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Fabrizio Illuminati

Publications and source records attributed to Fabrizio Illuminati.

At least 91 records · Page 5Linked to original sources
arXiv2003

Mixtures of Bosonic and Fermionic Atoms in Optical Lattices

We discuss the theory of mixtures of Bosonic and Fermionic atoms in periodic potentials at zero temperature. We derive a general Bose--Fermi Hubbard Hamiltonian in a one--dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean field criterion for the onset of a Bosonic superfluid transition. We investigate the ground state properties of the mixture in the Gutzwiller formulation of mean field theory, and present numerical studies of finite systems. The Bosonic and Fermionic density distributions and the onset of quantum phase transitions to demixing and to a Bosonic Mott--insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasi--degenerate ground states is related to a breaking of the mirror symmetry in the lattice.

cond-mat↗
arXiv2003

Stochastic collective dynamics of charged--particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by $λ_c\sqrt{N}$, where $N$ is the number of particles in the beam and $λ_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so--called ``quantum--like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam--field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

cond-mat.stat-mech↗
arXiv2003

A stochastic-hydrodynamic model of halo formation in charged particle beams

The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasi-stationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

cond-mat.stat-mech↗
arXiv2002

Critical temperature of Bose-Einstein condensation in trapped atomic Bose-Fermi mixtures

We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential to lowest order in both the Bose-Bose and Bose-Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson-boson and boson-fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.

cond-mat↗
arXiv2002

Hamiltonian models of multiphoton processes and four--photon squeezed states via nonlinear canonical transformations

We introduce nonlinear canonical transformations that yield effective Hamiltonians of multiphoton down conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton Hamiltonians. We study in detail the four-photon processes and the associated non-Gaussian four-photon squeezed states. The realization of squeezing, the behavior of the field statistics, and the structure of the phase space distributions show that these states realize a natural four-photon generalization of the two-photon squeezed states.

quant-ph↗
arXiv2002

Quantum field theory of dilute homogeneous Bose-Fermi-mixtures at zero temperature: general formalismand beyond mean-field corrections

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean-field stems from the boson-fermion interaction and is proportional to $a_{\scriptsize BF}k_{\scriptsize F}$. The total ground-state energy-density reads $E/V = ε_{\scriptsize F} + ε_{\scriptsize B} + (2π\hbar^{2}a_{\rm BF}n_{\scriptsize B}n_{\scriptsize F}/m) [1 + a_{\scriptsize BF}k_{\scriptsize F}f(δ)/π]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(δ)$ is a known function of $δ= (m_{\scriptsize B} - m_{\scriptsize F})/(m_{\scriptsize B} + m_{\scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.

cond-mat↗
arXiv2001

Quadrature-dependent Bogoliubov transformations and multiphoton squeezed states

We introduce a linear, canonical transformation of the fundamental single--mode field operators $a$ and $a^{\dagger}$ that generalizes the linear Bogoliubov transformation familiar in the construction of the harmonic oscillator squeezed states. This generalization is obtained by adding to the linear transformation a nonlinear function of any of the fundamental quadrature operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation quadrature--dependent. Remarkably, the conditions of canonicity do not impose any constraint on the form of the nonlinear function, and lead to a set of nontrivial algebraic relations between the $c$--number coefficients of the transformation. We examine in detail the structure and the properties of the new quantum states defined as eigenvectors of the transformed annihilation operator $b$. These eigenvectors define a class of multiphoton squeezed states. The structure of the uncertainty products and of the quasiprobability distributions in phase space shows that besides coherence properties, these states exhibit a squeezing and a deformation (cooling) of the phase--space trajectories, both of which strongly depend on the form of the nonlinear function. The presence of the extra nonlinear term in the phase of the wave functions has also relevant consequences on photon statistics and correlation properties. The non quadratic structure of the associated Hamiltonians suggests that these states be generated in connection with multiphoton processes in media with higher nonlinearities.

quant-ph↗
arXiv2001

Non-Newtonian Gravity, Fluctuative Hypothesis and the Sizes of Astrophysical Structures

