From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time

Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigate the crossover from few to many-body physics by studying quasi one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measure the interaction energy of such a system as a function of the number of majority atoms for different strengths of the interparticle interaction. As we increase the number of majority atoms one by one we observe the fast convergence of the normalized interaction energy towards a many-body limit calculated for a single impurity immersed in a Fermi sea of majority particles.Comment: 9 pages, 5 figure

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

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of non-interacting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.Comment: 18 page

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.Comment: 16 pages, 4 figure