Correlation induced localization of lattice trapped bosons coupled to a Bose–Einstein condensate

Abstract

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...

Many-body quantum dynamics and induced correlations of Bose polarons

“…again signals quasiparticle formation. However, in addition to this dynamical dressing the destructive (|ˆ( ) | á ñ = t S 0) and the constructive (|ˆ( ) | á ñ » t S 1) interference between the states of a single and two Bose polarons can be seen (see also equation (11) and its interpretation in section 4.1).…”

“…I I explaining two of the above identified peaks. The third dominant peak at ω f =18.35 appearing in the spectrum is attributed to the occupation of an excited state with S z =1 (see also equation (2)) according to equation (11). Recall that the | ñ 1, 1 spin state in the timeevolved wavefunction (equation (2)) corresponds to the two polaron case while | ñ 1, 0 contains only one polaron and the | -ñ 1, 1 describes impurities that do not interact with the bath and thus no polarons.…”

State engineering of impurities in a lattice by coupling to a Bose gas

“…In order to explore the range of validity of this crossover, we fix the lattice depth as well as the interspecies interaction strength such that for g AA =0 we arrive at a degenerate subspace of ground states given by equation (8), instead of the one given by equation (7) for g AA /E R λ=0.0236. The reader should note that for g AA =0 the correlated region, which is split into two sub-regions for g AA /E R λ=0.0236, is solely described by the degenerate manifold in equation (8) (see [59]). Again, we calculate the probability P n A ñ  (| ), while varying the coupling strength g AA for fixed V 0 and g AB .…”

“…The induced interaction hereby depends on the interplay between the lattice depth and the interspecies interaction strength, whereas the impurity repulsion can be directly influenced by the intraspecies interaction strength among the impurities. Setting the latter to zero and increasing the lattice depth and the interspecies interaction strength, the ground state 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 [59]. This means that all impurity atoms cluster in a single well, while the majority Bose gas atoms are expelled from it.…”

Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

“…In the extreme case such systems consist of a single impurity immersed in a majority species. These setups have been studied theoretically [25][26][27][28][29][30][31][32] and experimentally [33][34][35][36], for a single impurity, serving as a simulator of polaron physics, as well as for many impurities [37][38][39][40][41][42] and are indeed a subject of ongoing research. While the ground state properties of a single impurity in a bath are to a certain extent well understood, less focus has been placed on the transport properties and the emergent collisions of the impurity through the bath [43][44][45][46].…”