential, can disappear as the disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of the density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.     

Tunneling of a Dipolar Bose–Einstein Condensate in an Optical Lattice

We have studied the tunneling and fluctuations of a dipolar Bose–Einstein condensate in an optical lattice, it is found that there exist the tunneling and fluctuations between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l+1, and that l and l−1, in this case the fluctuations are a constant, and the magnetic soliton appears.     

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.     

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     

Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.     

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     

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose–Einstein condensation are discussed.     

Partial coherence in the core–halo picture of Bose–Einstein n-particle correlations

We study the influence of a possible coherent component in the boson source on the two-, three- and n-particle correlation functions in a generalized core–halo-type boson-emitting source. In particular, a simple formula is presented for the strength of the n-particle correlation functions for such systems. Graph rules are obtained to evaluate the correlation functions of arbitrarily high order. The importance of an experimental determination of the 4-th and 5-th order Bose–Einstein correlation function is emphasized. Received: 18 December 1998 / Published online: 20 May 1999     

Examples of Bosonic de Finetti States over Finite Dimensional Hilbert Spaces

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose–Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose–Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number     

Collisional effects on the collective laser cooling . of trapped bosonic gases

We analyse the effects of atom–atom collisions on a collective laser cooling scheme. We derive a quantum master equation which describes the laser cooling in presence of atom–atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose–Einstein distribution describing collisionally induced equilibrium, to a distribution with an effective zero temperature. We analyse also the effects of atom–atom collisions on the cooling into an excited state of the trap. Received: 18 June 1999 / Revised version: 24 September 1999 / Published online: 10 November 1999     

Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs

We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross–Pitaevskii functional, describing a Bose–Einstein condensate of fermion pairs.     

Phase fluctuations in Bose–Einstein condensates

We demonstrate the existence of phase fluctuations in elongated Bose–Einstein condensates (BECs) and study the dependence of these fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase-coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed. Received: 13 July 2001 / Revised version: 28 September 2001 / Published online: 23 November 2001     

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     

Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons. PACS 03.75.Lm; 71.36.+c; 42.50.Fx     

Gibbs Distributions for Random Partitions Generated by a Fragmentation Process

In this paper we study random partitions of {1,…,n} where every cluster of size j can be in any of w _j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among such partitions with k clusters. We provide conditions on the weight sequence w allowing construction of a partition valued random process where at step k the state has the Gibbs (n,k,w) distribution, so the partition is subject to irreversible fragmentation as time evolves. For a particular one-parameter family of weight sequences w _j , the time-reversed process is the discrete Marcus–Lushnikov coalescent process with affine collision rate K _i,j = a+b(i+j) for some real numbers a and b. Under further restrictions on a and b, the fragmentation process can be realized by conditioning a Galton–Watson tree with suitable offspring distribution to have n nodes, and cutting the edges of this tree by random sampling of edges without replacement, to partition the tree into a collection of subtrees. Suitable offspring distributions include the binomial, negative binomial and Poisson distributions. Research supported in part by N.S.F. Grant DMS-0405779.     

Characterization and control of phase fluctuations in elongated Bose–Einstein condensates

Quasi-one-dimensional Bose–Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time of flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that, under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. We also discuss our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BECs in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations. Received: 17 August 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +49-511/762-3023, E-mail: Helge.Kreutzmann@ITP.uni-hannover.de     

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