We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.

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We study few-boson tunneling in a one-dimensional double well. As we pass from weak interactions to the fermionization limit, the Rabi oscillations first give way to highly delayed pair tunneling (for medium coupling), whereas for very strong correlations multi-band Rabi oscillations emerge. All this is explained on the basis of the exact few-body spectrum and without recourse to the conventional two-mode approximation. Two-body correlations are found essential to the understanding of the different tunnel mechanisms. The investigation is complemented by discussing the effect of skewing the double well, which offers the possibility to access specific tunnel resonances.

We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both ansätze give inaccurate results.PACS numbers: 03.75. Ss, 05.30.Fk, Since interactions between atoms can be tuned to essentially any value, cold atomic gases provide a unique opportunity for studying experimentally manybody physics in regimes that cannot be realized in other systems. Recently, much attention has been given to the problem of a Fermi gas with a low concentration of a second species, a so-called highly imbalanced gas (see, e.g., [1][2][3]). One fundamental problem is the nature of the ground state of a single impurity atom in a Fermi gas. For weak interspecies attraction, the ground-state energy is well described in terms of a state with an impurity atom dressed by a single particle-hole excitation of the Fermi sea, often referred to as a "polaron" [4,5], while for strong attraction, a state based on a molecular picture gives a lower energy [6,7]. The transition between the two states is predicted to be sharp [6,8].It is natural to ask whether this picture persists in lower dimensions. This is of theoretical interest, since on general grounds one would expect quantum fluctuations, in this case the creation of many particle-hole pairs, to play an important role. In addition, the problem is on the verge of being investigated experimentally with the use of optical lattices [9]. In one dimension, a polaronic description gives qualitative agreement with known exact results [10]. In this paper, we consider the case of two dimensions. We perform simple variational calculations based on the polaron and molecule pictures, and these predict that the polaronic state has the lower energy for all interaction strengths, in marked contrast to what happens in three dimensions. For an infinitely massive impurity, the problem may be solved exactly, and the results show that the actual ground state incorporates aspects of both pictures: A two-body bound state is present for all coupling strengths, in addition to distortions of the continuum states. We show that the energy of an impurity gives important information about correlations in its vicinity and about mutual interactions between impurities at nonzero density.Model We consider a uniform two-dimensional (2D) Fermi gas of atoms of species a, to which is added a single impurity atom...

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.