TY - JOUR A1 - Weiss, Christoph A1 - Wilkens, Martin T1 - Particle number counting statistics in ideal Bose gases N2 - We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence. Y1 - 1997 UR - http://epubs.osa.org/oearchive/source/2372.htm ER - TY - JOUR A1 - Wilkens, Martin A1 - Weiss, Christoph T1 - Particle number fluctuations in an ideal Bose gas N2 - We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from theenvironment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of thegrand- canonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau-Ginzburg functional which - despite the non- interacting nature of the system - displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is base on the grand-canonical ensemble. We show that for an ideal Bose gas neither are the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir. Y1 - 1997 ER - TY - JOUR A1 - Power, W. L. A1 - Pfau, T. A1 - Wilkens, Martin T1 - Loading atoms into a surface trap: simulations of an experimental scheme N2 - We present simulations of a scheme for the continuous loading of pre-cooled atoms into the lowest energy states of an optical surface trap. The atoms fall under gravity towards the surface of a prism where evanescent waves are used to decelerate the falling atoms and to pump them into a trapped state in an optical standing wave. The simulations are performed using the Monte-Carlo wavefunction technique and are designed to represent the proposed experimental scheme as closely as is practically possible. The probabilities of atoms being pumped into the different trapped states have been calculated as a function of the properties of the braking and pumping fields. The effective temperature of the final distribution of the atoms is calculated in order to find the change in phase-space density. Y1 - 1997 ER - TY - JOUR A1 - Öhberg, P. A1 - Surkov, E. L. A1 - Tittonen, I. A1 - Stenholm, Stig A1 - Wilkens, Martin A1 - Shlyapnikov, G. V. T1 - Low-energy elementary excitations of a trapped Bose-condensed gas N2 - We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation Y1 - 1997 ER - TY - JOUR A1 - Javanainen, Juha A1 - Wilkens, Martin T1 - Phase and Phase Diffusion of a Split Bose-Einstein Condensate N2 - We analyze theoretically an experiment in which a trapped Bose-Einstein condensate is cut in half, and the parts are subsequently allowed to interfere. If the delay cutting and atom detection is small, the interference pattern of the two halves of the condensate is the same in every experiment. However, for longer delays the spatial phase of the interference shows random fluctuations from one experiment to the other. This phase diffusion is characterized quantitatively. Y1 - 1997 ER - TY - JOUR A1 - Stenholm, Stig A1 - Wilkens, Martin T1 - Jumps in quantum theory N2 - In this paper we review the discussion about quantum jumps. We sketch the historical background before we present the recent revival of this problem originating in the field of atomic investigations. We present both the theoretical methods and their motivations, the relevance to experiments and an attempt at a preliminary discussion of the role of these developments in our fundamental understanding of quantum physics. Y1 - 1997 ER - TY - JOUR A1 - Power, W. L. A1 - Tan, S. M. A1 - Wilkens, Martin T1 - A scheme for the simultaneous measurement of atomic position and momentum N2 - We propose an optical scheme for the simultaneous measurement of the position and momentum of a single atom. The scheme involves the coupling of the atom of two light fields with different spatical and polarization characteristics. The proposed technique is closely related to the Arthurs-Kelly measurement scheme; the principal difference is that in the present case the electromagnetic fields rather than from shifts in the position of a pointer. Y1 - 1997 ER - TY - JOUR A1 - Janicke, U. A1 - Wilkens, Martin T1 - Atomic matter wave amplification by optical pumping N2 - The atom laser (or `Boser') is a device that delivers a beam of atomic de Broglie waves with high coherence and monochromaticity. In this review, we concentrate on an all-optical scheme of an atom laser that is based on optical pumping. The model is first presented in terms of kinetic equations, and its relation to the ordinary laser and the Bose-Einstein condensation is discussed. We then derive a master equation for the quantum statistics dynamics of the atom laser. Neglecting photon reabsorption processes, the master equation is solved and the counting statistics is computed. Finally, the effects of the inelastic reabsorption processes are investigated for the particular case of two atoms. It is shown that the onset of atom-lasing is suppressed in large resonators, but may be achieved in small and/or low-dimensional resonators. Y1 - 1998 ER - TY - JOUR A1 - Busch, Thomas A1 - Englert, Bertold-Georg A1 - Rzazewski, Kazimierz A1 - Wilkens, Martin T1 - Two cold atoms in a harmonic trap N2 - Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time-independent Schrödinger equation under the assumption of a parabolic, spherically symmetric trapping potential. Y1 - 1998 ER - TY - JOUR A1 - Leonhardt, Ulf A1 - Wilkens, Martin T1 - Aharonov-Bohm scattering of neutral atoms N2 - We study the scattering of quantum particles in the presence of an Aharonov-Bohm vortex and in an arbitrary cylindrically symmetric potential. In particular we address the scattering of atoms carrying dipole moments induced by an electrically charged wire and a homogeneous magnetic field. We