Distribution In Momentum Space Research Articles

Gain-Induced Trapping of Microcavity Exciton Polariton Condensates

We have performed real and momentum space spectroscopy of exciton polariton condensates in a GaAs-based microcavity under nonresonant excitation with an intensity-stabilized laser. An effective trapping mechanism is revealed, which is due to the stimulated scattering gain inside the finite excitation spot combined with the short lifetime. We observe several quantized modes while the lowest state shows Heisenberg-limited real and momentum space distributions. The experimental findings are qualitatively reproduced by an open dissipative Gross-Pitaevskii equation model.

Coherent control in the classical limit: Symmetry breaking in an optical lattice

The quantum-to-classical transition of a symmetry-breaking coherent control scenario is computationally demonstrated in an optical lattice arrangement. Control is shown to survive in the classical limit and, for small effective $\ensuremath{\hbar}$, to be comparable in magnitude to quantum control. Moderate decoherence is seen to eliminate structure from the momentum space distribution, but not to cause loss of control. The proposed scenario is designed so as to be demonstrable experimentally in a moving or shaken one-dimensional optical lattice.

Comparative characterization of two-electron wavefunctions using information-theory measures

Information-theory measures, in particular the Shannon entropy, Fisher information and statistical complexity, are used to discuss the variations among several commonly encountered model two-electron correlated wavefunctions. The Hookean, Moshinsky, and three-parameter Chandrasekhar wavefunctions are considered in real and momentum space, with further comparisons to the Hookean–Hartree–Fock (HF) wavefunction of Ragot, the numerical HF limit, and the hydrogenic (pure Coulomb) limit. The purpose of the study is to quantitatively analyze the effect of different models for inclusion of electron–electron correlation on information-theoretical measures, including statistical complexity, which characterize the electron distribution in position and momentum space.

Landau damping in relativistic plasmas with power-law distributions and applications to solar wind electrons

The relativistic plasma dispersion relation is derived for Langmuir waves in a spatially homogeneous unmagnetized plasma in which the electrons have an isotropic power-law distribution in momentum space. The theory is applied to the study of Langmuir waves in the quiescent solar wind near the orbit of the Earth assuming that the electron distribution function can be approximated as a power-law from thermal energies ∼10eV to relativistic energies ≳100keV. Numerical solutions of the dispersion relation show that in the regime of weak Landau damping the phase speeds of the waves match the velocities of the high-energy particles, known in the solar wind literature as the superhalo, which lie in the range 0.09<v∕c<0.8. While this result raises the question of whether wave-particle interactions with a spectrum of Langmuir waves plays a role in the formation of the superhalo, the observed energy density of the waves near the orbit of the Earth at 1AU is so small that active acceleration of superhalo electrons by Langmuir waves, if it occurs at all, has ceased by the time the solar wind reaches the Earth.

Collective High Frequency Motions in Liquid Deuterium Fluoride

Abstract The collective motions in liquid deuterium fluoride (DF) have been investigated by neutron scattering motivated by a MD simulation, which predicted an optic-type mode at small momentum transfers. Spectra of the measured longitudinal current correlation function show two modes. The lower frequency one originates from acoustic-type movements. The intensity of the higher frequency excitation can be attributed to an out of phase motion of neighboring DF molecules, an optic-type mode. Both, the frequencies and the intensity distribution in momentum space agree well with the MD simulation. The widths of the experimental spectra exceed the widths from the MD simulation and indicate missing relaxation processes in the simulation.

Statistical properties of experimental coherent waves in microcavity lasers: Analogous study of quantum billiard wave functions

We use a microcavity laser to explore the properties of experimental coherent waves as an analogous study of the chaotic wave functions in quantum billiards. With the eigenstate expansion method, the experimental high-order chaotic coherent waves are well reconstructed. The reconstructed wave functions are employed to calculate the field and intensity correlations. It is found that the spreading of k-space (momentum space) distribution leads to not only wave localization in coordinate space but also enhancement of long-range correlations.

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q2/(2C) and p2/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively.

Localization in the quantum sawtooth map emulated on a quantum-information processor

Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.

THE PHYSICS OF LIQUID PARA-HYDROGEN

Macroscopic systems of hydrogen molecules exhibit a rich thermodynamic phase behavior. Due to the simplicity of the molecular constituents a detailed exploration of the thermal properties of these boson systems at low temperatures is of fundamental interest. Here, we report theoretical and experimental results on various spatial correlation functions and corresponding distributions in momentum space of liquid para-hydrogen close to the triple point. They characterize the structure of the correlated liquid and provide information on quantum effects present in this Bose fluid. Numerical calculations employ Correlated Density-Matrix (CDM) theory and Path-Integral Monte-Carlo(PIMC)simulations. A comparison of these theoretical results demonstrates the accuracy of CDM theory. This algorithm therefore permits a fast and efficient quantitative analysis of the normal phase of liquid para-hydrogen. We compare and discuss the theoretical results with available experimental data.

P.042 The use of miniplate osteosynthesis for skeletal anchorage

With the aim of discussing recent conflicting views of configurational entropy in frozen-in systems, we begin this paper with a brief review of the history of the entropy concept. Whereas the ‘conventional’ view of entropy had been elaborated after long and heated debates, a recently proposed ‘kinetic’ view has denied the existence of residual entropy in amorphous systems. We thus examine the validity of the ‘conventional’ view and then propose a more complete picture of the glassy state from the complementary roles of two conflicting views. Above all, we analyze the consistency of the ‘spatial sampling’ method and the difference from the other two methods by using three simple models and thought experiments. Our first conclusion is that, as defined for non-equilibrium systems within the framework of thermodynamics, entropy remains an objective state variable for which an observation time needs not to be specified. The second is that, owing to its extensive nature, entropy is in fact strongly linked to the distribution in configuration and momentum space rather than to temporal integration. As an obvious consequence, the degree of structural disorder remains an essential issue in glass thermodynamics. The third is that the new concepts of magnitude and phase factor of entropy indicate that the ‘conventional’ view, according to which configurational entropy does not vanish in irreversibly frozen-in systems, is not only consistent with thermodynamic theory and available data, but also accounts for kinetic effects such as fluctuation phenomena. With the concept of phase factor of entropy, the number of phase factors visited during the observation time in the ‘conventional’ view turns to be almost equivalent to the entropy value defined by the ‘kinetic’ view. Finally, non-zero values of residual entropies measured by calorimetry based on the ‘conventional’ view are real and useful features that have a fundamental bearing on the physics and chemistry of real crystals and glasses. The ‘kinetic’ view is also a useful tool as well to understand the kinetic effects, such the rapid slowdown from liquids to glass and the glass transition. It is strongly hoped that a complete picture of the glassy state will be advanced further.

APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

Subshell-pair correlation coefficients of atoms in momentum space

Angular correlation coefficients τnl,n^′ l^′ [p] between linear momenta of an electron in a subshell nl and another electron in a subshell n′ l′ are studied for the 102 neutral atoms He through Lr in their ground states, where n and l are the principal and azimuthal quantum numbers, respectively. We theoretically find that electron momenta are negatively correlated or uncorrelated; τnl,n^′ l^′ [p] < 0 when |l − l′|=1, while τnl,n^′ l^′ [p]=0 when |l − l′| ≠ 1. Numerical examinations of the atoms show that except for the He–B atoms, negative correlations are largest between 1s and 2p subshells, which have the most diffuse electron distributions in momentum space.

Polariton correlation in microcavities produced by parametric scattering

AbstractThe spontaneous and self‐stimulated parametric emission from a semiconductor microcavity after resonant pulsed excitation is measured. The emission of the lower polariton branch is resolved in two‐dimensional momentum space, using either time‐resolved or spectrally resolved detection. The polariton–polariton scattering dynamics is generally in good agreement with the theory using the nonlinearity due to the excitonic part and the dispersion due to the photonic part of the polariton. The peculiar figure‐8 shaped distribution in momentum space of the final states of the parametric scattering is observed. Renormalization of the dispersion due to the bound biexciton state is found to influence the final state distribution. Using two pump directions the shape of the final state distribution can be changed to a peanut or oval for the mixed parametric processes. In this dual pump configuration, we find that polaritons in two distinct idler‐modes interfere if and only if they share the same signal‐mode, showing the existence of polariton pair correlations that store the “which‐way” information. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Summary of experimental studies, at CERN, on a positron source using crystal effects

A new kind of positron sources for future linear colliders, where the converter is an aligned tungsten crystal, oriented on the 〈111〉-axis, has been studied at CERN in the WA103 experiment with tertiary electron beams from the SPS. In such sources the photons resulting from channeling radiation and coherent bremsstrahlung create the e+e− pairs.Electron beams, of 6 and 10GeV, were impinging on different kinds of targets: a 4mm thick crystal, a 8mm thick crystal and a compound target made of 4mm crystal followed by 4mm amorphous disk. An amorphous tungsten target 20mm thick was also used for the sake of comparison with the 8mm crystal and to check the ability of the detection system to provide the correct track reconstruction. The charged particles coming out from the target were detected in a drift chamber immersed partially in a magnetic field. The reconstruction of the particle trajectories provided the energy and angular spectrum of the positrons in a rather wide energy range (up to 150MeV) and angular domain (up to 30°). The experimental approach presented in this article provides a full description of this kind of source. A presentation of the measured positron distribution in momentum space (longitudinal versus transverse) is given to allow an easy determination of the available yield for a given momentum acceptance. Results on photons, measured downstream of the positron detector, are also presented. A significant enhancement of photon and positron production is clearly observed. This enhancement, for a 10GeV incident beam, is of 4 for the 4mm thick crystal and larger than 2 for the 8mm thick crystal. Another important result concerns the validation of the simulations for the crystals, for which a quite good agreement was met between the simulations and the experiment, for positrons as well as for photons. These results are presented after a short presentation of the experimental setup and of the track reconstruction procedure.

Fragment formation in central heavy ion collisions at relativistic energies

We perform a systematic study of the fragmentation path of excited nuclear matter in central heavy ion collisions at the intermediate energy of 0.4 A GeV . The theoretical calculations are based on a relativistic Boltzmann–Uehling–Uhlenbeck (RBUU) transport equation including stochastic effects. A relativistic mean field (RMF) approach is used, based on a non-linear Lagrangian, with coupling constants tuned to reproduce the high density results of calculations with correlations. At variance with the case at Fermi energies, a new fast clusterization mechanism is revealed in the early compression stage of the reaction dynamics. Fragments appear directly produced from phase space fluctuations due to two-body correlations. In-medium effects of the elastic nucleon–nucleon cross sections on the fragmentation dynamics are particularly discussed. The subsequent evolution of the primordial clusters is treated using a simple phenomenological phase space coalescence algorithm. The reliability of the approach, formation and recognition, is investigated in detail by comparing fragment momentum space distributions and simultaneously their yields with recent experimental data of the FOPI Collaboration by varying the system size of the colliding system, i.e., its compressional energy (pressure, radial flow). We find an excellent agreement between theory and experiment in almost all the cases and, on the other hand, some limitations of the simple coalescence model. Furthermore, the temporal evolution of the fragment structure is explored with a clear evidence of an earlier formation of the heavier clusters, that will appear as interesting relics of the high density phase of the nuclear equation of state (EoS).

The outer valance orbital electron densities of cyclopentane by binary (e,2e) spectroscopy.

