Production of superpositions of coherent states in traveling optical fields with inefficient photon detection

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS's) with large amplitudes out of CSS's with small amplitudes using inefficient photon detection. The small CSS's required to produce CSS's with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.

Nonclassicality of a photon-subtracted Gaussian field

We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

A simple proof of the strong subadditivity inequality

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Signatures for generalized macroscopic superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

Transfer of nonclassical properties from a microscopic superposition to macroscopic thermal states in the high temperature limit

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.

A novel and rational approach towards designing aluminium chelators

Aluminium (Al) is known to be neurotoxic and has been associated with the aetiology of Alzheimer's Disease. To date, only desferrioxamine (DFO), a trihydroxamic acid siderophore has been used in the clinical environment for the removal of Al from the body. However, this drug is expensive, orally inactive and is associated with many side effects. These studies employed a theoretical approach, with the use of quantum mechanics (QM) via semi-empirical molecular orbital (MO) calculations, and a practical approach using U87-MG glioblastoma cells as a model for evaluating the influence of potential chelators on the passage of aluminium into cells. Preliminary studies involving the Cambridge Structural Database (CSD) identified that Al prefers binding to bidentate ligands in a 3:1 manner, whereby oxygen was the exclusive donating atom. Statistically significant differences in M-O bond lengths when compared to other trivalent metal ions such as Fe3+ were established and used as an acceptance criterion for subsequent MO calculations. Of the semi-empirical methods parameterised for Al, the PM3 Hamiltonian was found to give the most reliable final optimised geometries of simple 3:1 Al complexes. Consequently the PM3 Hamiltonian was used for evaluating the Hf of 3:1 complexes with more complicated ligands. No correlation exists between published stability constants and individual parameters calculated via PM3 optimisations, although investigation of the dicarboxylates reveals a correlation of 0.961 showing promise for affinity prediction of closely related ligands. A simple and inexpensive morin spectrofluorescence assay has been developed and optimised producing results comparable to atomic absorption spectroscopy methods for the quantitative analysis of Al. This assay was used in subsequent in vitro models, initially on E. coli, which indicated that Al inhibits the antimicrobial action of ciprofloxacin, a potent quinolone antibiotic. Ensuing studies using the second model, U87-MG cells, investigated the influence of chelators on the transmembrane transport of Al, identifying 1,2-diethylhydroxypyridin-4-one as a ligand showing greatest potential for chelating Al in the clinical situation. In conclusion, these studies have explored semi-empirical MO Hamiltonians and an in-vitro U87-MG cell line, both as possible methods for predicting effective chelators of Al.

Microscopic optical buffering in a harmonic potential

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.

A fizikai matematika legújabb eredményei mint a közgazdaság-tudomány lehetséges vizsgálati eszközei (The newest results of physical mathematics as the possible investigation tools of economics)

A közgazdaság-tudomány számos problémája a fizika analóg modelljeinek segítségével nyert megoldást. A közgazdászok körében erőteljesen megoszlanak a vélemények, hogy a közgazdasági modellek mennyire redukálhatók a fizika, vagy más természettudományok eredményeire. Vannak,akik pontosan ezzel magyarázzák,hogy a mai mainstream közgazdasági elmélet átalakult alkalmazott matematikává,ami a gazdasági kérdéseket csak a társadalom-tudományi vonatkozásaitól eltekintve képes vizsgálni. Mások, e tanulmányszerzője is, viszont úgy vélekednek, hogy a közgazdasági problémák egy része, ahol lehetőség van a mérésre, jól modellezhetők a természettudományok technikai arzenáljával. A másik része, amelyekben nem lehet mérni,s tipikusan ilyenek a társadalomtudományi kérdések, ott sokkal komplexebb technikákra lesz szükség. Etanulmány célkitűzése, hogy felvázolja a fizika legújabb, az irreverzibilis dinamika, a relativitáselmélet és a kvantummechanika sztochasztikus matematikai összefüggéseit, amelyekből a közgazdászok választhatnak egy-egy probléma megfogalmazásában és megoldásában. Például az időoperátorok pontos értelmezése jelentős fordulatot hozhat a makroökonómiai elméletekben; vagy az eddigi statikus egyensúlyi referencia pontokat felválthatják a dinamikus,időben változó sztochasztikus egyensúlyi referenciafüggvények, ami forradalmian új megvilágításba helyezhet számos társadalomtudományi, s főleg nemegyensúlyi közgazdasági kérdést.A termodinamika és a biológiai evolúció fogalmait és definícióit Paul A. Samuelson (1947) már adaptálta a közgazdaságtanban, viszont a kvantummechanika legújabb eredményeit, az időoperátorokat stb. nem érintette. E cikk azokat a legújabb fizikai, kémiai és biológiai matematikai összefüggéseket foglalja össze,amelyek hasznosak lehetnek a közgazdasági modellek komplexebb megfogalmazásához. ___________________ The aim of this paper is to out line the newest results of physics,i.e.,the stochastic mathematical relations of relativity theory and quantum mechanics as well as irreversible dynamics which can be applied for some economic problems.For example,the correct interpretation of time operators using for the macroeconomic theories may provide a serious improvement in approach to the reality.The stochastic dynamic equilibrium reference functions will take over the role of recent static equilibrium reference points,which may also reveal some nonequilibrium questions of macroeconomics.The concepts and definitions of thermodynamics and biological evolution have been adopted in economics by Paul A. Samuelson, but he did not concern the newest results of quantum mechanics, e.g., the time operators. Now we do it.In addition, following Samuelson,we show that von Neumann growth model cannot be explained as a peculiar extension of thermodynamic irreversibility.

