We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.PACS numbers: 71.38.Mx, 71.38.Ht The lack of lattice phonons is a distinguishing feature of optical lattices, i.e., conservative optical potentials formed by counterpropagating laser beams, and contributes to the excellent coherence properties of atoms trapped in them [1]. However, some of the most interesting phenomena in condensed matter physics involve phonons, and thus it is also desirable to introduce them in a controlled way into optical lattices. Recently, it has been shown that immersing an optical lattice into a Bose-Einstein condensate (BEC) leads to interband phonons, which can be used to load and cool atoms to extremely low temperatures [2]. Here, we instead concentrate on the dynamics within the lowest Bloch band of an immersed lattice, and show how intraband phonons lead to the formation of polarons [3,4]. This has a profound effect on lattice transport properties, inducing a crossover from coherent to incoherent hopping as the BEC temperature increases. Furthermore, polarons aggregate on adjacent lattice sites into stable clusters, which are not prone to loss from inelastic collisions. Since these phenomena are relevant to the physics of conduction in solids, introducing phonons into an optical lattice system may lead to a better understanding of high-temperature superconductivity [3,5] and charge transport in organic molecules [6]. Additionally, this setup may allow the investigation of the dynamics of classically indistinguishable particles [7].Experimental progress in trapping and cooling atoms has recently made a large class of interacting many-body quantum systems [8] accessible. For instance, the formation of repulsively bound atom pairs on a single site has been demonstrated [9], and strongly correlated mixtures of degenerate quantum gases have been realized [10]. In such Bose-Fermi mixtures, rich phase diagrams can be expected, including charge and spin density wave phases [11,12], pairing of fermions with bosons [13], and a supersolid phase [14]. Here we instead consider one atomic species, denoted as the impurities, confined to a trapping potential, for example an optical lattice, immersed in a nearly uniform BEC, as shown in Fig. 1. Based on a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model in terms of polarons, which are composed of impurity atoms dressed by a coherent state of Bogoliubov phonons [3,4]. The model also includes attractive impurity-impurity interactions...

We study the interaction-induced localization -the so-called self-trapping -of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that -unlike repulsive impurities -attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value β ⋆ . Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.

We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strongcoupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.

Measuring heat flow through nanoscale devices poses formidable practical difficulties as there is no "ampere meter" for heat. We propose to overcome this problem in a chain of trapped ions, where laser cooling the chain edges to different temperatures induces a heat current of local vibrations (vibrons). We show how to efficiently control and measure this current, including fluctuations, by coupling vibrons to internal ion states. This demonstrates that ion crystals provide an ideal platform for studying quantum transport, e.g., through thermal analogues of quantum wires and quantum dots. Notably, ion crystals may give access to measurements of the elusive bosonic fluctuations in heat currents and the onset of Fourier's law. Our results are strongly supported by numerical simulations for a realistic implementation with specific ions and system parameters.