Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

Adiabatic propagation in potential structures

In this work the adiabatic approximation is applied to the propagation of matter waves in confined geometries like those experimentally realized in recent atom optical experiments. Adiabatic propagation along a channel is assumed not to mix the various transverse modes. Nonadiabatic corrections arise from the potential squeezing and bending. Here we investigate the effect of the former. Detailed calculations of two-dimensional propagation are carried out both exactly and in an adiabatic approximation. This offers the possibility to analyze the validity of adiabaticity criteria. A semiclassical (sc) approach, based on the sc Massey parameter is shown to be inadequate, and the diffraction due to wave effects must be included separately. This brings in the Fresnel parameter well known from optical systems. Using these two parameters, we have an adequate understanding of adiabaticity on the system analyzed. Thus quantum adiabaticity must also take cognizance of the intrinsic diffraction of matter waves.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.

Polarizing beam splitter for dipolar molecules

We propose a coherent beam splitter for polarized heteronuclear molecules based on a stimulated Raman adiabatic passage scheme that uses a tripod linkage of electrotranslational molecular states. We show that for strongly polarized molecules the rotational dynamics imposes significantly larger Rabi frequencies than would otherwise be expected, but within this limitation, a full transfer of the molecules to two counterpropagating ground-state wave packets is possible.

Dynamics of Bose-Einstein condensates in double-well potentials

We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.

Coherence dynamics of two-mode condensates in asymmetric potentials

Detection of weak forces with an accuracy beyond the standard quantum limit holds promise both for fundamental research and for technological applications. Schemes involving ultracold atoms for such measurements are now considered to be prime candidates for increased sensitivity. In this paper we use a combination of analytical and numerical techniques to investigate the possible subshot-noise estimation of applied force fields through detection of coherence dynamics of Bose-condensed atoms in asymmetric double-well traps. Following a semiclassical description of the system dynamics and fringe visibility, we present numerical simulations of the full quantum dynamics that demonstrate the dynamical production of phase squeezing beyond the standard quantum limit. Nonlinear interactions are found to limit the achievable amount to a finite value determined by the external weak force.

Single-mode acceleration of matter waves in circular waveguides

Ultracold gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.

Thomas-Fermi ground state of dipolar fermions in a circular storage ring

Recent developments in the field of ultracold gases has led to the production of degenerate samples of polar molecules. These have large static electric-dipole moments, which in turn causes the molecules to interact strongly. We investigate the interaction of polar particles in waveguide geometries subject to an applied polarizing field. For circular waveguides, tilting the direction of the polarizing field creates a periodic inhomogeneity of the interparticle interaction. We explore the consequences of geometry and interaction for stability of the ground state within the Thomas-Fermi model. Certain combinations of tilt angles and interaction strengths are found to preclude the existence of a stable Thomas-Fermi ground state. The system is shown to exhibit different behavior for quasi-one-dimensional and three-dimensional trapping geometries.

Bifurcations and bistability in cavity-assisted photoassociation of Bose-Einstein-condensed molecules

We study the photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between atoms and molecules. For weak cavity driving, we find a bifurcation in the atom and molecule number occurs that signals a transition from a stable steady state to nonlinear Rabi oscillations. For a strongly driven cavity, there exists bistability in the atom and molecule number.

Quantum control of electromagnetically induced transparency dispersion via atomic tunneling in a double-well Bose-Einstein condensate

Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level Lambda configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency Omega(mu), as in standard EIT systems. Tunneling between the wells at the frequency g provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by g. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.

Gravitational self-localization for spherical masses

In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, M≲10−17 kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schrödinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes R≈10−7 m, and the density of the material causes only minor variations in this value.

Resonant States in Negative Ions

Resonant states are multiply excited states in atoms and ions that have enough energy to decay by emitting an electron. The ability to emit an electron and the strong electron correlation (which is extra strong in negative ions) makes these states both interesting and challenging from a theoretical point of view. The main contribution in this thesis is a method, which combines the use of B splines and complex rotation, to solve the three-electron Schrödinger equation treating all three electrons equally. It is used to calculate doubly excited and triply excited states of 4S symmetry with even parity in He-. For the doubly excited states there are experimental and theoretical data to compare with. For the triply excited states there is only theoretical data available and only for one of the resonances. The agreement is in general good. For the triply excited state there is a significant and interesting difference in the width between our calculation and another method. A cause for this deviation is suggested. The method is also used to find a resonant state of 4S symmetry with odd parity in H2-. This state, in this extremely negative system, has been predicted by two earlier calculations but is highly controversial. Several other studies presented here focus on two-electron systems. In one, the effect of the splitting of the degenerate H(n=2) thresholds in H-, on the resonant states converging to this threshold, is studied. If a completely degenerate threshold is assumed an infinite series of states is expected to converge to the threshold. Here states of 1P symmetry and odd parity are examined, and it is found that the relativistic and radiative splitting of the threshold causes the series to end after only three resonant states. Since the independent particle model completely fails for doubly excited states, several schemes of alternative quantum numbers have been suggested. We investigate the so called DESB (Doubly Excited Symmetry Basis) quantum numbers in several calculations. For the doubly excited states of He- mentioned above we investigate one resonance and find that it cannot be assigned DESB quantum numbers unambiguously. We also investigate these quantum numbers for states of 1S even parity in He. We find two types of mixing of DESB states in the doubly excited states calculated. We also show that the amount of mixing of DESB quantum numbers can be inferred from the value of the cosine of the inter-electronic angle. In a study on Li- the calculated cosine values are used to identify doubly excited states measured in a photodetachment experiment. In particular a resonant state that violates a propensity rule is found.

