Photo-induced birefringence in semiconductors compared with optical fibers

We analyze the photon-induced birefringence in semiconductors based on pump-probe setups, within the semiconductor Bloch equations formalism and the Luttinger-Kohn model for the band structure. When the pump and probe pulses are well separated in time, the anisotropic momentum space filling of the photo-excited electrons is the only mechanism causing the induced birefringence. The birefringence ratio is then for pump and probe having perpendicular vs. parallel linear polarizations. This ratio is for opposite vs. identical circular polarization. When the pump and probe pulses overlap in time, these birefringence ratios become for linear polarizations and in case of circular polarizations. These predictions differ markedly from those for optical fibers.     

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂_t²+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

Coherence properties of the radiation from X-ray free electron laser

We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser (XFEL). We consider practically important case when XFEL is optimized for maximum gain. Such an optimization allows to reduce significantly parameter space. Application of similarity techniques to the results of numerical simulations allows to present all output characteristics of the optimized XFEL as functions of the only parameter, ratio of the emittance to the radiation wavelength, . Our studies show that optimum performance of the XFEL in terms of transverse coherence is achieved at the value of the parameter of about unity. At smaller values of the degree of transverse coherence is reduced due to strong influence of poor longitudinal coherence on a transverse one. At large values of the emittance the degree of transverse coherence degrades due to poor mode selection. Comparative analysis of existing XFEL projects, European XFEL, LCLS, and SCSS is presented as well.     

Radiative corrections with 5D mixed position-/momentum-space propagators

In higher dimensional field theories with compactified dimensions there are three standard ways to do perturbative calculations: (i) by the summation over Kaluza-Klein towers; (ii) by the summation over winding numbers making use of the Poisson-resummation formula; and (iii) by using mixed propagators, where the coordinates of the four infinite dimensions are Fourier-transformed to momentum space while those of the compactified dimension are kept in configuration space. The third method is broadly used in finite temperature field theory calculations. One of its advantages is that one can easily separate the ultraviolet divergent terms of the uncompactified theory from the non-local finite corrections arising from windings around the compact dimensions. In this note we demonstrate the use of this formalism by calculating one-loop self-energy corrections in a 5D theory formulated on the manifold and on the orbifold .     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

Conditional displacement operator for traveling fields

We show that the conditional displacement operator acting upon arbitrary states of traveling waves can be well approximated by the action of a Kerr-medium placed between two beam splitters whose respective second ports are fed by highly excited coherent states. The scheme is deterministic, since it does not employ any detection event. Applications for generation of nonclassical states and measurement of Wigner function of arbitrary states are also considered.     

Antiresonance of electron tunneling through a four-quantum-dot ring with two side-coupled quantum dots

Making use of the equation of motion method and Keldysh Green function technique, we obtain the current formula for a two-terminal four-quantum-dot-ring with two side-coupled quantum dots under a DC bias voltage. Antiresonance and resonance of electron tunneling is studied by numerical calculations. Only when the quantum dots in the ring has the same single electron energy level with that of the side-coupled quantum dots, i.e. and both side-coupling are turned on at the same time, the antiresonance appear exactly at ε₀.     

Theoretical calculation of the isoelectronic line ratio of Li-like Ti and Cr under different mixture ratios

With the consideration of coronal conditions, a simplified model and the steady-state rate-equation are used to calculate the isoelectronic line ratio for transition in Li-like Ti and Cr from the electron temperature 400 to . The relation between the isoelectronic line ratio and the electron temperature are provided under different mixture ratios of Ti and Cr. Then, the mixture ratio from 2:1 to 3:1 between Ti and Cr are obtained that are suitable for the electron temperature diagnostic by using isoelectronic line ratio of Li-like Ti and Cr. The relative abundance of two close ionization stages, which is from bare nucleus to Be-like ionization stage, are given and show that the He-, Li- and Be-like are the principal ionization stages from 400 to for Ti and from 500 to for Cr. The Li-like charge state will reach the maximum distribution approximately from 400 to for Ti and from 547 to for Cr. The paper also shows that the dielectronic recombination and spontaneous radiative recombination rates only have small effects on the isoelectronic line ratio in the electron temperature 400-.     

Generalized M factor of hard-edged diffracted controllable dark-hollow beams

On the basis of the truncated second-order moments method on the cylindrical coordinate systems, an analytical expression of the generalized beam propagation factor ( factor) of hard-edged diffracted controllable dark-hollow beams is derived and illustrated numerically. It is shown that the factor of truncated controllable dark-hollow beams is dependent on the beam truncation parameter δ and the beam parameters N and ε. The result can be reduced to that for the non-truncated case as the truncation parameter approaches to be infinite. The power fraction is also discussed analytically and numerically.     

Ion formation in laser-irradiated cesium vapor

We study theoretically the formation of Cs⁺ and during cw laser radiation resonant with 6s-7p transition of Cs atomic vapor. This is done by numerically solving rate equations for the evolution of atomic state and electron populations. The results of calculations for the atomic and molecular ions density at different values of laser power clarified that the associative ionization and Penning ionization process play an important role for producing the and Cs⁺, respectively, during the plasma formation. Also, the results showed that laser power of the order of 150 mW and 40-50 ns irradiation time are optimal in producing a fully ionized plasma.     

A relativistic wave equation for the Skyrmion

We propose a relativistically invariant wave equation for the Skyrme soliton. It is a differential equation on the space R^1,3×S³ which is invariant under the Lorentz group and isospin. The internal variable valued in SU(2)≡S³ describes the orientation of the soliton. The mass of a particle of spin and isospin both equal to is predicted to be which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be , where Σ is the spin.     

Periodic boundary conditions and the correct molecular-dynamics ensemble

The use of periodic boundary conditions in molecular-dynamics simulations leads to the microcanonical ensemble of Ray and Zhang [J.R. Ray, H. Zhang, Phys. Rev. E 59 (1999) 4781] in which the total linear momentum and the generator of infinitesimal Galilean boosts are conserved quantities in addition to the total energy E, the volume V, and the number of particles N of the system. We find that the invariance of should be of importance in the analysis of ensemble averages of quantities that only depend on the spatial coordinate . As an application we study the density profile of an isolated system of hard disks with periodic boundary conditions in the absence of external forces. We find that the periodic boundary conditions give rise to an anomalous inhomogeneity in the density profile of the system. This inhomogeneity is only relevant for systems with a very small number of disks and is related to the conservation of the center of mass coordinates.     

On the size distribution of Poisson Voronoi cells

Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells. Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed.     

Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields

The scaling properties of various composite information-theoretic measures (Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by and . Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behavior is discussed.