3,300 research outputs found
Balanced diagonals in frequency squares
We say that a diagonal in an array is λ-balanced if each entry occurs λ times. Let L be a frequency square of type F (n; λ); that is, an n ✕ n array in which each entry from {1, 2, …, m=n / λ } occurs λ times per row and λ times per column. We show that if m≤3 , L contains a λ -balanced diagonal, with only one exception up to equivalence when m=2. We give partial results for m≥4 and suggest a generalization of Ryser’s conjecture, that every Latin square of odd order has a transversal. Our method relies on first identifying a small substructure with the frequency square that facilitates the task of locating a balanced diagonal in the entire array
Identification of flexible structures for robust control
Documentation is provided of the authors' experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. A multi-input/multi-output (MIMO) model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Chebyshev polynomials are employed to fit the data with single-input/multi-output (SIMO) transfer function models. Combining these SIMO models leads to a MIMO model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included
Entangling the optical frequency comb: simultaneous generation of multiple 2x2 and 2x3 continuous-variable cluster states in a single optical parametric oscillator
We report on our research effort to generate large-scale multipartite
optical-mode entanglement using as few physical resources as possible. We have
previously shown that cluster- and GHZ-type N-partite continuous-variable
entanglement can be obtained in an optical resonator that contains a suitably
designed second-order nonlinear optical medium, pumped by at most O(N^2)
fields. In this paper, we show that the frequency comb of such a resonator can
be entangled into an arbitrary number of independent 2x2 and 2x3
continuous-variable cluster states by a single optical parametric oscillator
pumped by just a few optical modes.Comment: Third version has corrected eqs. (10-14) and revised notation "Q" in
lieu of "X" for amplitude quadrature operato
A macroscopic quantum state analysed particle by particle
Explaining how microscopic entities collectively produce macroscopic
phenomena is a fundamental goal of many-body physics. Theory predicts that
large-scale entanglement is responsible for exotic macroscopic phenomena, but
observation of entangled particles in naturally occurring systems is extremely
challenging. Synthetic quantum systems made of atoms in optical lattices have
been con- structed with the goal of observing macroscopic quantum phenomena
with single-atom resolution. Serious challenges remain in producing and
detecting long-range quantum correlations in these systems, however. Here we
exploit the strengths of photonic technology, including high coherence and
efficient single-particle detection, to study the predicted large-scale
entanglement underlying the macroscopic quantum phenomenon of polarization
squeezing. We generate a polarization-squeezed beam, extract photon pairs at
random, and make a tomographic reconstruction of their joint quantum state. We
present experimental evidence showing that all photons arriving within the
squeezing coherence time are entangled, that entanglement monogamy dilutes
entanglement with increasing photon density and that, counterintuitively,
increased squeezing can reduce bipartite entanglement. The results provide
direct evidence for entanglement of macroscopic numbers of particles and
introduce micro-analysis to the study of macroscopic quantum phenomena
Mixed symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices
We study localized modes in binary mixtures of Bose-Einstein condensates
embedded in one-dimensional optical lattices. We report a diversity of
asymmetric modes and investigate their dynamics. We concentrate on the cases
where one of the components is dominant, i.e. has much larger number of atoms
than the other one, and where both components have the numbers of atoms of the
same order but different symmetries. In the first case we propose a method of
systematic obtaining the modes, considering the "small" component as
bifurcating from the continuum spectrum. A generalization of this approach
combined with the use of the symmetry of the coupled Gross-Pitaevskii equations
allows obtaining breather modes, which are also presented.Comment: 11 pages, 16 figure
Reconstruction of the joint state of a two-mode Bose-Einstein condensate
We propose a scheme to reconstruct the state of a two-mode Bose-Einstein
condensate, with a given total number of atoms, using an atom interferometer
that requires beam splitter, phase shift and non-ideal atom counting
operations. The density matrix in the number-state basis can be computed
directly from the probabilities of different counts for various phase shifts
between the original modes, unless the beamsplitter is exactly balanced.
Simulated noisy data from a two-mode coherent state is produced and the state
is reconstructed, for 49 atoms. The error can be estimated from the singular
values of the transformation matrix between state and probability data.Comment: 4 pages (REVTeX), 5 figures (PostScript
On the optimality of the neighbor-joining algorithm
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy
algorithm for finding the balanced minimum evolution (BME) tree associated to a
dissimilarity map. From this point of view, NJ is ``optimal'' when the
algorithm outputs the tree which minimizes the balanced minimum evolution
criterion. We use the fact that the NJ tree topology and the BME tree topology
are determined by polyhedral subdivisions of the spaces of dissimilarity maps
to study the optimality of the neighbor-joining
algorithm. In particular, we investigate and compare the polyhedral
subdivisions for . A key requirement is the measurement of volumes of
spherical polytopes in high dimension, which we obtain using a combination of
Monte Carlo methods and polyhedral algorithms. We show that highly unrelated
trees can be co-optimal in BME reconstruction, and that NJ regions are not
convex. We obtain the radius for neighbor-joining for and we
conjecture that the ability of the neighbor-joining algorithm to recover the
BME tree depends on the diameter of the BME tree
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