We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.
The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the
Li+ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients
Cn in the potential energy for the three well-separated constituents, where
n refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients
C4,C6,C7,C8,C9 and the nonadditive interaction coefficients
C7,C9. The obtained coefficients
Cn are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of
6Li and
7Li.
In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.