776 research outputs found
Mott insulator states of ultracold atoms in optical resonators
We study the low temperature physics of an ultracold atomic gas in the
potential formed inside a pumped optical resonator. Here, the height of the
cavity potential, and hence the quantum state of the gas, depends not only on
the pump parameters, but also on the atomic density through a dynamical
a.c.-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in
one dimension, and use the strong coupling expansion to determine the parameter
regime in which the system is in the Mott-insulator state. We predict the
existence of overlapping, competing Mott states, and bistable behavior in the
vicinity of the shifted cavity resonance, controlled by the pump parameters.
Outside these parameter regions, the state of the system is in most cases
superfluid.Comment: 4 pages, 3 figures. Substantially revised version. To appear in Phys.
Rev. Let
Entangled light pulses from single cold atoms
The coherent interaction between a laser-driven single trapped atom and an
optical high-finesse resonator allows to produce entangled multi-photon light
pulses on demand. The mechanism is based on the mechanical effect of light. The
degree of entanglement can be controlled through the parameters of the laser
excitation. Experimental realization of the scheme is within reach of current
technology. A variation of the technique allows for controlled generation of
entangled subsequent pulses, with the atomic motion serving as intermediate
memory of the quantum state.Comment: 4 pages, 3 figures, revised version (new scheme for generation of
subsequent pairs of entangled pulses included). Accepted for publication in
Phys. Rev. Let
An iterative method with error estimators
AbstractIterative methods for the solution of linear systems of equations produce a sequence of approximate solutions. In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small. This paper presents a new iterative method based on the Lanczos process for the solution of linear systems of equations with a symmetric matrix. The method is designed to allow the computation of estimates of the Euclidean norm of the error in the computed approximate solutions. These estimates are determined by evaluating certain Gauss, anti-Gauss, or Gauss–Radau quadrature rules
A Convex-Nonconvex variational method for the additive decomposition of functions on surfaces
We present a Convex-NonConvex variational approach for the additive decomposition of noisy scalar f ields defined over triangulated surfaces into piecewise constant and smooth components. The energy functional to be minimized is defined by the weighted sum of three terms, namely an L2 fidelity term for the noise component, a Tikhonov regularization term for the smooth component and a Total Variation (TV)-like non-convex term for the piecewise constant component. The last term is parametrized such that the free scalar parameter allows to tune its degree of non- convexity and, hence, to separate the piecewise constant component more effectively than by using a classical convex TV regularizer without renouncing to convexity of the total energy functional. A method is also presented for selecting the two regularization parameters. The unique solution of the proposed variational model is determined by means of an efficient ADMM-based minimization algorithm. Numerical experiments show a nearly perfect separation of the different components
A Unified Surface Geometric Framework for Feature-Aware Denoising, Hole Filling and Context-Aware Completion
Technologies for 3D data acquisition and 3D printing have enormously developed in the past few years, and, consequently, the demand for 3D virtual twins of the original scanned objects has increased. In this context, feature-aware denoising, hole filling and context-aware completion are three essential (but far from trivial) tasks. In this work, they are integrated within a geometric framework and realized through a unified variational model aiming at recovering triangulated surfaces from scanned, damaged and possibly incomplete noisy observations. The underlying non-convex optimization problem incorporates two regularisation terms: a discrete approximation of the Willmore energy forcing local sphericity and suited for the recovery of rounded features, and an approximation of the l(0) pseudo-norm penalty favouring sparsity in the normal variation. The proposed numerical method solving the model is parameterization-free, avoids expensive implicit volumebased computations and based on the efficient use of the Alternating Direction Method of Multipliers. Experiments show how the proposed framework can provide a robust and elegant solution suited for accurate restorations even in the presence of severe random noise and large damaged areas
Inelastic scattering of light by a cold trapped atom: Effects of the quantum center-of-mass motion
The light scattered by a cold trapped ion, which is in the stationary state
of laser cooling, presents features due to the mechanical effects of
atom-photon interaction. These features appear as additional peaks (sidebands)
in the spectrum of resonance fluorescence. Among these sidebands the literature
has discussed the Stokes and anti-Stokes components, namely the sidebands of
the elastic peak. In this manuscript we show that the motion also gives rise to
sidebands of the inelastic peaks. These are not always visible, but, as we
show, can be measured in parameter regimes which are experimentally accessible.Comment: 10 pages, 4 figures, submitted to Phys. Rev.
Coherent generation of EPR-entangled light pulses mediated by a single trapped atom
We show that a single, trapped, laser-driven atom in a high-finesse optical
cavity allows for the quantum-coherent generation of entangled light pulses on
demand. Schemes for generating simultaneous and temporally separated pulse
pairs are proposed. The mechanical effect of the laser excitation on the
quantum motion of the cold trapped atom mediates the entangling interaction
between two cavity modes and between the two subsequent pulses, respectively.
The entanglement is of EPR-type, and its degree can be controlled through
external parameters. At the end of the generation process the atom is
decorrelated from the light field. Possible experimental implementations of the
proposals are discussed.Comment: 11 pages, 4 figure
Correlations and pair emission in the escape dynamics of ions from one-dimensional traps
We explore the non-equilibrium escape dynamics of long-range interacting ions
in one-dimensional traps. The phase space of the few ion setup and its impact
on the escape properties are studied. As a main result we show that an
instantaneous reduction of the trap's potential depth leads to the synchronized
emission of a sequence of ion pairs if the initial configurations are close to
the crystalline ionic configuration. The corresponding time-intervals of the
consecutive pair emission as well as the number of emitted pairs can be tuned
by changing the final trap depth. Correlations between the escape times and
kinetic energies of the ions are observed and analyzed.Comment: 17 pages, 9 figure
Entanglement at the quantum phase transition in a harmonic lattice
The entanglement properties of the phase transition in a two dimensional
harmonic lattice, similar to the one observed in recent ion trap experiments,
are discussed both, for finite number of particles and thermodynamical limit.
We show that for the ground state at the critical value of the trapping
potential two entanglement measures, the negativity between two neighbouring
sites and the block entropy for blocks of size 1, 2 and 3, change abruptly.
Entanglement thus indicates quantum phase transitions in general; not only in
the finite dimensional case considered in [Phys. Rev. Lett. {\bf 93}, 250404
(2004)]. Finally, we consider the thermal state and compare its exact
entanglement with a temperature entanglement witness introduced in [Phys. Rev.
A {\bf 77} 062102 (2008)].Comment: extended published versio
- …