We unravel the correlated tunneling dynamics of an impurity trapped in a double well and interacting repulsively with a majority species of lattice trapped bosons. Upon quenching the tilt of the double well it is found that the quench-induced tunneling dynamics depends crucially on the interspecies interaction strength and the presence of entanglement inherent in the system. In particular, for weak couplings the impurity performs a rather irregular tunneling process in the double well. Increasing the interspecies coupling it is possible to control the response of the impurity which undergoes a delayed tunneling while the majority species effectively acts as a material barrier. For very strong interspecies interaction strengths the impurity exhibits a self-trapping behavior. We showcase that a similar tunneling dynamics takes place for two weakly interacting impurities and identify its underlying transport mechanisms in terms of pair and single-particle tunneling processes.
We investigate the ground state properties and the nonequilibrium dynamics of a lattice trapped bosonic mixture consisting of an impurity species and a finite-sized medium. For the case of one as well as two impurities we observe that, depending on the lattice depth and the interspecies interaction strength, a transition from a strongly delocalized to a localized impurity distribution occurs. In the latter regime the two species phase separate, thereby forming a particle–hole pair. For two impurities we find that below a critical lattice depth they are delocalized among two neighboring outer lattice wells and are two-body correlated. This transition is characterized by a crossover from strong to a suppressed interspecies entanglement for increasing impurity-medium repulsion. Turning to the dynamical response of the mixture, upon quenching the interspecies repulsion to smaller values, we reveal that the predominant tunneling process for a single impurity corresponds to that of a particle–hole pair, whose dynamical stability depends strongly on the quench amplitude. During the time-evolution a significant increase of the interspecies entanglement is observed, caused by the build-up of a superposition of states and thus possesses a many-body nature. In the case of two bosonic impurities the particle–hole pair process becomes unstable in the course of the dynamics with the impurities aggregating in adjacent lattice sites while being strongly correlated.
We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb-Liniger type gas. Our main goal is the description and in depth exploration and analysis of the twospecies many-body quantum system including all relevant correlations beyond the standard meanfield approach. To achieve this, we use the multi-configuration time-dependent Hartree method for mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function's structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations. through the bath [17] and correlation effects due to the entanglement of the species [18]. In particular, 1D impurity-bath systems exhibit large interaction effects, bringing to light many peculiar phenomena [19][20][21][22][23]. In addition, impurities in Bose-Einstein condensates (BECs) can be exploited as a quantum simulator for polaron physics [25,24,26]. One of the first theoretical descriptions of polarons, including phonon clouds, was introduced by Fröhlich [27]. Since then a lot of progress has been made in the limiting cases of weak [28,29] and strong electron-phonon coupling [30]. While the ongoing theoretical study of 1D polarons [31][32][33][34][35] has predicted a lot of intriguing properties, recent experiments [17,23,36,37] have finally opened the door to the implementation of 1D polaronic systems, providing a deeper understanding of 1D polarons. When immersing more than one impurity in the bath, an induced interaction among the polarons appears, which counteracts the repulsive interaction among the impurities. The description in terms of polarons is in general of major interest for the understanding of the electron-phonon coupling in condensed matter physics. In order to manipulate impurities in a controlled, systematic way in ultracold physics, it would be useful to load the impurities first in a lattice, which is in turn inserted into the bath, since lattices allow for single-site excitation as well as collective excitations. To some extent, such a setup has been investigated in the tight-binding limit recently [38][39][40], where the authors especially focussed on the behavior of the combined systems under the influence of increasing temperature, e.g. the clustering of polarons in the wells of the lattice due to an attractive in...
We investigate the localization pattern of interacting impurities, which are trapped in a lattice potential and couple to a Bose gas. For small interspecies interaction strengths, the impurities populate the energetically lowest Bloch state or localize separately in different wells with one extra particle being delocalized over all the wells, depending on the lattice depth. In contrast, for large interspecies interaction strengths we find that due to the fractional filling of the lattice and the competition of the repulsive contact interaction between the impurities and the attractive interaction mediated by the Bose gas, the impurities localize either pairwise or completely in a single well. Tuning the lattice depth, the interspecies and intraspecies interaction strength correspondingly allows for a systematic control and engineering of the two localization patterns. The sharpness of the crossover between the two states as well as the broad region of their existence supports the robustness of the engineering. Moreover, we are able to manipulate the ground state's degeneracy in the form of triplets, doublets and singlets by implementing different boundary conditions, such as periodic and hard wall boundary conditions. where ĉ † is the field operator of the lattice A bosons, m A their mass, V 0 the lattice depth, g AA the intraspecies interaction strength, k the number of wells in the lattice and L is the length of the system. The B species is described by the Hamiltonian of the Lieb-Liniger model [63-65] for periodic boundary conditions New J. Phys. 20 (2018) 103042 K Keiler and P Schmelcher
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