Feed-forward and its role in conditional linear optical quantum dynamics

Nonlinear optical quantum gates can be created probabilistically using only single photon sources, linear optical elements and photon-number resolving detectors. These gates are heralded but operate with probabilities much less than one. There is currently a large gap between the performance of the known circuits and the established upper bounds on their success probabilities. One possibility for increasing the probability of success of such gates is feed-forward, where one attempts to correct certain failure events that occurred in the gate's operation. In this brief report we examine the role of feed-forward in improving the success probability. In particular, for the non-linear sign shift gate, we find that in a three-mode implementation with a single round of feed-forward the optimal average probability of success is approximately given by p= 0.272. This value is only slightly larger than the general optimal success probability without feed-forward, P= 0.25.Comment: 4 pages, 3 eps figures, typeset using RevTex4, problems with figures resolve

Black Hole Boundary Conditions and Coordinate Conditions

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.Comment: 13 pages LaTeX, revtex. No figure

Characterization of the domain chaos convection state by the largest Lyapunov exponent

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism

Hot entanglement in a simple dynamical model

How mixed can one component of a bi-partite system be initially and still become entangled through interaction with a thermalized partner? We address this question here. In particular, we consider the question of how mixed a two-level system and a field mode may be such that free entanglement arises in the course of the time evolution according to a Jaynes-Cummings type interaction. We investigate the situation for which the two-level system is initially in mixed state taken from a one-parameter set, whereas the field has been prepared in an arbitrary thermal state. Depending on the particular choice for the initial state and the initial temperature of the quantised field mode, three cases can be distinguished: (i) free entanglement will be created immediately, (ii) free entanglement will be generated, but only at a later time different from zero, (iii) the partial transpose of the joint state remains positive at all times. It will be demonstrated that increasing the initial temperature of the field mode may cause the joint state to become distillable during the time evolution, in contrast to a non-distillable state at lower initial temperatures. We further assess the generated entanglement quantitatively, by evaluating the logarithmic negativity numerically, and by providing an analytical upper bound.Comment: 5 pages, 2 figures. Contribution to the proceedings of the 'International Conference on Quantum Information', Oviedo, July 13-18, 2002. Discusses sudden changes of entanglement properties in a dynamical quantum mode

Traveling waves in rotating Rayleigh-Bénard convection: Analysis of modes and mean flow

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshhold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius

Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found to be stable, except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure

Explicit solution of the linearized Einstein equations in TT gauge for all multipoles

We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to appear in Class. Quantum Gra

Casimir-Polder interaction between an atom and a small magnetodielectric sphere

On the basis of macroscopic quantum electrodynamics and point-scattering techniques, we derive a closed expression for the Casimir-Polder force between a ground-state atom and a small magnetodielectric sphere in an arbitrary environment. In order to allow for the presence of both bodies and media, local-field corrections are taken into account. Our results are compared with the known van der Waals force between two ground-state atoms. To continuously interpolate between the two extreme cases of a single atom and a macroscopic sphere, we also derive the force between an atom and a sphere of variable radius that is embedded in an Onsager local-field cavity. Numerical examples illustrate the theory.Comment: 9 pages, 4 figures, minor addition

Atomic multipole relaxation rates near surfaces

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface we find a hierarchy of scaling laws depending on the atom-surface distance z.Comment: Updated to journal version. 16 page