Radiation-Pressure-Mediated Control of an Optomechanical Cavity

We describe and demonstrate a method to control a detuned movable-mirror Fabry-Perot cavity using radiation pressure in the presence of a strong optical spring. At frequencies below the optical spring resonance, self-locking of the cavity is achieved intrinsically by the optomechanical (OM) interaction between the cavity field and the movable end mirror. The OM interaction results in a high rigidity and reduced susceptibility of the mirror to external forces. However, due to a finite delay time in the cavity, this enhanced rigidity is accompanied by an anti-damping force, which destabilizes the cavity. The cavity is stabilized by applying external feedback in a frequency band around the optical spring resonance. The error signal is sensed in the amplitude quadrature of the transmitted beam with a photodetector. An amplitude modulator in the input path to the cavity modulates the light intensity to provide the stabilizing radiation pressure force

Towards magnetic slowing of atoms and molecules

We outline a method to slow paramagnetic atoms or molecules using pulsed magnetic fields. We also discuss the possibility of producing trapped particles by adiabatic deceleration of a magnetic trap. We present numerical simulation results for the slowing and trapping of molecular oxygen

New Coordinate Systems for Axisymmetric Black Hole Collisions

We describe a numerical grid generating procedure to construct new classes of orthogonal coordinate systems that are specially adapted to binary black hole spacetimes. The new coordinates offer an alternative approach to the conventional \v{C}ade\v{z} coordinates, in addition to providing a potentially more stable and flexible platform to extend previous calculations of binary black hole collisions.Comment: 3 pages, 5 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes

We have developed a general method for finding apparent horizons in 3D numerical relativity. Instead of solving for the partial differential equation describing the location of the apparent horizons, we expand the closed 2D surfaces in terms of symmetric trace--free tensors and solve for the expansion coefficients using a minimization procedure. Our method is applied to a number of different spacetimes, including numerically constructed spacetimes containing highly distorted axisymmetric black holes in spherical coordinates, and 3D rotating, and colliding black holes in Cartesian coordinates.Comment: 19 pages, 13 figures, LaTex, to appear in Phys. Rev. D. Minor changes mad

Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.

Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde

The Asymmetric Merger of Black Holes

We study event horizons of non-axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non-generic and how new features emerge. Most of the details of black hole formation and black hole merger are known only in the axisymmetric case, in which numerical evolution has successfully produced dynamical space-times. The work that is presented here uses a new approach to construct the geometry of the event horizon, not by locating it in a given spacetime, but by direct construction. In the axisymmetric case, our method produces the familiar pair-of-pants structure found in previous numerical simulations of black hole mergers, as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter. The main purpose of this paper is to show how new - substantially different - features emerge in the non-axisymmetric case. In particular, we show how black holes generically go through a toroidal phase before they become spherical, and how this fits together with the merger of black holes.Comment: 28 pages, 10 figures, uses REVTEX. Improved quality figures and additional color images are provided at http://www.phyast.pitt.edu/~shusa/EH

Tracking Black Holes in Numerical Relativity

This work addresses and solves the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon, as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative physics for the asymmetric collision; including: 1. Bounds on the topology of the throat connecting the holes following merger, 2. Time of merger, and 3. Continuous accounting for the surface of section areas of the black hole sources.Comment: 14 pages, 16 figure