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Alessandra Gatti

Publications and source records attributed to Alessandra Gatti.

At least 19 recordsLinked to original sources
arXiv2025

Quantum-enhanced second harmonic generation beyond the photon pairs regime

Two-photon processes are crucial in applications like microscopy and microfabrication, but their low cross-section requires intense illumination and limits, e.g., the penetration depth in nonlinear microscopy. Entangled states have been proposed to enhance the efficiency of two-photon interactions and have shown effectiveness at low intensities. This quantum enhancement is generally believed to be lost at high intensities, for more than one photon per mode, raising doubts about its usefulness. We explored experimentally and theoretically two-photon processes driven by entangled photons at intensities beyond this threshold and compared the results with the classical case. We found that a quantum advantage can still be observed at nearly one order of magnitude higher intensities than previously assumed. Our findings show a potential path for exploiting quantum-enhanced two-photon processes in practical applications.

quant-ph↗
arXiv2024

Unified space-time description of pulsed twin beams

This work provides a mathematical derivation of a quasi-stationary model for multimode parametric down-conversion, which was presented in [Gatti et al., Sci. Rep. 13, 16786] with heuristic arguments. The model is here derived from the 3D+1 propagation equation of the quantum fields in a nonlinear crystal, and its approximations discussed thoroughly. Thanks to its relative simplicity, and to the fact that it is valid in any gain regime, both at a quantum and classical level, it allows a unified description of disparate experimental observations conducted over the last 20 years, often described in the past by means of limited ad hoc models.

quant-ph↗
arXiv2023

Modeling the space-time correlation of pulsed twin beams

Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications, due their multimodal nature in space and time. However, a satisfactory theoretical description is still lacking. In this work we propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory. The model is used to study the quantum correlation and the coherence in the angle-frequency domain of the parametric emission, and demonstrates a $g^{1/2} $ growth of their size as the gain $g$ increases, with a corresponding contraction of the space-time distribution. These predictions are systematically compared with the results of stochastic numerical simulations, performed in the Wigner representation, of the full model equations: an excellent agreement is shown even for parameters well outside the expected limit of validity of the model.

quant-ph↗
arXiv2021

Multipartite spatial entanglement generated by concurrent nonlinear processes

Continuous variables multipartite entanglement is a key resource for quantum technologies. This works considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources: a standard $χ^{(2)}$ medium pumped by two pumps, a single-pump nonlinear photonic crystal, and a doubly pumped nonlinear photonic crystal. These sources have in common the coexistence of several concurrent nonlinear processes in the same medium, which allows the generation of non-standard 3 and 4-mode couplings. We test the genuine nature of the multipartite entangled states thereby generated in a common framework, using both criteria based on proper bounds for the variances of nonlocal observables and on the positive partial transpose criterion. The relative simplicity of these states allows a (hopefully) useful comparison of the different inseparability tests.

quant-ph↗
arXiv2021

Roadmap on multimode light shaping

Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community.

physics.optics↗
arXiv2020

Engineering multipartite entangled states in doubly pumped parametric down-conversion processes

We investigate the quantum state generated by optical parametric down-conversion in a $χ^{(2) } $ medium driven by two noncollinear light modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the spatio-temporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups: i) Non-critical phase-matching in a periodically poled Lithium Tantalate slab, characterized by a 3-mode entangled state among hot spots. ii) A type I setup in a Beta-Barium Borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a quadripartite entangled state. In both cases we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.

quant-ph↗
arXiv2020

Hot-spots and gain enhancement in a doubly pumped parametric down-conversion process

We experimentally investigate the parametric down-conversion process in a nonlinear bulk crystal, driven by two non-collinear pump modes. The experiment shows the emergence of bright hot-spots in modes shared by the two pumps, in analogy with the phenomenology recently observed in 2D nonlinear photonic crystals. By exploiting the spatial walk-off between the two extraordinary pump modes we have been able to recreate a peculiar resonance condition, reported by a local enhancement of the parametric gain, which corresponds to a transition from a three-mode to a four-mode coupling. From a quantum point of view this opens the way to the generation of multimode entangled states of light such as tripartite or quadripartite states, in simple bulk nonlinear sources.

quant-ph↗
arXiv2018

Golden Ratio entanglement in hexagonally poled nonlinear crystals

This work analyses the quantum state of twin photons and twin beams generated by parametric-down conversion in a hexagonally poled photonic crystal,characterized by the simultaneous presence of two nonlinear processes sustained by two vectors of the reciprocal lattice. In those special points of the fluorescence spectrum where the two processes coexist,we show that a tripartite entangled state is realized, equivalent to a single parametric process followed by a beam-splitter. By proper angle tuning a peculiar resonance condition is reached, with a transition to a 4-mode entanglement, dominated by the Golden Ratio of the segment $ϕ= (1+\sqrt 5)/2$. A maximal coherence between the two nonlinear processes is here estabilished, as the overall process is shown to be equivalent to two independent parametric processes followed by a beam-splitter. We offer an interpretation of the occurrence of the golden ratio in this system based on an analogy between the evolution of the light modes and the Fibonacci sequence.

