Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry-Pérot optical filters

This paper reports an investigation on techniques for determining elastic modulus and intrinsic stress gradient in plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The elastic property of the silicon nitride thin films was determined using the nanoindentation method on silicon nitride/silicon bilayer systems. A simple empirical formula was developed to deconvolute the film elastic modulus. The intrinsic stress gradient in the films was determined by using micrometric cantilever beams, cross-membrane structures and mechanical simulation. The deflections of the silicon nitride thin film cantilever beams and cross-membranes caused by in-thickness stress gradients were measured using optical interference microscopy. Finite-element beam models were built to compute the deflection induced by the stress gradient. Matching the deflection computed under a given gradient with that measured experimentally on fabricated samples allows the stress gradient of the PECVD silicon nitride thin films introduced from the fabrication process to be evaluated.

Characterization of optically driven fluid stress fields with optical tweezers

We present a controlled stress microviscometer with applications to complex fluids. It generates and measures microscopic fluid velocity fields, based on dual beam optical tweezers. This allows an investigation of bulk viscous properties and local inhomogeneities at the probe particle surface. The accuracy of the method is demonstrated in water. In a complex fluid model (hyaluronic acid), we observe a strong deviation of the flow field from classical behavior. Knowledge of the deviation together with an optical torque measurement is used to determine the bulk viscosity. Furthermore, we model the observed deviation and derive microscopic parameters.

Quantum analysis of the nondegenerate optical parametric oscillator with injected signal

In this paper we study the nondegenerate optical parametric oscillator with injected signal, both analytically and numerically. We develop a perturbation approach which allows us to find approximate analytical solutions, starting from the full equations of motion in the positive-P representation. We demonstrate the regimes of validity of our approximations via comparison with the full stochastic results. We find that, with reasonably low levels of injected signal, the system allows for demonstrations of quantum entanglement and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical parametric oscillator operating below threshold, these features are demonstrated with relatively intense fields.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure

The acceptance-probability-controlled simulated annealing with an adaptive move generation procedure, an optimization technique derived from the simulated annealing algorithm, is presented. The adaptive move generation procedure was compared against the random move generation procedure on seven multiminima test functions, as well as on the synthetic data, resembling the optical constants of a metal. In all cases the algorithm proved to have faster convergence and superior escaping from local minima. This algorithm was then applied to fit the model dielectric function to data for platinum and aluminum.

Ideal soliton environment using parametric band gaps

Simultaneous solitary wave solutions for laser propagation in nonlinear parametric media with up to (3 + 1) dimensions are proved to exist. The combination of the large dispersion of a Bragg grating and the strong nonlinearity of chi((2)) optical material results in stable behavior with short interaction distances and low power requirements. The solutions are obtained by using the effective mass approximation to reduce the coupled propagation equations to those describing a dispersive parametric nonlinear waveguide, and are verified by solving the complete set of coupled band-gap equations numerically.

Optical mesons

An ''optical meson'' (two-photon quantum soliton) is proven to exist in a parametric waveguide. This could provide an ideal quantum soliton environment, because of more realistic formation lengths and much larger binding energies than chi((3)) quantum solitons. We estimate the binding energy, radius, and interaction length in comparison to the chi((3)) case in optical fibers.

Simulated-annealing-based genetic algorithm for modeling the optical constants of solids

We propose a simulated-annealing-based genetic algorithm for solving model parameter estimation problems. The algorithm incorporates advantages of both genetic algorithms and simulated annealing. Tests on computer-generated synthetic data that closely resemble optical constants of a metal were performed to compare the efficiency of plain genetic algorithms against the simulated-annealing-based genetic algorithms. These tests assess the ability of the algorithms to and the global minimum and the accuracy of values obtained for model parameters. Finally, the algorithm with the best performance is used to fit the model dielectric function to data for platinum and aluminum. (C) 1997 Optical Society of America.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.