The Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show that a bosonic version of the Kondo effect can occur in degenerate atomic Fermi gases near a Feshbach resonance. We also discuss how this bosonic Kondo effect can be observed experimentally.PACS numbers: 03.75. Kk, 32.80.Pj Introduction. -The Kondo effect is an intricate many-body phenomenon, that was originally put forward to explain the anomalous resistance minimum of metals contaminated with magnetic impurities. Today the Kondo effect is known to be also responsible for the existence of heavy-fermion materials [1], and is speculated to play an important role in the physics of high-temperature superconductors [2]. Moreover, a particularly clear manifestation of this effect occurs in semiconductor quantum dots [3,4,5]. In all these examples the Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. Here we show that a new version of the Kondo effect can occur in the degenerate atomic Fermi gases that have recently been created [6,7,8,9,10]. In contrast to the fermionic version, the many-body ground state of the gas shows now coherence between bosons, in fact bosonic molecules, and the free fermions in the gas. We explore the conditions under which this bosonic Kondo effect occurs and also discuss how it can be observed experimentally.

Zero temperature properties of a dilute weakly interacting d-dimensional Bose gas in a random potential are studied. We calculate geometrical and energetic characteristics of the localized state of a gas confined in a large box or in a harmonic trap. Different regimes of the localized state are found depending on the ratio of two characteristic length scales of the disorder, the Larkin length and the disorder correlation length. Repulsing bosons confined in a large box with average density n well below a critical value n c are trapped in deep potential wells of extension much smaller than distance between them. Tunneling between these wells is exponentially small. The ground state of such a gas is a random singlet with no long-range phase correlation For n > n c repulsion between particles overcomes the disorder and the gas transits from the localized to a coherent superfluid state. The critical density n c is calculated in terms of the disorder parameters and the interaction strength. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random ␦-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasiparticle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.Comment: 11 pages, 11 figures, revtex

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.