No Arabic abstract
We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very different quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. In the composite fermionization regime, where the interactions between both components are large, none of the species show large occupation of any natural orbital. Our results show that by increasing the interaction in one of the species, one can reach the phase-separated regime. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting component is displaced to the edges of the trap. The crossover is sharp, as observed in the in the energy and the in the largest occupation of a natural orbital of the weakly interacting species. Such a transition is a purely mesoscopic effect which disappears for large atom numbers.
Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasi-condensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the Time Evolving Block Decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure emph{in situ} to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give new insight into the dynamics of strongly correlated many-body systems.
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 Schrodinger 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.
Based on a one-dimensional double-well superlattice with a unit filling of ultracold atoms per site, we propose a scheme to generate scalable entangled states in the superlattice through resonant lattice shakings. Our scheme utilizes periodic lattice modulations to entangle two atoms in each unit cell with respect to their orbital degree of freedom, and the complete atomic system in the superlattice becomes a cluster of bipartite entangled atom pairs. To demonstrate this we perform $ab initio$ quantum dynamical simulations using the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons, which accounts for all correlations among the atoms. The proposed clusters of bipartite entanglements manifest as an essential resource for various quantum applications, such as measurement based quantum computation. The lattice shaking scheme to generate this cluster possesses advantages such as a high scalability, fast processing speed, rich controllability on the target entangled states, and accessibility with current experimental techniques.
Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wave length that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order, such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wave lengths the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely non-superfluid and superfluid phases, respectively, displaying quasi-periodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the onsite interaction and is favourable at fractional densities. Experimental observables are identified and discussed.
A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of the entropy uncertainty relation (EUR) is approached by making $N$ very small in our numerical work. We examine the effect of correlations in the calculation of information entropy. Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies. We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value. Next we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC.