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Quantum Optics in 2D Nonlinear Lattices

Katarina Stensson

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In this work the properties of light produced by spontaneous parametric downconversion (SPDC) in 2D nonlinear lattices have been studied. A quantum mechanical model of 2D SPDC was formulated, solved in the general case, and analyzed in the special case when two di erent signals are coupled as a consequence of their idlers being degenerate in frequency and spatial propagation. According to the model these 'twin signals' are correlated in phase and amplitude, and the gain coe cient of the coupled processes enhanced by a factor √ 2. The analytically derived correlations and the gain enhancement was supported experimentally by measurements on a hexagonal lattice in a LiTaO3 crystal.

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In this work the properties of light produced by spontaneous parametric downconversion (SPDC) in 2D nonlinear lattices have been studied. A quantum mechanical model of 2D SPDC was formulated, solved in the general case, and analyzed in the special case when two di erent signals are coupled as a consequence of their idlers being degenerate in frequency and spatial propagation. According to the model these 'twin signals' are correlated in phase and amplitude, and the gain coe cient of the coupled processes enhanced by a factor √ 2. The analytically derived correlations and the gain enhancement was supported experimentally by measurements on a hexagonal lattice in a LiTaO3 crystal.
We review recent experimental and theoretical progress in the study of optical parametric generation and cascaded frequency up conversion in two-dimensional purely nonlinear lattices, relying on acoherent coupling of multiple resonances in the quadratic lattice. Since their original proposal (1), two dimensional (2D) nonlinear photonic crystals in periodically poled materials have been the subject of a number of experimental and theoretical investigations, exploring the enhanced possibilities to engineer the nonlinear dynamics of quadratic interactions afiorded in such structures (2,3). Most of the studies have concerned frequency up-conversion, until the recent demonstration of twin-beam optical parametric generation (TB-OPG) in 2D hexagonally poled crystals (4,5). TB-OPG experiments in hexagonally poled MgO:LiTaO3 lattices demonstrated enhanced para- metric gains as well as a rich spectral and angular response underpinned bythe coherent coupling of concurrent nonlinear processes throughshared signal or idlermodes. They provided evidence forrich interaction scenarios, generating multiple outputs in the infrared as well in the visible and encompassing also self-phase modulation and cascaded upconversion processes arising from the interplay of multiple lattice resonances.A good agreement was found with a simple model in- volving the cross-seeding of two non-collinear OPG processes via a common signal (idler), while the development of advanced ad-hoc simulation tools enabled to fully account for the complex nonlinear dynamics in the 2D lattices and faithfully reproduce the rich spectral-angular response seen in the experiments (6).
We propose a novel scheme for the all-optical quantum simulation of topological phases by means of implementation of a discrete-time quantum walk architecture. The main novel ingredient is the inclusion of the nonlinear process of spontaneous parametric downconversion (SPDC) along the quantum network. By means of a simple theoretical model, the interplay between quantum walk lattice topology and spatial correlations of biphotons produced by SPDC is numerically explored. We describe different optical detection methods suitable for the implementation of our proposed experimental scheme.
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
In this paper we study photon pairs generated in a nonlinear cavity composed of a nonlinear crystal surrounded by mirrors, by the process of spotaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness from the presence of the cavity.
Single-photon and correlated two-photon sources are important elements for optical information systems. Nonlinear downconversion light sources are robust and stable emitters of single photons and entangled photon pairs. However, the rate of downconverted light emission, dictated by the properties of low-symmetry nonlinear crystals, is typically very small, leading to significant constraints in device design and integration. In this Letter, we study principles of spontaneous emission control (i.e., the Purcell effect) generalized to describe the enhancement of nonlinear generation of quantum light through spontaneous parametric downconversion. We develop a theoretical framework based on eigenmode analysis to study quantum nonlinear emission in a general anisotropic, dispersive, and lossy media. Our theory provides an unprecedented insight into the emission process. We find that spontaneous parametric downconversion in a media with hyperbolic dispersion is broadband and phase-mismatch-free. We further predict a significant enhancement of the downconverted emission rate in experimentally realistic nanostructures. Our theoretical formalism and approach to Purcell enhancement of nonlinear optical processes provides a framework for description of quantum nonlinear optical phenomena in complex nanophotonic structures.