R. Fedele

New uncertainty relations for tomographic entropy: application to squeezed states and solitons

Abstract.nUsing the tomographic probability distribution (symplectic tomogram)ndescribing the quantum state (instead of the wave function orndensity matrix) and properties of recently introduced tomographicnentropy associated with the probability distribution, the newnuncertainty relation for the tomographic entropy is obtained.nExamples of the entropic uncertainty relation for squeezed statesnand solitons of the Bose-Einstein condensate are considered.nn

Probability representation and new entropic uncertainty relations for symplectic and optical tomograms

Entropic uncertainty relations for Shannon entropies associated with tomographic probability distributions of continuous quadratures are reviewed. New entropie uncertainty relations in the form of inequalities for integrals containing the tomograms of quantum states and deformation parameter are obtained.

Quantum ring solitons and nonlocal effects in plasma wake field excitations

A theoretical investigation of the quantum transverse beam motion for a cold relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma is carried out. This is done by taking into account both the individual quantum nature of the beam particles (single-particle uncertainty relations and spin) and the self consistent interaction generated by the plasma wake field excitation. By adopting a fluid model of a strongly magnetized plasma, the analysis is carried out in the overdense regime (dilute beams) and in the long beam limit. It is shown that the quantum description of the collective transverse beam dynamics is provided by a pair of coupled nonlinear governing equations. It comprises a Poisson-like equation for the plasma wake potential (driven by the beam density) and a 2D spinorial Schrodinger equation for the wave function, whose squared modulus is proportional to the beam density, that is obtained in the Hartrees mean field approximation, after disregarding the ...

Controlling potential traps for filtering solitons in Bose-Einstein condensates

We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).

Tomography of solitons

We develop the tomographic representation of wavefunctions which are solutions of the generalized nonlinear Schrodinger equation (NLSE) and show its connection with the Weyl–Wigner map. The generalized NLSE is presented in the form of a nonlinear Fokker–Planck-type equation for the standard probability distribution function (tomogram). In particular, this theory is applied to solitons, where tomograms for envelope bright solitons of a family of modified NLSEs are presented and numerically evaluated. Examples of symplectic tomography and Fresnel tomography of linear and nonlinear signals are discussed.

Modification of the Ion Background Profile in the Nonlinear Electron Plasma Oscillations

We give an approximate analytical solution, correct to the first order in m/M, the electron to ion mass ratio, for the ion background modification under the influence of the free non linear electron plasma oscillations driven by the initial unbalance between electron and ion density distribution, ne(x, 0) = n0 and ni(x, 0) = n0(1 + α cos kx). When the electron plasma oscillations grow starting from a very small perturbation (α 0.02), we find a remarkable modification in the ion background profile before the electron oscillation wavebreaking takes place.

Quantum Tomography, Wave Packets and Solitons

The wave packets, both linear and nonlinear (like solitons) signals described by a complex time-dependent function, are mapped onto positive probability distributions (tomograms). The quasidistributions, wavelets, and tomograms are shown to have an intrinsic connection. The analysis is extended to signals obeying to the von Neumann-like equation. For solitons (nonlinear signals) obeying the nonlinear Schrodinger equation, the tomographic probability representation is introduced. It is shown that in the probability representation the soliton satisfies a nonlinear generalization of the Fokker–Planck equation. Solutions to the Gross–Pitaevskii equation corresponding to solitons in a Bose–Einstein condensate are considered.

Entropic uncertainty relations for electromagnetic beams

The symplectic tomograms of two-dimensional (2D) Hermite–Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of electromagnetic–radiation modes. Furthermore, entropic uncertainty relations associated with these tomograms are found and applied to establish the compatibility conditions of the field profile properties with Hermite–Gauss beam description. Numerical evaluations for some Hermite–Gauss modes illustrating the corresponding entropic uncertainty relations are finally given.

Charged-particle-beam propagator in wave-electron optics: phase-space and tomographic pictures

Within the framework of the thermal-wave model, the quantumlike description of electron optics in terms of the propagator is given. First we briefly review the standard description in configuration space by analogy to quantum mechanics and in connection with recent investigations of charged-particle-beam transport that have used the concept of propagator. Then new insights are given by extension of the analysis of the particle-beam propagator to the phase-space context for which our system is described by the Wigner quasi-distribution function, as well as to the tomography context for which our system is described by the marginal distribution. Furthermore, the integrals of motion of a charged-particle beam and their relation to the propagator concept are discussed. Finally, the perturbation theory for a charged-particle-beam propagator is developed in the above-described two contexts and is applied to some simple optical devices.

Coherent states for particle beams in the thermal wave model

In this paper, by using an analogy among quantum mechanics, electromagnetic beam optics in optical fibers, and charge particle beam dynamics, we introduce the concept of coherent states for charged particle beams in the framework of the Thermal Wave Model (TWM). We give a physical meaning of the Gaussian-like coherent structures of charged particle distribution that are both naturally and artificially produced in an accelerating machine in terms of the concept of coherent states widely used in quantum mechanics and in quantum optics. According to TWM, this can be done by using a Schrodinger-like equation for a complex function, the so-called beam wave function (BWF), whose squared modulus is proportional to the transverse beam density profile, where Plancks constant and the time are replaced by the transverse beam emittance and by the propagation coordinate, respectively. The evolution of the particle beam, whose initial BWF is assumed to be the simplest coherent state (ground-like state) associated with the beam, in an infinite 1-D quadrupole-like device with small sextupole and octupole aberrations, is analytically and numerically investigated.