Theoretical investigation of moir\'e patterns in quantum images

Moir\'e patterns are produced when two periodic structures with different spatial frequencies are superposed. The transmission of the resulting structure gives rise to spatial beatings which are called moir\'e fringes. In classical optics, the interest in moir\'e fringes comes from the fact that the spatial beating given by the frequency difference gives information about details(high spatial frequency) of a given spatial structure. We show that moir\'e fringes can also arise in the spatial distribution of the coincidence count rate of twin photons from the parametric down-conversion, when spatial structures with different frequencies are placed in the path of each one of the twin beams. In other words,we demonstrate how moir\'e fringes can arise from quantum images

Quantization of multidimensional cat maps

In this work we study cat maps with many degrees of freedom. Classical cat maps are classified using the Cayley parametrization of symplectic matrices and the closely associated center and chord generating functions. Particular attention is dedicated to loxodromic behavior, which is a new feature of two-dimensional maps. The maps are then quantized using a recently developed Weyl representation on the torus and the general condition on the Floquet angles is derived for a particular map to be quantizable. The semiclassical approximation is exact, regardless of the dimensionality or of the nature of the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit

Ultimate periodicity of b-recognisable sets : a quasilinear procedure

It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986. We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can verified in linear time if a given minimal automaton meets this description. This thus yields a O(n log(n)) procedure for deciding whether a general deterministic automaton accepts an ultimately periodic set of numbers.Comment: presented at DLT 201

On the propagation of semiclassical Wigner functions

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 Nov 2001) by the addition of two references, a few extra words of explanation and an augmented figure captio

Experimental quantum computing without entanglement

Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in order to offer any speed up over a classical computer. However, deterministic quantum computation with one pure qubit (DQC1), which employs noisy (mixed) states, is an efficient model that generates at most a marginal amount of entanglement. Although this model cannot implement any arbitrary algorithm it can efficiently solve a range of problems of significant importance to the scientific community. Here we experimentally implement a first-order case of a key DQC1 algorithm and explicitly characterise the non-classical correlations generated. Our results show that while there is no entanglement the algorithm does give rise to other non-classical correlations, which we quantify using the quantum discord - a stronger measure of non-classical correlations that includes entanglement as a subset. Our results suggest that discord could replace entanglement as a necessary resource for a quantum computational speed-up. Furthermore, DQC1 is far less resource intensive than universal quantum computing and our implementation in a scalable architecture highlights the model as a practical short-term goal.Comment: 5 pages, 4 figure

Moir\'e patterns in quantum images

We observed moir\'e fringes in spatial quantum correlations between twin photons generated by parametric down-conversion. Spatially periodic structures were nonlocally superposed giving rise to beat frequencies typical of moir\'e patterns. This result brings interesting perspectives regarding metrological applications of such a quantum optical setup.Comment: 4 pages, 5 figure

Conservation of Orbital Angular Momentum in Stimulated Down-Conversion

We report on an experiment demonstrating the conservation of orbital angular momentum in stimulated down-conversion. The orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion, but it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.Comment: Submitted for publication in Phys. Rev. Let

Magentically-Induced Lattice Distortions and Ferroelectricity in Magnetoelectric GdMnO3

In this work we investigate the magnetic field dependence of Ag octahedra rotation (tilt) and B2g symmetric stretching modes frequency at different temperatures. Our field-dependent Raman investigation at 10K is interpreted by an ionic displacive nature of the magnetically induced ferroelectric phase transition. The frequency change of the Ag tilt is in agreement with the stabilization of the Mn-Gd spin arrangement, yielding the necessary conditions for the onset of ferroelectricity on the basis of the inverse Dzyaloshinskii-Moriya interaction. The role of the Jahn-Teller cooperative interaction is also evidenced by the change of the B2g mode frequency at the ferroelectric phase transition. This frequency change allows estimating the shift of the oxygen position at the ferroelectric phase transition and the corresponding spontaneous polarization of 480 {\mu}C/m2, which agrees with earlier reported values in single crystals. Our study also confirms the existence of a large magnetic hysteresis at the lowest temperatures, which is a manifestation of magnetrostiction.Comment: 5 pages, 3 figure