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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 study the long-time evolution of the bipartite entanglement in translationally invariant gapped harmonic lattice systems with finite-range interactions. A lower bound for the von Neumann entropy is derived in terms of the purity of the reduced density matrix. It is shown that starting from an initially Gaussian state the entanglement entropy increases at least linearly in time. This implies that the dynamics of gapped (non-critical) harmonic lattice systems cannot be efficiently simulated by algorithms based on matrix-product decompositions of the quantum state., Comment: Introduction modified: new references added

We propose a new method of creating solitons in elongated Bose-Einstein Condensates (BECs) by sweeping three laser beams through the BEC. If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal phase slip which can be transferred to the atoms creating a soliton. Using this method it is possible to circumvent the restriction set by the diffraction limit inherent to conventional methods such as phase imprinting. The method allows one to create multicomponent (vector) solitons of the dark-bright form as well as the dark-dark combination. In addition it is possible to create in a controllable way two or more dark solitons with very small velocity and close to each other for studying their collisional properties., Comment: 10 figures

We study the ground-state entanglement of one-dimensional harmonic chains that are coupled to each other by a collective interaction as realized e.g. in an anisotropic ion crystal. Due to the collective type of coupling, where each chain interacts with every other one in the same way,the total system shows critical behavior in the direction orthogonal to the chains while the isolated harmonic chains can be gapped and non-critical. We derive lower and most importantly upper bounds for the entanglement,quantified by the von Neumann entropy, between a compact block of oscillators and its environment. For sufficiently large size of the subsystems the bounds coincide and show that the area law for entanglement is violated by a logarithmic correction., Comment: 5 pages, 1 figure

We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance., Comment: 8 pages, 4 figures

The phase transition to mirrorless oscillation in resonantly enhanced four-wave mixing in double-$\Lambda$ systems are studied analytically for the ideal case of infinite lifetimes of ground-state coherences. The stationary susceptibilities are obtained in all orders of the generated fields and analytic solutions of the coupled nonlinear differential equations for the field amplitudes are derived and discussed., Comment: proceedings ICLPQO'99 (Shanghai 99), 10 pages, 4 figures

Summary form only given. Theoretical and experimental work of past few years on atomic coherence and interference has demonstrated a potential to improve significantly the existing nonlinear optical techniques. In this contribution we present theoretical and experimental results demonstrating the possibility of efficient parametric oscillation in Raman-like double-/spl Delta/ systems. We discuss the possible applications of this process for quantum noise suppression and nonlinear mixing at a very low (few photon) power level.