Generalised quadrangles with a group of automorphisms acting primitively on points and lines

We show that if G is a group of automorphisms of a thick finite generalised quadrangle Q acting primitively on both the points and lines of Q, then G is almost simple. Moreover, if G is also flag-transitive then G is of Lie type.Comment: 20 page

Improved Semiclassical Approximation for Bose-Einstein Condensates: Application to a BEC in an Optical Potential

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schrodinger equation, but the solution incorporates correct 3D aspects of the problem. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with full 3D and Thomas-Fermi ones are presented.Comment: 14 pages, 5 figure

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Modal and Polarization Qubits in Ti:LiNbO3_3 Photonic Circuits for a Universal Quantum Logic Gate

Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes. We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO$_3$ photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial paths; the mode rotator, which rotates the state by an angle in mode space; and modal Pauli spin operators that effect related operations. We also describe the design of a deterministic, two-qubit, single-photon, CNOT gate, a key element in certain sets of universal quantum logic gates. It is implemented as a Ti:LiNbO$_3$ photonic quantum circuit in which the polarization and mode number of a single photon serve as the control and target qubits, respectively. It is shown that the effects of dispersion in the CNOT circuit can be mitigated by augmenting it with an additional path. The performance of all of these components are confirmed by numerical simulations. The implementation of these transformations relies on selective and controllable power coupling among single- and two-mode waveguides, as well as the polarization sensitivity of the Pockels coefficients in LiNbO$_3$

Theory of four-wave mixing of matter waves from a Bose-Einstein condensate

A recent experiment [Deng et al., Nature 398, 218(1999)] demonstrated four-wave mixing of matter wavepackets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this description to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.Comment: 18 pages Revtex preprint form, 13 eps figure

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure

Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.Comment: 6 pages, 3 figures small typos fixe

Del Pezzo surfaces of degree 1 and jacobians

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.Comment: 24 page

Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.Comment: 23 pages, 5 figure