Alessandra Gatti

Spatio-temporal entanglement of twin photons: An intuitive picture

We draw an intuitive picture of the spatio–temporal properties of the entangled state of twin photons, where they are described as classical wave-packets. This picture predicts a precise relation between their temporal and transverse spatial separations at the crystal output. The space-time coupling described by classical arguments turns out to determine in a precise way the spatio–temporal structure of the quantum entanglement, analyzed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.

Continuous variable entanglement of counter-propagating twin beams

This work describes the continuous-variable entanglement of the counter-propagating twin beams generated in a Mirrorless Optical Parametric Oscillator below threshold, encompassing both their quadrature and photon-number correlation. In the first case, a comparison with the single-pass co-propagating geometry outlines the huge difference of the bandwidth involved and a completely different stability of the two sources with respect to the phase-angle. In the second case, stimulated by the critical divergence of the correlation time evidenced by Corti et al., we address the issue of the temporal bandwidth of the intensity squeezing.

Space-time coupling in upconversion of broadband downconverted light

We investigate the upconversion process of broadband incoherent light generated by parametric downconversion. We focus on the incoherent component of the sum-frequency generated (SFG) radiation, analyzing its spatiotemporal properties. We show that its spectrum has a skewed geometry in space-time, originating from a compensation between the group-velocity mismatch and the spatial walk-off of the fundamental and the SFG fields. The results are illustrated by a theoretical modeling of the optical system and by experimental measurements.

Spatio-temporal structures from four-wave mixing and phase modulation

Abstract We analyse a non-inverted two-level system contained in a resonant cavity with spherical mirrors, and driven by an external field matched to a mode of the resonator. In an appropriate limit (Kerr medium limit) we derive from the complete model a cubic parametric model which allows for extensive analytical calculations. We consider various cases of three-mode interaction and find coexisting stable stationary states, dynamical structures, period doubling and chaos, phase singularities, periodic alternance.

Spontaneous spatial structures and spatial squeezing in optical parametric oscillators

We demonstrate that the optical parametric oscillator is an ideal system for studying spatial pattern formation and quantum effects in spatial structures. In the first part of the article we analyze a semiclassical model which includes diffraction in the paraxial approximation, and we show the formation of rolls, zig-zag patterns, dislocations, filamentation, and optical chaos. In the second part of the paper we describe the spatial structure of the squeezed vacuum state emitted by the optical parametric oscillator below the threshold for signal generation.

Experimental Observation of the Ultra-narrow Temporal Entanglement of Twin Beams by Means of Frequency Up-conversion

We report here about the experimental observation of an ultra-narrow temporal correlation (6,7 fs FWHM) of twin beams produced by a type I BBO crystal, detected by means of the inverse process of sum-frequency generation.

Tailoring the Spatio-temporal Bandwidth of Biphotons via the Non-factorable Structure of Entanglement

We investigate the spatio-temporal structure of the biphoton entanglement in Parametric Down Conversion (PDC). In particular we study the biphoton amplitude at the output face of the nonlinear crystal (near-field) and we demonstrate its X-shaped geometry in the space-time dimensions, i.e. the non-factorability of the state with respect to spatial and temporal variables. Our analysis provides a precise and quantitative characterization of this structure in various regimes and types of phase matching of PDC. The key elements of novelty emerging from our analysis are the non-factorability of the state with respect to spatial and temporal variables, and the extreme relative localization of the entangled photons, both in space (few microns) and time (few femtoseconds). This extreme localization is connected to our ability to resolve the photon positions in the source near-field. The non factorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of freedom of twin photons.

Spatial Entanglement in Optical Parametric Down-Conversion

This chapter and Chapter 5 constitute a direct continuation of Chapter 1, with a description of the developments in the continuous variable approach to quantum imaging, achieved in the framework of QUANTIM. Whereas Chapter 2 treats the traveling-wave configuration for PDC, the discussion of Chapter 5 focuses on the cavity configuration of optical parametric oscillators. The structure of this chapter is as follows. Section 2.2 presents the theoretical picture of spatial entanglement in type-II materials. Contrary to most literature on PDC, the emphasis is on the high-gain regime. Section 2.3 describes the experimental observations of those theoretical predictions outlined in Section 2.2, which concern the quantum correlations in the far field, with an associated phenomenon of photon antibunching in space. In the final Section 2.4 we illustrate the multiphoton, multimode polarization entanglement in the high-gain PDC. Instead of considering the standard polarization entanglement in single pairs of signal–idler photons, we focus on collective polarization entanglement properties at the macroscopic level.