We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of mixture of indistinguishable particles, be it fermions or bosons.Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra-and inter-species correlations. The versatility and efficiency of ML-MCTDHX is demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi type. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e. it is suppressed in the mean-field approximation.
We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incorporates few-body and inhomogeneous systems extending the scope of induced interactions where two particles interact via a bosonic bath-type environment. Employing the example of a one-dimensional ultracold Bose-Fermi mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with short-range attraction and long-range repulsion. With this, we show how beyond species mean-field physics visible in the two-body correlation functions can be understood via the induced interactions.
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi-one-dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are able to numerically obtain the exact many-body ground state of the atomic ensemble in the presence of an ion. We analyze the influence of the atom number and the atom-atom interaction on the ground state properties. Interestingly, for weakly interacting atoms, we find that the ion impedes the transition from the ideal gas behavior to the Thomas-Fermi limit. Furthermore, we show that this effect can be exploited to infer the presence of the ion both in the momentum distribution of the atomic cloud and by observing the interference fringes occurring during an expansion of the quantum gas. In the strong interacting regime, the ion modifies the fragmentation process in dependence of the atom number parity which allows a clear identification of the latter in expansion experiments. Hence, we propose in both regimes experimentally viable strategies to assess the impact of the ion on the many-body state of the atomic gas. This study serves as the first building block for systematically investigating the many-body physics of such hybrid system.
We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can build-up when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures of ultracold bosonic species for solving the underlying many-body Schrödinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.
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