We show that the characteristic sizes of astrophysical and cosmological structures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whose order of magnitude is essentially ruled by the Compton wavelength of the proton. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa correcting terms in the Newtonian potential which introduce typical interaction lengths. Furthermore, we are able to justify, in a straightforward way, the Sanders--postulated mass of a vector boson considered in order to obtain the characteristic sizes of galaxies.

gr-qc↗
arXiv2000

Dependence of the BEC transition temperature on interaction strength: a perturbative analysis

We compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93 aρ^{1/3}$, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and $ρ$ is the particle number density.

cond-mat.stat-mech↗
arXiv1999

Thermodynamic identities and particle number fluctuations in weakly interacting Bose--Einstein condensates

We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of {\it auxiliary partition functions} for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, at variance with the anomalous scaling behavior V^{4/3} of the fluctuations in the ideal Bose gas.

cond-mat↗
arXiv1999

Controlled quantum evolutions

We perform a detailed analysis of the non stationary solutions of the evolution (Fokker-Planck) equations associated to either stationary or non stationary quantum states by the stochastic mechanics. For the excited stationary states of quantum systems with singular velocity fields we explicitely discuss the exact solutions for the HO case. Moreover the possibility of modifying the original potentials in order to implement arbitrary evolutions ruled by these equations is discussed with respect to both possible models for quantum measurements and applications to the control of particle beams in accelerators.

quant-ph↗
arXiv1999

Stability and size of galaxies from Planck's constant

Stability and characterisitic geometrical and kinematical sizes of galaxies are strictly related to a minimal characteristic action whose value is of order $h$, the Planck constant. We infer that quantum mechanics, in some sense, determines the structure and the size of galaxies.

gr-qc↗
arXiv1999

Inference of Planck action constant by a classical fluctuative postulate holding for stable microscopic and macroscopic dynamical systems

The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary condition for classical chaotic fluctuations to affect confined dynamical systems, on any scale, ranging from microscopic to macroscopic domains. As a consequence we obtain, both for microscopic and macroscopic aggregates, dimensional relations defining the minimum unit of action of individual constituents, yielding in all cases Planck action constant.

quant-ph↗
arXiv1999

Broadband detection of squeezed vacuum: A spectrum of quantum states

We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the time domain we evaluated the first order correlation function of the squeezed output field, showing good agreement with the theory.

quant-ph↗
arXiv1998

Quantum Signature of Cosmological Large Scale Structures

We demonstrate that to all large scale cosmological structures where gravitation is the only overall relevant interaction assembling the system (e.g. galaxies), there is associated a characteristic unit of action per particle whose order of magnitude coincides with the Planck action constant $h$. This result extends the class of physical systems for which quantum coherence can act on macroscopic scales (as e.g. in superconductivity) and agrees with the absence of screening mechanisms for the gravitational forces, as predicted by some renormalizable quantum field theories of gravity. It also seems to support those lines of thought invoking that large scale structures in the Universe should be connected to quantum primordial perturbations as requested by inflation, that the Newton constant should vary with time and distance and, finally, that gravity should be considered as an effective interaction induced by quantization.

gr-qc↗
arXiv1998

A stochastic model for the semiclassical collective dynamics of charged beams in particle accelerators

A recent proposal (see quant-ph/9803068) to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations is applied to the specific instance of charged beam dynamics in particle accelerators. The resulting picture is that the collective beam dynamics, at the leading semiclassical order in Planck constant can be described by a particular diffusion process, the Nelson process, which is time-reversal invariant. Its diffusion coefficient $\sqrt{N}λ_{c}$ represents a semiclassical unit of emittance (here $N$ is the number of particles in the beam, and $λ_{c}$ is the Compton wavelength). The stochastic dynamics of the Nelson type can be easily recast in the form of a Schroedinger equation, with the semiclassical unit of emittance replacing Planck constant. Therefore we provide a physical foundation to the several quantum-like models of beam dynamics proposed in recent years. We also briefly touch upon applications of the Nelson and Schroedinger formalisms to incorporate the description of collective coherent effects.

physics.acc-ph↗
arXiv1997

Theory of controlled quantum dynamics

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.

quant-ph↗