Related papers: Eigenstates of Linear Combinations of Phase Operat…
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…
We construct a new class of coherent states labeled by points z of the complex plane and depending on three numbers (gamma, nu) and epsilon positive by replacing the coefficients of the canonical coherent states by Laguerre polynomials.…
We present a Gaussian state description of squeezed light generated in an optical parametric oscillator. Using the Gaussian state description we describe the dynamics of the system conditioned on homodyne detection on the output field. Our…
Projected squeezed (PS) states are multipartite entangled states generated by unitary spin squeezing, followed by a collective quantum measurement and post-selection. They can lead to an appreciable decrease in the state preparation time of…
We show that a class of even and odd nonlinear coherent states, defined as the eigenstates of product of a nonlinear function of the number operator and the square of the boson annihilation operator, can be generated in the center-of-mass…
For decades, most research on high harmonic generation (HHG) considered matter as quantum but light as classical, leaving the quantum-optical nature of the harmonics an open question. Here we explore the quantum properties of high…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
We report mixed lag synchronization in coupled counter-rotating oscillators. The trajectories of counter-rotating oscillators has opposite directions of rotation in uncoupled state. Under diffusive coupling via a scalar variable, a mixed…
Susskind-Glogower coherent states, whose Fock expansion coefficients include Bessel functions, have recently attracted considerable attention for their optical properties. Nevertheless, identity resolution is still an open question, which…
We show how sub-Planck phase-space structures in the Wigner function can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent…
The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The evolution of the star is supposed to be governed by the Euler-Poisson equations…
We consider the phase space for a system of $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$ points and use the finite field $GF(d^{n})$ to label the corresponding axes. The…
We prove that temporal control of the strengths of springs connecting $N$ harmonic oscillators in a chain provides complete access to all Gaussian states of $N-1$ collective modes. The proof relies on the construction of a suitable basis of…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$,…
The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different…
We investigate how entangled coherent states and superpositions of low intensity coherent states of non-Gaussian nature can be generated via non-resonant interaction between either two linearly or circularly polarized field modes and an…
In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in…
Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a novel non commutative…