Squeezed states generation in an array of Linear and Nonlinear Waveguides

We demonstrate the generation of squeezed states of light due to the second harmonic generation and Kerr effect in an array of nonlinear waveguides mediated through a linear one. We characterized the electromagnetic field by a quantum mechanical Hamiltonian and the density operator time evolution is obtained from the Von-Neumann equation of motion. Using the quasiprobability positive P of phase space representation, the classical Fokker-Planck equation is obtained from the master equation and translated to its classical matching set of nonlinear differential equations. We showed that because of the new possibilities of correlation between the linear and nonlinear channel waveguides, highly nonclassical light may be produced.

The two-spin model of a tracking chamber: a phase-space perspective

We study the dynamics of classical localization in a simple, one-dimensional model of a tracking chamber. The emitted particle is represented by a superposition of Gaussian wave packets moving in opposite directions, and the detectors are two spins in fixed, opposite positions with respect to the central emitter. At variance with other similar studies, we give here a phase-space representation of the dynamics in terms of the Wigner matrix of the system. This allows a better visualization of the phenomenon and helps in its interpretation. In particular, we discuss the relationship of the localization process with the properties of entanglement possessed by the system.

Automated classification of human lung sound signals using phase space representation of intrinsic mode function

Bronchiectasis and chronic obstructive pulmonary disease (COPD) are common human lung diseases. In general, the expert pulmonologistcarries preliminary screening and detection of these lung abnormalities by listening to the adventitious lung sounds. The present paper is an attempt towards the automatic detection of adventitious lung sounds ofBronchiectasis,COPD from normal lung sounds of healthy subjects. For classification of the lung sounds into a normaland adventitious category, we obtain features from phase space representation (PSR). At first, the empirical mode decomposition (EMD) is applied to lung sound signals to obtain intrinsic mode functions (IMFs). The IMFs are then further processed to construct two dimensional (2D) and three dimensional (3D) PSR. The feature space includes the 95% confidence ellipse area and interquartile range (IQR) of Euclidian distances computed from 2D and 3D PSRs, respectively. The process is carried out for the first four IMFs correspondings to normal and adventitious lung sound signals. The computed features depicta significant ability to discriminate the two categories of lung sound signals.To perform classification, we use the least square support vector machine with two kernels, namely, polynomial and radial basis function (RBF).Simulation outcomes on ICBHI 2017 lung sound dataset show the ability of the proposed method in effectively classifying normal and adventitious lung sound signals. LS-SVM is employing RBF kernel provides the highest classification accuracy of 97.67 % over feature space constituted by first, second, and fourth IMF.

Inverse ray mapping in phase space for two-dimensional reflective optical systems

A new method to compute the target photometric variables of non-imaging optical systems is presented. The method is based on the phase space representation of each surface that forms the optical system. All surfaces can be modeled as detectors of the incident light and emitters of the reflected light. Moreover, we assume that the source can only emit light and the target can only receive light. Therefore, one phase space is taken into account for the source and one for the target. For the other surfaces both the source and target phase spaces are considered. The output intensity is computed from the rays that leave the source and hit the target. We implement the method for two-dimensional optical systems, and we compare the new method with Monte Carlo (MC) ray tracing. This paper is a proof of principle. Therefore, we present the results for systems formed by straight lines which are all located in the same medium. Numerical results show that the intensity found with the ray mapping method equals the exact intensity. Accuracy and speed advantages of several orders are observed with the new method.

From the Bloch Sphere to Phase-Space Representations with the Gottesman–Kitaev–Preskill Encoding

In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman–Kitaev–Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity corresponds to encoded stabilizer states, while the maximum negativity is associated with the most non-stabilizer states, H-type and T-type quantum states.

Symplectic Schrödinger equation for many-body systems

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

PSR-based research of feature extraction from one-second EEG signals: a neural network study

The speed and accuracy of signal classification are the most valuable parameters to create real-time systems for interaction between the brain and the computer system. In this work, we propose a schema of the extraction of features from one-second electroencephalographic (EEG) signals generated by facial muscle stress. We have tested here three sorts of EEG signals. The signals originate from different facial expressions. The phase-space reconstruction (PSR) method has been used to convert EEG signals from these three classes of facial muscle tension. For further processing, the data has been converted into a two-dimensional (2D) matrix and saved in the form of color images. The 2D convolutional neural network (CNN) served to determine the accuracy of the classifications of the previously unknown PSR generated images from the EEG signals. We have witnessed an improvement in the accuracy of the signal classification in the phase-space representation. We have found that the CNN network better classifies colored trajectories in the 2D phase-space graph. At the end of this work, we compared our results with the results obtained by a one-dimensional convolution neural network.