argue that, despite the strong attraction of the wire, an Aharoniv-Bohm effect will be visible. Y1 - 1998 ER - TY - JOUR A1 - Wilkens, Martin T1 - Quantum Phase of a Moving Dipole N2 - It is shown that a neutral particle with an electric dipole moment which moves in a magnetic field acquires a topological phase. This phase may be observed in atom or molecular interferometry. Y1 - 1998 ER - TY - JOUR A1 - Javanainen, Juha A1 - Wilkens, Martin T1 - Phase and phase diffusion of a split Bose-Einstein condensate Y1 - 1998 ER - TY - JOUR A1 - Navez, Patrick A1 - Wilkens, Martin T1 - Single molecule in a Bose-Einstein condensate N2 - We study a model describing a rotating linear rigid molicule interacting with a Bose-Einstein condensate. A generalization of the Landau criterion is established and gives the limit for which the molecule moves translationally and rotationally into the condensate without any friction. In particular, we show that the rotational energy released by the molecule is large enough to eject one atom out of the condensate. The detection of such an atom provides a direct measurement of the low-energy cross section of the scattering with the rotating molecule. Finally, increases of inertia and of centrifugal distortion of the molecule due to the surrounding condensate are estimated and compared with the experimental data obtained for a He4 droplet. Y1 - 1999 ER - TY - JOUR A1 - Idziaszek, Zbigniew A1 - Gajda, M. A1 - Navez, Patrick A1 - Wilkens, Martin A1 - Rzazewski, Kazimierz T1 - Fluctuation of the Weakly Interacting Bose-Einstein Condensate N2 - We consider the role of weak interaction on the fluctuations of the number of condensed atoms within canonical and microanonical ensembles. Unlike the correspinding case of the ideal gas this is not a clean, well-defined problem of mathematical physics. Two related reasons are the following: there is no unique way of defining the condensate fraction of the interacting system and no exact energy levels of the interacting system are known. Y1 - 1999 ER - TY - JOUR A1 - Idziaszek, Zbigniew A1 - Wilkens, Martin T1 - Scattering of atoms on the Bose-Einstein condensate N2 - We investigate the scattering of slowly moving atoms on the Bose-Einstein condensate. The condensate excitations are described by Bogolyubov-de Gennes equatins. We derive the analytic expressions for the differential cross section for both elastic and ineladtic channels. For the elastic channel we obtain analytic results for total cross sections, and discuss their scaling with the number of condensed atoms. For inelastic channels we present numerical results for the total cross section. Y1 - 1999 ER - TY - JOUR A1 - Illuminati, Fabrizio A1 - Navez, Patrick A1 - Wilkens, Martin T1 - Thermodynamic identities and paricle number fluctuations in weakly interacting Bose-Einstein condensates N2 - We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean- square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of auxiliary partition functions for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, in contrast wiht the anomalous scaling behaviour V3/ 4 of the fluctuations in the ideal Bose gas. Y1 - 1999 ER - TY - JOUR A1 - Eisert, Jens A1 - Wilkens, Martin A1 - Lewenstein, Maciej T1 - Quantum Games and Quantum Strategies N2 - We investigate the quantization of nonzero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy. Y1 - 1999 ER - TY - JOUR A1 - Felbinger, Timo A1 - Wilkens, Martin T1 - Stochastic Wave-function Simulation of Two-time Correlation Functions N2 - We propose an algorithm for the numerical simulation of two-time correlation functions by means of stochastic wave function. As a first application, we investigate the two-time correlation function of a nonlinear optical parametric oscillator. Y1 - 1999 ER - TY - JOUR A1 - Henkel, Carsten A1 - Wilkens, Martin T1 - Heating of trapped atoms near thermal surfaces N2 - We study the electromagnetic coupling and concomitant heating of a particle in a miniaturized trap close to a solid surface. Two dominant heating mechanisms are identified: proximity fields generated by thermally exicted currents in the absorbing solid and timedependent image potentials due to elastic surfaces distortions (Rayleigh phonons. Estimates for the lifetime of the trap ground state are given. Ions are paricularly sinsitive to electric proximity fields: for a silver substrate, we find a lifetime below one second at distrances closer than some ten 10^-6m to the surfaces. Neutral atoms may approach the surface more closely: if they have a magnetic moment, a minimum distance of one 10^-6m is estimatied in tight traps, the heat being transferred via magnetic proximity fields. For spinless atoms, heat is transferred by inelastic scattering of virtual photons off sorface phonons. The corresponding lifetime, however, is estimated to be extremely long compared to the timescale of typical experiments. Y1 - 1999 ER - TY - JOUR A1 - Henkel, Carsten A1 - Poetting, Sierk A1 - Wilkens, Martin T1 - Loss and heating of particles in small and noisy traps N2 - We derive the time and loss rate for a trapped atom that is coupled to fluctuating fields in the vicinity of a room-temperature metallic and/or dielectric surface. Our results indicate a clear predominance of near-field effects over ordinary blackbody radiation. We develop a theoretical framework for both charged ions and neutral atoms with and without spin. Loss processes that are due to a transition to an untrapped internal state are included. Y1 - 1999 ER -