Super-Resolution in Phase Space

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super- resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.Comment: 10 Pages, short paper in part accepted to ICASSP 201

Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation

A powerful theoretical structure has emerged in recent years on the characterization and quantification of entanglement in continuous-variable systems. After reviewing this framework, we will illustrate it with an original set-up based on a type-II OPO with adjustable mode coupling. Experimental results allow a direct verification of many theoretical predictions and provide a sharp insight into the general properties of two-mode Gaussian states and entanglement resource manipulation

From quantum pulse gate to quantum pulse shaper -- enigneered frequency conversion in nonlinear optical waveguides

Full control over the spatio-temporal structure of quantum states of light is an important goal in quantum optics, to generate for instance single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source-engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by means of single-photon frequency conversion. In this paper we explore new routes towards complete control of the inherent pulse-modes of ultrafast pulsed quantum states by employing specifically designed nonlinear waveguides with adapted dispersion properties. Starting from our recently proposed quantum pulse gate (QPG) we further generalize the concept of spatio-spectral engineering for arbitrary \chitwo-based quantum processes. We analyse the sum-frequency generation based QPG and introduce the difference-frequency generation based quantum pulse shaper (QPS). Together, these versatile and robust integrated optics devices allow for arbitrary manipulations of the pulse-mode structure of ultrafast pulsed quantum states. The QPG can be utilized to select an arbitrary pulse mode from a multimode input state, whereas the QPS enables the generation of specific pulse modes from an input wavepacket with Gaussian-shaped spectrum.Comment: 21 pages, 9 figure

Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.Comment: 27 pages, 10 figures, version published in Rev. Mod. Phys. as a Colloquiu

The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2

The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in solition theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.Comment: 10 page

Frontiers of Inflationary Cosmology

After a brief review of the theory of cosmological perturbations, I highlight some recent progress in the area of reheating in inflationary cosmology, focusing in particular on parametric amplification of super-Hubble cosmological fluctuations, and on the role of noise in the resonance dynamics (yielding a new proof of Anderson localization). I then discuss several important conceptual problems for the current realizations of inflation based on fundamental scalar matter fields, and review some new approaches at solving these problems.Comment: 15 pages, invited lecture at the XXI Brazilian National Meeting on Particles and Fields, Oct. 23 - 26, 2000, to be published in the proceedings (special issue, Brazilian Journal of Physics, eds. L. de Paula and M. Menon