Interaction-based nonlinear quantum metrology with a cold atomic ensemble

In this manuscript we present an experimental and theoretical investigation of quantum-noise-limited measurement by nonlinear interferometry, or from another perspective, quantum-noise-limited interaction-based measurement. The experimental work is performed using a polarization-based quantum interface between propagating light pulses and cold rubidium-87 atoms trapped in an optical dipole trap. We first review the theory of quantum metrology and estimation theory, and we describe theoretical proposals for nonlinear quantum metrology as developed by the group of Carlton M. Caves in the University of New Mexico. We then describe our proposal, made in 2010, to implement the Caves group's ideas using nonlinear optical interactions in a cold atomic ensemble to implement a nonlinear spin measurement. To evaluate this proposal we develop two theoretical approaches, first an extension of the collective quantum variables approach, often employed to describe quantum interfaces and atomic spin ensembles, to nonlinear optical processes. This results in an effective Hamiltonian containing nonlinear terms of the form described by the Caves group, and demonstrates a qualitative equivalence of the two schemes. The second approach uses the Maxwell-Bloch equations to describe nonlinear propagation of pulses through an atomic spin ensemble, including inhomogeneities and relaxation effects. This latter method makes quantitative predictions about optical rotation signals under realistic experimental conditions. We then describe the implementation of the proposal in a polarization-based light-atom quantum interface. We describe the existing trapping and probing system, focusing on the characteristics that make it suitable for shot-noise-limited and projection-noise-limited atomic spin measurements. We then describe adaptations to use the apparatus with shorter, higher-intensity pulses as required for nonlinear measurement, as well as characterization of the photodetection system under these modified conditions. Calibration of the nonlinear polarization rotation versus probe laser detuning allows us to produce a nearly pure nonlinear rotation signal. Finally, experimental results are presented showing shot-noise-limited nonlinear rotation signals over three orders of magnitude in photon number N. The results are consistent with our theoretical models and confirm a major prediction of the Caves group's work, in that a two-photon interaction gives a scaling for the measurement sensitivity as N^{-3/2}. A brief discussion relates this experimental observation to theoretical discussions of the ¿Heiseinberg limit¿ of quantum metrology, and possible further applications of nonlinear measurement techniques.En aquest manuscrit presentem una recerca experimental i teòrica sobre mesures limitades pel soroll quàntic fetes mitjançant interferometria no lineal, o des de un altra perspectiva, mitjançant interacció. En el treball experimental es va fer servir una interfície quàntica de polarització entre polsos de llum en propagació i àtoms freds de rubidi-87 atrapats en una trampa òptica de dipol. Primer, farem un repàs de la teoria de la metrologia quàntica i de la teoria de la estimació, descriurem la proposició teòrica sobre metrologia quàntica no lineal tal i com la va desenvolupar el grup de Carlton M. Caves al Universitat de Nou Mèxic. A continuació descriurem la nostra proposta, feta al 2010, de com implantar la idea del grup de Caves fent servir interaccions òptiques no lineals en un conjunt d’àtoms freds amb la finalitat d’efectuar una mesura no lineal de spin. Per avaluar aquesta proposta vam desenvolupar dues aproximacions teòriques fent ús de dos mètodes diferents. En primer lloc vam estendre la tècnica de variables quàntiques col lectives cap als processos òptics no lineals, aquesta tècnica sovint és utilitzada per descriure interfícies quàntiques i conjunts de spin atòmics. Això dóna com a resultat un Hamiltonià efectiu que conté termes no lineals de la forma descrita pel grup de Caves, i demostra una equivalència qualitativa entre el nostre esquema i el seu. El segon mètode fa ús de les equacions de Maxwell-Bloch per descriure la propagació no lineal dels polsos a través del conjunt de spins atòmics, tenint en compte deshomogeneïtats i efectes de relaxació. D’aquesta manera podem fer prediccions quantitatives sobre senyals de rotació de polarització òptica en les condicions d’un experiment real. Seguirem amb la descripció de com vam implementar al laboratori la nostra proposta teòrica mitjançant una interfície quàntica de polarització entre llum i àtoms. Descriurem el ja existent sistema de confinament i sondeig dels àtoms, concentrant-nos en les característiques que permeten fer mesures al limit del soroll quàntic i del soroll de projecció. Aleshores detallarem com vam adaptar el sistema per l’ús amb polsos més curts i intensos, tal i com requereix la mesura no lineal, i al mateix temps com vam calibrar el sistema de detecció de llum en aquestes diferents condicions. El calibratge de la rotació no lineal de polarització en funció de la freqüència del làser de sonda, ens permet obtenir un senyal de rotació casi purament no lineal. Finalment, presentarem els resultats experimentals que mostren senyals de rotació no lineal limitats pel soroll quàntic al llarg de tres ordres de magnitud en el número N de fotons. Tals resultats son consistents amb els nostres models teòrics i confirmen una important predicció del treball del grup de Caves, és a dir que la interacció de dos fotons dóna una llei d’escala de N-3/2 per a la sensibilitat de la mesura. Per concloure, una concisa discussió relaciona aquesta observació experimental amb discussions teòriques sobre el “limit d’Heisenberg” de la metrologia quàntica, i amb d’altres possibles aplicacions de tècniques de mesura no linea

