Search

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 present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrelativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as e.g. generated by nonlinear interactions. Finally a possible realisation of such a system is proposed., 2 pages

We propose and analyze a scheme that makes use of interactions between spins to protect certain correlated many-body states from decoherence. The method exploits the finite energy gap of properly designed Hamiltonians to generate a manifold insensitive to local noise fluctuations. We apply the scheme to achieve decoherence-resistant generation of many particle GHZ states and show that it can improve the sensitivity in precision spectroscopy with trapped ions. Finally we also show that cold atoms in optical lattices interacting via short range interactions can be utilized to engineer the required long range interactions for a robust generation of entangled states., 5 Pages, 3 Figures

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

Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter $\gamma $ from a separable ($\gamma =\infty $) to a maximally entangled many-particle state ($\gamma =0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point $\gamma =0$. For $% \gamma =0$ the entanglement grows logarithmically with the system size with no upper bound, for $\gamma \neq 0$ it saturates at a level only depending on $\gamma $. For finite systems with total spin $J=N/2$ the scaling behavior changes at $\gamma =\gamma _{\mathrm{crit}}=1/J$., Comment: 8 pages, 5 figures, submitted to Phys. Rev. A

We discuss the creation of many-particle entanglement in an ion trap where all ions are simultaneously coupled to bichromatic laser fields. It is shown that in a time-averaged, coarse-grained picture the system can be mapped onto a spin ensemble with controllable collective interactions. An adiabatic change of laser parameters allows a transfer from separable to entangled eigenstates of the many-particle Hamiltonian. Of particular interest is a transition in the ground state which in some cases corresponds to a quantum phase transition. The influence of decoherence mechanisms can be substantially reduced if at all times a sufficiently large energy gap between the ground state and the first excited state is maintained., 4 pages, 3 figures

A coherent technique for the control of photon propagation in optically thick media and its application for quantum memories is discussed. Raman adiabatic passage with an externally controlled Stokes field can be used to transfer the quantum state of a light pulse (``flying'' qubit) to a collective spin-excitation (stationary qubit) and thereby slow down its propagation velocity to zero. The process is reversible and has a potential fidelity of unity without the necessity for strongly coupling resonators. A simple quasi-particle picture (dark-state polariton) of the transfer is presented. The analytic theory is supplemented with exact numerical solutions. Finally the influence of decoherence mechanisms on collective storage states, which are N-particle entangled states, is analyzed., 18 pages, lecture notes Enrico-Fermi school, Varenna 2001

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, Quantum Noise (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic di erence equations in discretised time.

The recently proposed idea to generate entanglement between photon states via exchange interactions in an ensemble of atoms (J.D. Franson and T.B. Pitman, Phys. Rev. A 60, 917 (1999) and J.D. Franson et al., (quant-ph/9912121)) is discussed using an S-matix approach. It is shown that if the nonlinear response of the atoms is negligible and no additional atom-atom interactions are present, exchange interactions cannot produce entanglement between photons states in a process that returns the atoms to their initial state. Entanglement generation requires the presence of a nonlinear atomic response or atom-atom interactions., Comment: 6 pages, no figures

Local field effects on the rate of spontaneous emission and Lamb shift in a dense gas of atoms are discussed taking into account correlations of atomic center-of-mass coordinates. For this the exact retarded propagator in the medium is calculated in independent scattering approximation and employing a virtual-cavity model. The resulting changes of the atomic polarizability lead to modifications of the medium response which can be of the same order of magnitude but of opposite sign than those due to local field corrections of the dielectric function derived by Morice, Castin, and Dalibard [Phys.Rev.A 51, 3896 (1995)]., 10 pages, 2 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

We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response., Comment: 4 pages, 3 figures, RevTeX, submitted to PRL; changed three numbers in Fig. 3 (caption)