Unidimensional Time Domain Quantum Optics

Choosing the right first quantization basis in quantum optics is critical for the interpretation of experimental results. The usual frequency basis is, for instance, inappropriate for short, subcycle waveforms. Deriving first quantization in time domain shows that the electromagnetic field is not directly proportional, nor even causally related, to the photonic field (the amplitude probability of a photon detection). We derive the relation between the two and calculate the statistics of the electromagnetic field for specific states in time domain, such as the single photon Fock state. We introduce the dual of the Hamiltonian in time domain and extend the concept of quadratures to all first quantization bases.Comment: 4 pages, 3 figures; supplementary material: 6 pages, 1 figure; changes from version 1: discussion of results largely extende

Conception de sources non-classiques dans les fibres optiques

Les sources non-classiques constituent l'un des éléments indispensables à la réalisation d'un possible futur réseau global de télécommunications qui utiliserait la cryptographie quantique pour sécuriser les échanges. Dans ce travail, nous analysons, d'un point de vue aussi bien théorique que pratique, la conception de sources non-classiques dans les fibres optiques. Ces sources reposent sur des effets non-linéaires qui font apparaître des corrélations fortes entre photons. Des outils de calcul sont proposés pour analyser ces effets non-linéaires, y compris dans le cadre d'une pompe incohérente, ce qui constitue un élément original du travail ici présenté. L'aspect quantifié des sources est traité de manière originale au travers de ses implications statistiques. Là encore, des outils pratiques de conception sont développés. Ces outils permettent de déterminer à l'avance l'état quantique du signal en sortie de source. Enfin, ce travail met en avant des applications pratiques des concepts développés, avec en particulier la conception d'une nouvelle fibre et les premières étapes de la réalisation d'une source de photons intriqués en polarisation, fondée sur une instabilité de modulation vectorielle de type orthogonal, dans le domaine des longueurs d'ondes des réseaux de télécommunications.----------Abstract The goal of this work is to provide theoretical and experimental tools for the analysis of optical bre-based nonclassical sources. Strong correlations lie at the heart of nonclassical sources. In optical bers, these correlations are provided by nonlinear processes. The analysis of such processes requires a number of theoretical steps that are explored in this work. This includes a novel approach to treat the case of an incoherent pump, which may constitute the beginning of a comprehensive treatment of incoherent nonlinear optics. Instead of using the heavy quantum formalism to describe the discretized aspect of these sources, a statistical approach is favored. This approach enables a complete determination of the output quantum state, used as a predictor for the implemented source. The last part describes practical applications of all the concepts introduced in the work. In particular, we show the rst steps in the implementation of a source of polarization-entangled photons in the ber optics telecommunication bandwidth. This source is based on vectorial modulation instabilities with the polarization of the daughter photons orthogonal to that of the pump. The design requires the use of a novel optical ber that was developed in the course of this work

Direct measurement of the Husimi-Q function of the electric-field in the time-domain

We develop the theoretical tools necessary to promote electro-optic sampling to a time-domain quantum tomography technique. Our proposed framework implements detection of the time evolution of both the electric-field of a propagating electromagnetic wave and its Hilbert transform (quadrature). Direct detection of either quadrature is not strictly possible in the time-domain, detection efficiency approaching zero when an exact mode-matching to either quadrature is reached. As all real signals have a limited bandwidth, we can trace out the irrelevant sampling bandwidth to optimize the detection efficiency while preserving quantum information of the relevant signal. Through the developed understanding of the mode structure of the amplitude and Hilbert transform quadratures, we propose multiplexing and mode-matching operations on the gating function to extract full quantum information on both quantities, simultaneously. The proposed methology is poised to open a novel path toward quantum state tomography and quantum spectroscopy directly in the time domain.Comment: 9 pages, 7 figure

Photocount statistics of the Josephson parametric amplifier: a question of detection

Parametric amplifiers are known to squeeze the vacuum state of the electromagnetic field, which results in predictable statistics of the photocounts at their output. However, recent theoretical work arXiv:1112.4159 predicts a very different statistical distribution for an amplifier based on a Josephson junction. We test the hypothesis experimentally and recover the expected squeezed vacuum statistics. We explain this discrepancy by showing theoretically how the photocount statistics is dictated by the detection process, from single mode (our experiment) to multimode, fully resolved in frequency (as in arXiv:1112.4159).Comment: 5 pages, 5 figure

Limits of heralded single-photon sources based on parametric photon-pair generation

ABSTRACT: We derive calculations on the statistics of a heralded single-photon source based on parametric photon-pair generation. These calculations highlight fundamental and practical limits for these sources and show which physical parameters can be optimized to improve the quality of a real source

Observation of the spectral bifurcation in the Fractional Nonlinear Schr\"{o}dinger Equation

We report a comprehensive investigation and experimental realization of spectral bifurcations of ultrafast soliton pulses. These bifurcations are induced by the interplay between fractional group-velocity dispersion and Kerr nonlinearity (self-phase modulation) within the framework of the fractional nonlinear Schr\"{o}dinger equation. To capture the dynamics of the pulses under the action of the fractional dispersion and nonlinearity, we propose an effective `force' model based on the frequency chirp, which characterizes their interactions as either `repulsion', `attraction', or `equilibration'. By leveraging the `force' model, we design segmented fractional dispersion profiles that directly generate spectral bifurcations \{1\}$\rightarrow$ \{N\} at relevant nonlinearity levels. These results extend beyond the traditional sequence of bifurcations \{1\}$\rightarrow$ \{2\}$\rightarrow$ \{3\} ... $\rightarrow$ \{N\} associated with the growth of the nonlinearity. The experimental validation involves a precisely tailored hologram within a pulse shaper setup, coupled to an alterable nonlinear medium. Notably, we achieve up to N=5 in \{1\}$\rightarrow$ \{N\} bifurcations at a significantly lower strength of nonlinearity than otherwise would be required in a sequential cascade. The proposal for engineering spectral bifurcation patterns holds significant potential for ultrafast signal processing applications. As a practical illustration, we employ these bifurcation modes to optical data squeezing and transmitting it across a 100-km-long single-mode fiber.Comment: 16 pages and 5 figures; welcome comment

A microstructured fiber source of photon pairs at widely separated wavelengths

We demonstrate a source of photon pairs with widely separated wavelengths, 810 nm and 1548 nm, generated through spontaneous four-wave mixing in a microstructured fiber. The second-order auto-correlation function g^{(2)}(0) was measured to confirm the non-classical nature of a heralded single photon source constructed from the fiber. The microstructured fiber presented herein has the interesting property of generating photon pairs with wavelengths suitable for a quantum repeater able to link free-space channels with fiber channels, as well as for a high quality telecommunication wavelength heralded single photon source. It also has the advantage of straightforward coupling into optical fiber. These reasons make this photon pair source particularly interesting for long distance quantum communication.Comment: 3 pages, 3 figures. Published versio