Trace of broken integrability in stationary correlation properties

We show that the breaking of integrability in the fundamental one-dimensional model of bosons with contact interactions has consequences on the stationary correlation properties of the system. We calculate the energies and correlation functions of the integrable Lieb-Liniger case, comparing the exact Bethe-ansatz solution with a corresponding Jastrow ansatz. Then we examine the non-integrable case of different interaction strengths between each pair of atoms by means of a variationally optimized Jastrow ansatz, proposed in analogy to the Laughlin ansatz. We show that properties of the integrable state are more stable close to the Tonks-Girardeau regime than for weak interactions. All energies and correlation functions are given in terms of explicit analytical expressions enabled by the Jastrow ansatz. We finally compare the correlations of the integrable and non-integrable cases and show that apart from symmetry breaking the behavior changes dramatically, with additional and more pronounced maxima and minima interference peaks appearing.Comment: 19 pages, 5 figures. Published with minor change

Few-boson tunneling in a double well with spatially modulated interaction

We study few-boson tunneling in a one-dimensional double well with a spatially modulated interaction. The dynamics changes from Rabi oscillations in the non-interacting case to a highly suppressed tunneling for intermediate coupling strengths followed by a revival near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations we observe tunneling between the higher bands. The dynamics is explained on the basis of the few-body spectrum and stationary eigenstates. For higher number of particles, N > 2, it is shown that the inhomogeneity of the interaction can be tuned to generate tunneling resonances. Finally, a tilted double-well and its interplay with the interaction asymmetry is discussed.Comment: 10 Pages. Published with minor change

Quantum Speed Limit and Optimal Control of Many-Boson Dynamics

We extend the concept of quantum speed limit -- the minimal time needed to perform a driven evolution -- to complex interacting many-body systems. We investigate a prototypical many-body system, a bosonic Josephson junction, at increasing levels of complexity: (a) within the two-mode approximation {corresponding to} a nonlinear two-level system, (b) at the mean-field level by solving the nonlinear Gross-Pitaevskii equation in a double well potential, and (c) at an exact many-body level by solving the time-dependent many-body Schr\"odinger equation. We propose a control protocol to transfer atoms from the ground state of a well to the ground state of the neighbouring well. Furthermore, we show that the detrimental effects of the inter-particle repulsion can be eliminated by means of a compensating control pulse, yielding, quite surprisingly, an enhancement of the transfer speed because of the particle interaction -- in contrast to the self-trapping scenario. Finally, we perform numerical optimisations of both the nonlinear and the (exact) many-body quantum dynamics in order to further enhance the transfer efficiency close to the quantum speed limit.Comment: 5 pages, 3 figures, and supplemental material (4 pages 1 figure