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We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean- field stems from the boson-fermion interaction and is proportional to $a_{scriptsize BF}k_{scriptsize F}$. The total ground-state energy-density reads $E/V =epsilon_{scriptsize F} + epsilon_{scriptsize B} + (2pihbar^{2}a_{
m BF}n_{scriptsize B}n_{scriptsize F}/m) [1 + a_{scriptsize BF}k_{scriptsize F}f(delta)/pi]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(delta)$ is a known function of $delta= (m_{scriptsize B} - m_{scriptsize F})/(m_{scriptsize B} + m_{scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.
Portal alumni
(2010)
Das gerade begonnene Jahr wird für die Universität Potsdam ein besonderes werden, ist es doch das 20. Jahr ihres Bestehens. Auf das Erreichte ist die Hochschule mit Recht stolz. Die Universität Potsdam ist für Studieninteressierte ungebrochen attraktiv, was die steigenden Bewerberzahlen zeigen. Allein im vergangenen Jahr haben Uni-Wissenschaftler knapp 42 Millionen Euro Drittmittel eingeworben und die Liste gemeinsamer Verbundprojekte mit außeruniversitären Forschungseinrichtungen der Region wächst weiter. Zu den Erfolgen zählt weiterhin auch die steigende Anzahl von Absolventinnen und Absolventen der Hochschule.
In die Gründung der Universität Potsdam am 15. Juli 1991 flossen zwei Vorgängereinrichtungen ein. Die wichtigste war die Brandenburgische Landeshochschule, vorher Pädagogische Hochschule, die über vier Jahrzehnte hinweg Lehrerinnen und Lehrer ausgebildet hat. Die Lehrerbildung hat auch für die Universität Potsdam profilbildenden Charakter, denn allein vier der fünf Fakultäten sind an der Lehrerbildung beteiligt und haben Generationen von jungen Leuten für den Lehrerberuf qualifiziert. Heute ist das Ziel aller an der Lehrerbildung Beteiligten, eine professionsorientierte, qualitativ hochwertige Lehrerbildung zu sichern, die sich an den Kompetenzen Erziehen, Unterrichten, Beraten, Betreuen, Innovieren und Organisieren orientiert. Eine besondere Herausforderung sieht die Universität Potsdam dabei in der Vernetzung von wissenschaftlicher Forschung und Lehrerbildung.
Portal alumni stellt in der hier vorliegenden Ausgabe im Jubiläumsjahr zwölf Absolventen der Lehrerbildung vor. Sie berichten aus jeweils individueller Perspektive, wie sie ihr Studium an der Universität Potsdam erlebt haben und wie es sie geprägt hat. Und natürlich stellt das Magazin zugleich aktuelle Entwicklungstrends in der Lehrerbildung vor. Wie in allen Heften zuvor berichten wir von der Alumni-Arbeit des Jahres 2010 und stellen Höhepunkte des Unialltags vor. Wir wünschen Ihnen eine unterhaltsame Lektüre und sind gespannt auf Ihr Feedback zu diesem Heft.
We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using menthods that have been developed for the optimal purification of miced states, we find a class of miced states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.
We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.
Quantum games
(2000)
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.
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.
We analyze the multi-time correlations of a laser-induced Bose Einstein condensate. We use quantum stochastic methods to obtain under certain circumstances a Fokker-Planck equation which describes the phase-difussion process, and obtain an analytical expression of the two-time correlations. We perform also quantum Monte Carlo numerical simulations of the correlations, which are in good agreement with the predicted analytical results.
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.
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.
We discuss heating and decoherencw in traps fpr ions and neutral paricles close to metallic surfaces. We focus on simple trap geometries and compute noise spectra of thermally excited electromagnetic fields. If the trap is located in the near field of the substrate, the field fluctuations are largely increased compared to the level of the blackbody field, leading to much shorter coherence and life times of the trapped atoms. The correspinding time constants are computed for ion traps and magnetic traps. Analytical estimates for the size dependence of the noise spectrum are given. We finally discuss prospects for the coherent transport of matter waves in integrated surface waveguides.
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.
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.
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.
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.
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.