quant-ph↗
arXiv2018

Theory of Kerr frequency combs in Fabry-Perot resonators

We derive a spatiotemporal equation describing nonlinear optical dynamics in Fabry-Perot (FP) cavities containing a Kerr medium. This equation is an extension of the equation that describes dynamics in Kerr-nonlinear ring resonators, referred to as the Lugiato-Lefever equation (LLE) due to its formulation by Lugiato and Lefever in 1987. We use the new equation to study the properties of Kerr frequency combs in FP resonators. The derivation of the equation starts from the set of Maxwell-Bloch equations that govern the dynamics of the forward and backward propagating envelopes of the electric field coupled to the atomic polarization and population difference variables in a FP cavity. The final equation is formulated in terms of an auxiliary field $ψ(z,t)$ that evolves over a slow time $t$ on the domain $-L \leq z \leq L$ with periodic boundary conditions, where $L$ is the cavity length. We describe how the forward and backward propagating field envelopes are obtained after solving the equation for $ψ$. This formulation makes the comparison between the FP and ring geometries straightforward. The FP equation includes an additional nonlinear term relative to the LLE for the ring cavity, with the effect that the value of the detuning parameter $α$ of the ring LLE is increased by twice the average of $|ψ|^2$. This feature establishes a connection between the stationary phenomena in the two geometries. For the FP-LLE, we discuss the linear stability analysis of the flat stationary solutions, analytic approximations of solitons, Turing patterns, and nonstationary patterns. We note that Turing patterns with different numbers of rolls may exist for the same values of the system parameters. We then discuss some implications of the nonlinear integral term in the FP-LLE for the kind of experiments which have been conducted in Kerr-nonlinear ring resonators.

physics.optics↗
arXiv2017

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.

quant-ph↗
arXiv2017

Heralding pure single photons: a comparision between counter-propagating and co-propagating twin photons

We investigate different strategies suitable to generate pure heralded single photons through spontaneous parametric down-conversion, comparing the counter-propagating geometry studied in [1] with more conventional co-propagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. Our analysis is based on the correlation of twin photons in the temporal domain,a non-standard approach that provides a physical view of the mechanisms that permit to eliminate the temporal entanglement of the state and to generate high-purity heralded photons. The Schmidt number associated to the temporal modes, which provides a more quantitative estimate of the purity, is then calculated. The efficiency of the various strategies and the individual properties of the heralded photons thereby generated are also compared.

quant-ph↗
arXiv2015

Critical behaviour of coherence and correlation of counterpropagating twin beams

This work analyses the temporal coherence and correlation of twin beams generated in a quasi-phase matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the MOPO (Mirrorless Optical Parametric Oscillator) threshold. Here we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible of the MOPO threshold.

quant-ph↗
arXiv2015

Temporal coherence and correlation of counterpropagating twin photons

This work analyses the temporal coherence and correlation of counterpropagating twin photons generated in a quasi-phase matched nonlinear cristal by spontaneous parametric-down conversion. We find out different pictures depending on the pump pulse duration relative to two characteristic temporal scales, determined respectively by the temporal separation between the counter-propagating and the co-propagating wavepackets. When the pump duration is intermediate between the two scales, we show a transition from a highly entangled state to an almost separable state, with strongly asymmetric spectral properties of the photons.

quant-ph↗
arXiv2014

Coherence properties of high-gain twin beams generated in pump-depletion regime

Twin-beam coherence properties are analyzed both in the spatial and spectral domains at high-gain regime including pump depletion. The increase of the size of intensity auto- and cross-correlation areas at increasing pump power is replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatio-spectral modes from $g^{(2)} $-function measurements confirms this explanation.

quant-ph↗
arXiv2014

Space-time coupling in the up-conversion of broadband down-converted light

We investigate the up-conversion process of broadband light from parametric down-conversion (PDC), focusing on the spatio-temporal spectral properties of the sum-frequency generated (SFG) radiation. We demonstrate that the incoherent component of the SFG spectrum is characterized by a skewed geometry in space-time, which originates from a compensation between the group-velocity mismatch and the spatial walk-off of the fundamental and the SFG fields. The results are illustrated both by a theoretical modeling of the optical system and by experimental measurements.

physics.optics↗
arXiv2014

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, analysed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.

quant-ph↗
arXiv2012

Disclosing the spatio-temporal structure of PDC entanglement through frequency up-conversion

In this work we propose and analyse a scheme where the full spatio-temporal correlation of twin photons/beams generated by parametric down-conversion is detected by using its inverse process, i.e. sum frequency generation. Our main result is that, by imposing independently a temporal delay Δt and a transverse spatial shift Δx between two twin components of PDC light, the up-converted light intensity provides information on the correlation of the PDC light in the full spatio-temporal domain, and should enable the reconstruction of the peculiar X-shaped structure of the correlation predicted in [gatti2009,caspani2010,brambilla2010]. Through both a semi-analytical and a numerical modeling of the proposed optical system, we analyse the feasibility of the experiment and identify the best conditions to implement it. In particular, the tolerance of the phase-sensitive measurement against the presence of dispersive elements, imperfect imaging conditions and possible misalignments of the two crystals is evaluated.

physics.optics↗