The binding energy spectra and electron distributions in momentum space of the valence orbitals of cyclopentane (C(5)H(10)) are studied by Electron Momentum Spectroscopy (EMS) in a noncoplanar symmetric geometry. The impact energy was 1200 eV plus binding energy and energy resolution of the EMS spectrometer was 1.2 eV. The experimental momentum profiles of the outer valence orbitals are compared with the theoretical momentum distributions calculated using Hartree-Fock and density functional theory (DFT) methods. The shapes of the experimental momentum distributions are generally quite well described by both the Hartree-Fock and DFT calculations when the large and diffuse basis sets are used.

Time-resolved Excitonic Lyman Spectroscopy of Cu2O

Using ultrafast time-resolved IR spectroscopy, we measure the transition from the populated 1s state to the 2p state of the yellow excitonic series of Cu 2 O. We show that this technique can provide information on the populations of n =1 ortho- and paraexcitons, their distribution in momentum space, their inter-conversion rate, as well as their expansion through the crystal.

Classical Structures Arising in the Autoionization of He

In this work, a classical mechanics study of the autoionization process induced by ion impact is performed. The electron distribution in momentum space is obtained and compared with the results of the continuum distorted wave quantum theory. Typical structures arising in quantum and classical treatments are identified and compared. Oscillatory profiles for the autoionization spectrum are obtained within the present classical picture, in contrast with existing models which attach them to a purely quantum behavior.

Moon–magnetosphere interactions: a tutorial

The interactions between the Galilean satellites and the plasma of the Jovian magnetosphere, acting on spatial scales from that of ion gyroradii to that of magnetohydrodynamics (MHD), change the plasma momentum, temperature, and phase space distribution functions and generate strong electrical currents. In the immediate vicinity of the moons, these currents are often highly structured, possibly because of varying ionospheric conductivity and possibly because of non-uniform pickup rates. Ion pickup changes the velocity space distribution of energetic particles, f( v), where v is velocity. Distributions become more anisotropic and can become unstable to wave generation. That there would be interesting plasma responses near Io was fully anticipated, but one of the surprises of Galileo's mission was the range of effects observed at all of the Galilean satellites. Electron beams and an assortment of MHD and plasma waves develop in the regions around the moons, although each interaction region is different. Coupling of the plasma near the moons to the Jovian ionosphere creates auroral footprints and, in the case of Io, produces a leading trail in the ionosphere that extends almost half way around Jupiter. The energy source driving the auroral signatures is not fully understood but must require field aligned electric fields that accelerate elections at the feet of the flux tubes of Io and Europa, bodies that interact directly with the incident plasma, and at the foot of the flux tube of Ganymede, a body that is shielded from direct interaction with the background plasma by its magnetospheric cavity.

Moon?magnetosphere interactions: a tutorial

The interactions between the Galilean satellites and the plasma of the Jovian magnetosphere, acting on spatial scales from that of ion gyroradii to that of magnetohydrodynamics (MHD), change the plasma momentum, temperature, and phase space distribution functions and generate strong electrical currents. In the immediate vicinity of the moons, these currents are often highly structured, possibly because of varying ionospheric conductivity and possibly because of non-uniform pickup rates. Ion pickup changes the velocity space distribution of energetic particles, f ( v ), where v is velocity. Distributions become more anisotropic and can become unstable to wave generation. That there would be interesting plasma responses near Io was fully anticipated, but one of the surprises of Galileo's mission was the range of effects observed at all of the Galilean satellites. Electron beams and an assortment of MHD and plasma waves develop in the regions around the moons, although each interaction region is different. Coupling of the plasma near the moons to the Jovian ionosphere creates auroral footprints and, in the case of Io, produces a leading trail in the ionosphere that extends almost half way around Jupiter. The energy source driving the auroral signatures is not fully understood but must require field aligned electric fields that accelerate elections at the feet of the flux tubes of Io and Europa, bodies that interact directly with the incident plasma, and at the foot of the flux tube of Ganymede, a body that is shielded from direct interaction with the background plasma by its magnetospheric cavity.