8,261 research outputs found

    Harmonically Trapped Quantum Gases

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    We solve the problem of a Bose or Fermi gas in dd-dimensions trapped by δ≤d% \delta \leq d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature TcT_{c} if and only if d+δ>2d+\delta >2, and a jump in the specific heat at TcT_{c} if and only if d+δ>4d+\delta >4. Specific heats for both gas types precisely coincide as functions of temperature when d+δ=2d+\delta =2. The trapped system behaves like an ideal free quantum gas in d+δd+\delta dimensions. For δ=0\delta =0 we recover all known thermodynamic properties of ideal quantum gases in dd dimensions, while in 3D for δ=\delta = 1, 2 and 3 one simulates behavior reminiscent of quantum {\it wells, wires}and{\it dots}, respectively.Comment: 14 pages including 3 figures and 3 table

    Equilibration of Quantum Gases

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    Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators and correlation functions. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists of N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1/N).Comment: 9 + 10 pages, 5 figures; v2 is expanded to include extended results involving local equilibration on lattice systems, together with new examples and minor improvement

    Disordered quantum gases under control

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    When attempting to understand the role of disorder in condensed-matter physics, one faces severe experimental and theoretical difficulties and many questions are still open. Two of the most challenging ones, which have been debated for decades, concern the effect of disorder on superconductivity and quantum magnetism. Recent progress in ultracold atomic gases paves the way towards realization of versatile quantum simulators which will be useful to solve these questions. In addition, ultracold gases offer original situations and viewpoints, which open new perspectives to the field of disordered systems.Comment: text unchanged, submitted on June 2009; Final version on the website of Nature Physics at http://www.nature.com/nphys/journal/v6/n2/abs/nphys1507.htm

    Quantum gases in optical lattices

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    The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and tools to describe the many-body physics of quantum gases in optical lattices. This includes the derivation of effective lattice Hamiltonians from first principles and an overview of the emerging quantum phases. Additionally, state-of-the-art numerical tools to quantitatively treat bosons or fermions on different lattices are introduced.Comment: 29 pages, 3 figures. This article will be published as Chapter 2 in "Quantum gas experiments - exploring many-body states", edited by P. Torma and K. Sengstock, Imperial College Press, London, to be published 201

    Degenerate quantum gases of strontium

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    Degenerate quantum gases of alkaline-earth-like elements open new opportunities in research areas ranging from molecular physics to the study of strongly correlated systems. These experiments exploit the rich electronic structure of these elements, which is markedly different from the one of other species for which quantum degeneracy has been attained. Specifically, alkaline-earth-like atoms, such as strontium, feature metastable triplet states, narrow intercombination lines, and a non-magnetic, closed-shell ground state. This review covers the creation of quantum degenerate gases of strontium and the first experiments performed with this new system. It focuses on laser-cooling and evaporation schemes, which enable the creation of Bose-Einstein condensates and degenerate Fermi gases of all strontium isotopes, and shows how they are used for the investigation of optical Feshbach resonances, the study of degenerate gases loaded into an optical lattice, as well as the coherent creation of Sr_2 molecules.Comment: Review paper, 43 pages, 24 figures, 249 reference

    Thermodynamics of quantum gases for the entire range of temperature

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    We have analytically explored thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials of the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible specially in the intermediate regime between the classical and quantum limits.Comment: 5 pages, 3 figures. Teaching Articl

    Theory of Interacting Quantum Gases

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    We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive interatomic interactions, i.e.\ between a gas with either a positive or a negative scattering length.Comment: Invited paper for the NIST Journal of Researc
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