Experimental Analysis of Neural Approaches for Synthetic Angle-of-Attack Estimation

Synthetic sensors enable flight data estimation without devoted physical sensors. Within modern digital avionics, synthetic sensors can be implemented and used for several purposes such as analytical redundancy or monitoring functions. The angle-of-attack, measured at air data system level, can be estimated using synthetic sensors exploiting several solutions, e.g. model-based, data-driven and model-free state observers. In the class of data-driven observers, multilayer perceptron neural networks are widely used to approximate the input-output mapping angle-of-attack function. Dealing with experimental flight test data, the multilayer perceptron can provide reliable estimation even though some issues can arise from noisy, sparse and unbalanced training domain. An alternative is offered by regularisation networks, such as radial basis function, to cope with training domain based on real flight data. The present work's objective is to evaluate performances of a single layer feed-forward generalised radial basis function network for AoA estimation trained with a sequential algorithm. The proposed analysis is performed comparing results obtained using a multilayer perceptron network adopting the same training and validation data

Polarization-based Light-Atom Quantum Interface with an All-optical Trap

We describe the implementation of a system for studying light-matter interactions using an ensemble of $10^6$ cold rubidium 87 atoms, trapped in a single-beam optical dipole trap. In this configuration the elongated shape of the atomic cloud increases the strength of the collective light-atom coupling. Trapping all-optically allows for long storage times in a low decoherence environment. We are able to perform several thousands of measurements on one atomic ensemble with little destruction. We report results on paramagnetic Faraday rotations from a macroscopically polarized atomic ensemble. Our results confirm that strong light-atom coupling is achievable in this system which makes it attractive for single-pass quantum information protocols.Comment: 8 pages, 4 figure

AMICO galaxy clusters in KiDS-DR3: weak-lensing mass calibration

We present the mass calibration for galaxy clusters detected with the AMICO code in KiDS DR3 data. The cluster sample comprises $\sim$ 7000 objects and covers the redshift range 0.1 < $z$ < 0.6. We perform a weak lensing stacked analysis by binning the clusters according to redshift and two different mass proxies provided by AMICO, namely the amplitude $A$ (measure of galaxy abundance through an optimal filter) and the richness $\lambda^*$ (sum of membership probabilities in a consistent radial and magnitude range across redshift). For each bin, we model the data as a truncated NFW profile plus a 2-halo term, taking into account uncertainties related to concentration and miscentring. From the retrieved estimates of the mean halo masses, we construct the $A$-$M_{200}$ and the $\lambda^*$-$M_{200}$ relations. The relations extend over more than one order of magnitude in mass, down to $M_{200} \sim 2 (5) \times 10^{13} M_\odot/h$ at $z$ = 0.2 (0.5), with small evolution in redshift. The logarithmic slope is $\sim 2.0$ for the $A$-mass relation, and $\sim 1.7$ for the $\lambda^*$-mass relation, consistent with previous estimations on mock catalogues and coherent with the different nature of the two observables.Comment: 19 pages, 16 figures, accepted by MNRA