Radikalcyklisering vid syntes av polycykliska indoler och pyrroler

I de senaste två decennierna har radikalcyklisering, intramolekylär radikaladdition, utvecklats till en viktig syntesmetod för polycykliska indoler och pyrroler. De erhållna produktmolekylerna eller deras derivat är ofta naturliga eller syntetiska alkaloider som väckt biologiskt eller medicinskt intresse. Avhandlingen behandlar både intramolekylära radikaladditioner av pyrrolyl-, indolyl- eller indolylacylradikaler till -bindningar och intramolekylära additioner av flera olika radikaler till indolens eller pyrrolens -system. Också cykliseringar som delreaktioner i radikalkaskader behandlas. Radikalreaktioner kan släckas både oxidativt och reduktivt. För att bibehålla heteroarenens aromaticitet måste cykliseringar till pyrrol- eller indolringen släckas oxidativt. Oxidativa radikaladditioner till aromater benämns homolytiska aromatiska substitutioner. Det finns olika sätt att erhålla en reaktantradikal från en radikalprekursor. I vissa fall har radikalprekursorn en mycket labil bindning som kan brytas fotokemiskt eller med hjälp av en initiator. Till exempel kol-svavelbindningen av en O-etyl-S-alkylxanthat kan brytas på detta sätt. Ofta används dock en radikalmediator för att bilda en reaktantradikal från dess prekursor. Mediatorer är ofta föreningar, som under reaktionsförhållandena själv bildar radikaler med en stor affinitet för en prekursors specifika atom eller atomgrupp vilken abstraheras. Således fungerar mediatorn som mellanhand vid bildning av reaktantradikalen. Exempel på mediatorer av detta slag som använts vid syntes av polycykliska pyrroler och indoler är tributyltennhydrid, hexabutylditenn, tris(trimetylsilyl)silan, tributylgermaniumhydrid, dicumylperoxid, trietylboran, natriumarensulfinater (med ättiksyra) och Se-fenyl-p-toluenselenosulfonat. Också dimetylsulfoxid kan ses som mediator då den bildar metylradikaler vid Fentonreaktion i lösningsmedlet. Övergångsmetallsalter kan även bilda reaktantradikalen från prekursorn genom enelektronoxidationer eller -reduktioner. Vid syntes av polycykliska pyrroler och indoler har reaktantradikalen bildats genom enelektronoxidationer med Mn(OAc)3 eller Ag2+ (Miniscireaktion) och elektronreduktioner med ett Ni(I)-komplex eller SmI2. Avhandlingen är indelad enligt reagenset eller reagensen, som åstadkommer bildning av reaktantradikalen vid syntes av polycykliska indoler och pyrroler. Cirka hälften av avhandlingen behandlar tributyltennhydridmedierade cykliseringar då reagenset trots dess toxicitet är det överlägset mest använda. Avhandlingen diskuterar mekanismen för bildning av reaktantradikalen från prekursorn, cykliseringen och dess möjliga regioselektivitet, andra radikalreaktioner vid radikalkaskader och hur produktradikalen släcks.

[Den musikindustriella förändringen fortsätter och en tjänstebaserad musikekonomi börjar ta form] [in Swedish]

Det har nu gått mer än tio år sedan en student vid Northeastern University i USA lanserade den första fildelningstjänsten som blev framgångsrik bland den breda allmänheten (e.g. Alderman 2001). Lanseringen av tjänsten, som kallades Napster, ses ofta som inledningen på ett av de mest dramatiska decennierna i musikbranschens historia. En lång rad internetbaserade tjänster som följt i Napsters spår har gjort det möjligt att sprida musik till miljontals användare utan att upphovsmän och rättighetsinnehavare fått någon ersättning. Katt-och-råtta-leken mellan lagstiftning och teknik har varit intensiv och har utvecklats till ett av decenniets allra hetaste diskussionsämnen bland politiker och ledarskribenter. Försäljningen av inspelad musik har sjunkit dramatiskt och musikbranschen har tvingats ifrågasätta många väletablerade sanningar. Det här kapitlet belyser ett antal fundamentala aspekter av denna förändring och utforskar några av den ”nya” musikbranschens viktigaste karaktäristika. Under den tid som musikbranschen har beforskats har vanligtvis betoningen legat på fonogrammen, det vill säga den del av branschen som rör produktion och konsumtion av inspelad musik. På grund av branschens förändrade struktur kommer dock det här kapitlet att vidga perspektivet en smula och även inkludera musikbranschens andra delar som exempelvis konserter och förlagsverksamhet...