Non-uniqueness through duality in the von Neumann growth models

Duality can be viewed as the soul of each von Neumann growth model. This is not at all surprising because von Neumann (1955), a mathematical genius, extensively studied quantum mechanics which involves a “dual nature” (electromagnetic waves and discrete corpuscules or light quanta). This may have had some influence on developing his own economic duality concept. The main object of this paper is to restore the spirit of economic duality in the investigations of the multiple von Neumann equilibria. By means of the (ir)reducibility taxonomy in Móczár (1995) the author transforms the primal canonical decomposition given by Bromek (1974) in the von Neumann growth model into the synergistic primal and dual canonical decomposition. This enables us to obtain all the information about the steadily maintainable states of growth sustained by the compatible price-constellations at each distinct expansion factor.

Modelagem molecular voltada para a construção de um nanobiossensor para detecção do herbicida Imazaquin

In this study, our goal was develop and describe a molecular model of the enzyme-inhibiting interaction which can be used for an optimized projection of a Microscope Force Atomic nanobiosensor to detect pesticides molecules, used in agriculture, to evaluate its accordance with limit levels stipulated in valid legislation for its use. The studied herbicide (imazaquin) is a typical member of imidazolinone family and is an inhibitor of the enzymatic activity of Acetohydroxiacid Synthase (AHAS) enzyme that is responsible for the first step of pathway for the synthesis of side-chains in amino acids. The analysis of this enzyme property in the presence of its cofactors was made to obtain structural information and charge distribution of the molecular surface to evaluate its capacity of became immobilized on the Microscopy Atomic Force tip. The computational simulation of the system, using Molecular Dynamics, was possible with the force-field parameters for the cofactor and the herbicides obtained by the online tool SwissParam and it was implemented in force-field CHARMM27, used by software GROMACS; then appropriated simulations were made to validate the new parameters. The molecular orientation of the AHAS was defined based on electrostatic map and the availability of the herbicide in the active site. Steered Molecular Dynamics (SMD) Simulations, followed by quantum mechanics calculations for more representative frames, according to the sequential QM/MM methodology, in a specific direction of extraction of the herbicide from the active site. Therefore, external harmonic forces were applied with similar force constants of AFM cantilever for to simulate herbicide detection experiments by the proposed nanobiosensor. Force value of 1391 pN and binding energy of -14048.52 kJ mol-1 were calculated.

Optically injected multi-mode semiconductor lasers

As a device, the laser is an elegant conglomerate of elementary physical theories and state-of-the-art techniques ranging from quantum mechanics, thermal and statistical physics, material growth and non-linear mathematics. The laser has been a commercial success in medicine and telecommunication while driving the development of highly optimised devices specifically designed for a plethora of uses. Due to their low-cost and large-scale predictability many aspects of modern life would not function without the lasers. However, the laser is also a window into a system that is strongly emulated by non-linear mathematical systems and are an exceptional apparatus in the development of non-linear dynamics and is often used in the teaching of non-trivial mathematics. While single-mode semiconductor lasers have been well studied, a unified comparison of single and two-mode lasers is still needed to extend the knowledge of semiconductor lasers, as well as testing the limits of current model. Secondly, this work aims to utilise the optically injected semiconductor laser as a tool so study non-linear phenomena in other fields of study, namely ’Rogue waves’ that have been previously witnessed in oceanography and are suspected as having non-linear origins. The first half of this thesis includes a reliable and fast technique to categorise the dynamical state of optically injected two mode and single mode lasers. Analysis of the experimentally obtained time-traces revealed regions of various dynamics and allowed the automatic identification of their respective stability. The impact of this method is also extended to the detection regions containing bi-stabilities. The second half of the thesis presents an investigation into the origins of Rogue Waves in single mode lasers. After confirming their existence in single mode lasers, their distribution in time and sudden appearance in the time-series is studied to justify their name. An examination is also performed into the existence of paths that make Rogue Waves possible and the impact of noise on their distribution is also studied.