Neurophysiological Measures and Alcohol Use Disorder (AUD): Hypothesizing Links between Clinical Severity Index and Molecular Neurobiological Patterns

In 1987, Cloninger proposed a clinical description and classification of different personality traits genetically defined and independent from each other. Moreover, he elaborated a specific test the TCI to investigate these traits/states. The study of craving in Alcohol Use Disorder (AUD) assumed a greater significance, since ever more data seems to suggest a direct correlation between high levels of craving and a higher risk of relapse in alcoholics. Thus, our study aim is to explore the possible correlations among TCI linked molecular neurobiological pattern (s), craving and alcohol addiction severity measures in a sample of Italian alcoholics

Statistical analysis of probability density functions for photometric redshifts through the KiDS-ESO-DR3 galaxies

Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because it is difficult to accurately assess the contribution from different sources of errors, namely internal to the method itself and from the photometric features defining the available parameter space. Second, because the problem of defining a robust statistical method, always able to quantify and qualify the PDF estimation validity, is still an open issue. We present a comparison among PDFs obtained using three different methods on the same data set: two ML techniques, METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) and ANNz2, plus the spectral energy distribution template fitting method, BPZ. The photometric data were extracted from the KiDS (Kilo Degree Survey) ESO Data Release 3, while the spectroscopy was obtained from the GAMA (Galaxy and Mass Assembly) Data Release 2. The statistical evaluation of both individual and stacked PDFs was done through quantitative and qualitative estimators, including a dummy PDF, useful to verify whether different statistical estimators can correctly assess PDF quality. We conclude that, in order to quantify the reliability and accuracy of any zphot PDF method, a combined set of statistical estimators is required.Comment: Accepted for publication by MNRAS, 20 pages, 14 figure

Interval Fuzzy Model for Robust Aircraft IMU Sensors Fault Detection

This paper proposes a data-based approach for a robust fault detection (FD) of the inertial measurement unit (IMU) sensors of an aircraft. Fuzzy interval models (FIMs) have been introduced for coping with the significant modeling uncertainties caused by poorly modeled aerodynamics. The proposed FIMs are used to compute robust prediction intervals for the measurements provided by the IMU sensors. Specifically, a nonlinear neural network (NN) model is used as central prediction of the sensor response while the uncertainty around the central estimation is captured by the FIM model. The uncertainty has been also modelled using a conventional linear Interval Model (IM) approach; this allows a quantitative evaluation of the benefits provided by the FIM approach. The identification of the IMs and of the FIMs was formalized as a linear matrix inequality (LMI) optimization problem using as cost function the (mean) amplitude of the prediction interval and as optimization variables the parameters defining the amplitudes of the intervals of the IMs and FIMs. Based on the identified models, FD validation tests have been successfully conducted using actual flight data of a P92 Tecnam aircraft by artificially injecting additive fault signals on the fault free IMU readings

Robustness against parametric noise of non ideal holonomic gates

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev.

Air Data Sensor Fault Detection with an Augmented Floating Limiter

Although very uncommon, the sequential failures of all aircraft Pitot tubes, with the consequent loss of signals for all the dynamic parameters from the Air Data System, have been found to be the cause of a number of catastrophic accidents in aviation history. This paper proposes a robust data-driven method to detect faulty measurements of aircraft airspeed, angle of attack, and angle of sideslip. This approach first consists in the appropriate selection of suitable sets of model regressors to be used as inputs of neural network-based estimators to be used online for failure detection. The setup of the proposed fault detection method is based on the statistical analysis of the residual signals in fault-free conditions, which, in turn, allows the tuning of a pair of floating limiter detectors that act as time-varying fault detection thresholds with the objective of reducing both the false alarm rate and the detection delay. The proposed approach has been validated using real flight data by injecting artificial ramp and hard failures on the above sensors. The results confirm the capabilities of the proposed scheme showing accurate detection with a desirable low level of false alarm when compared with an equivalent scheme with conventional “a priori set” fixed detection thresholds. The achieved performance improvement consists mainly in a substantial reduction of the detection time while keeping desirable low false alarm rates