132,024 research outputs found
Vortices in trapped bose - Einstein condensates
No full textIn this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigen-modes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEG transition. We end the thesis by describing a simple finite- temperature model to describe mean-field coupling between condensed and non- condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion
Josephson effect in multicomponent Bose-Einstein condensates
No full text[cat]En aquesta Tesi s'estudia i es caracteritza el comportament dels condensats de Bose-Einstein en una junció bosònica de Josephson (BJJ), tot utilitzant dos formalismes teòrics diferents: l'aproximació de camp mig (amb l'equació de Gross-Pitaevskii) i càlculs de molts cossos (basats en models de Bose-Hubbard). En condensats d'una sola component, ens hem centrat en l'estudi de l'estructura de l'estat fonamental en funció dels paràmetres del sistema. Hem identificat estats altament correlacionats que no es poden descriure amb teories de camp mig, i hem proposat una funció d'ona variacional que captura l'estructura de l'estat fonamental en un ampli ventall de valors d'aquests paràmetres. També hem estudiat els efectes no lineals de l'equació de Gross-Pitaevskii, visibles quan les interaccions entre àtoms són fortes. Per condensats formats per dues components hem fet un estudi intensiu dels diferents règims que es poden formar i en quines condicions. Hem utiltizat el formalisme de camp mig i hem derivat l'aproximació bimodal estàndard millorada (I2M) tot comprovant-ne la seva validesa, comparant-la amb simulacions numèriques de l'equació de Gross-Pitaevskii tridimensional. També hem estudiat condensats espinorials en una BJJ externa. Ens hem centrat en condensats formats per àtoms amb spin , que poden estar en qualsevol dels tres estats interns . Primer, hem estudiat aquest sistema dins la teoria de camp mig, tot utilitzant l'equació de Gross-Pitaevskii. Hem derivat les equacions de l'aproximació bimodal, i ens hem centrat en estudiar com es desacobla l'efecte Josephson de la dinàmica d'intercanvi de partícules. Segon, hem utilitzant el formalisme de Bose-Hubbard i hem caracteritzat l'estat fonamental, tot fixant-nos en els effectes de la creació de singlets. Finalment, hem estudiat l'efecte de temperatura finita en condensats de Bose-Einstein espinorials en presència d'un camp magnètic, per dos casos ben diferenciats: 1) un condensat amb i interaccions de contacte i 2) un condensat amb i interaccions de contacte i dipolars. Per a tots dos cassos, proposem un mètode per fer termometria a molt baixes temperatures, i un mètode per refredar el sistema tot variant el camp magnètic extern.[eng]
In this thesis we study and characterize the behavior of Bose-Einstein condensates in a BJJ, using two different theoretical formalisms: the mean-field approximation (with the Gross-Pitaevskii equation) and many-body calculations (based on Bose-Hubbard models). With single-component Bose-Einstein condensates, we have focused on the study of the structure of the ground state as a function of the system parameters. We have looked for strongly correlated states, that cannot be described with mean-field theories, and we have proposed a variational wave function that captures the structure of the ground state for a broad interval of the system parameters. We have also studied the nonlinear effects of the Gross-Pitaevskii equation, visible when atom-atom interactions are strong. In the case of binary mixtures of Bose-Einstein condensates we have performed an intensive study of the different regimes that can arise and in which conditions. The standard two-mode approximation is one of the most used in the study of the Josephson effect, as it gives simple analytic equations that capture, to a great extend, the behavior of the system. When the link between condensates is not weak enough, one has to consider a correction to this approximation, namely, the improved two-mode approximation. In this thesis, we have derived this last approximation for the binary mixture and we have checked its validity comparing it with numerical simulations of the three-dimensional Gross-Pitaevskii equation. Moreover, as the Josephson dynamics is almost one-dimensional, we have considered the two most common reductions of the dimensionality of the Gross-Pitaevskii equation. In this case, we have also compared, using simulations, these one-dimensional reductions with the three-dimensional equation. We have also studied spinor condensates in an external BJJ. We have focused on condensates formed by atoms with spin , which can be in any of the three internal states . Furthermore, in contrast to the binary mixture, spin interchange is allowed, so that the number of particles of each component becomes a dynamic variable. First, we have studied this system within the mean-field framework, using the Gross-Pitaevskii equation. We have derived the two-mode approximation equations and we have focused in studying the decoupling of the Josephson effect and the population transfer dynamics. In this case, we also compare the results with numerical simulations of the three dimensional Gross-Pitaevskii equation. Second, we have studied the spinor BJJ using the Bose-Hubbard formalism, because some features of quantum fluctuations are better captured than with the mean-field. We have characterized the ground state, paying special attention to the regions where it is strongly correlated. We have seen how the spin singlet formation (strongly correlated state between two particles) affects the structure of the ground state. Finally, we have studied finite temperature effects on spinor Bose-Einstein condensates in the presence of a magnetic field, for two different cases. First, we have analyzed a condensate formed by atoms with contact interactions. We have considered that the condensate was formed by atoms in the internal state and we have studied the dependence of the fluctuations of the other two components as a function of temperature. We have used the Bogoliubov formalism applied to an homogeneous system, and then, we have generalized the result to an harmonic trap by using the local density approximation. Second, we have studied a condensate formed by particles with with contact interactions and moreover, dipolar interactions. In a similar way as the previous case, we consider that the condensate is formed by particles with and we study the fluctuations in and $m_F = -3
Theoretical Studies of dilute Bose-Einstein condensates in a double-well potential
No full textIn this Thesis we apply the Gross-Pitaevskii equation (GPE) to describe properties of a dilute, near zero temperature Bose gas for various confining geometries. We start by reviewing some basic information about the density, the chemical potential and elementary excitations of a dilute atomic condensate confined in a single harmonic trap for a Bose condensate with repulsive and attractive interactions and we also discuss the stability in the case of attractive interactions. We extend our study to a one and three dimensional double-well trap. We investigate the eigenenergy levels and show that the nonlinearity leads to triangular structures which appear either in the ground or excited states for the case of a Bose condensate with attractive or repulsive interactions respectively. We apply the eigenenergy level picture to analyse Josephson effects induced when the barrier IS moved at a constant velocity across the trapping potential or by the application of a time-dependent potential gradient. The GPE simulations are compared to the predictions of a nonlinear two state model. Above a critical velocity there is a transition to a superposition of ground and excited states which leads to sudden changes in the population difference. The direction of Josephson flow depends critically on the initial state of the system and we discuss the feasibility of experimental control of the atomic flow using phase-imprinting. The stability of a low temperature Bose-Einstein condensate with attract interactions in one and three dimensional double-well potentiate is discussed. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. Finally we investigate the stability and tunnelling effects in a multi-well system
Lasing in Bose-Fermi mixtures
No full textA.K. acknowledges the support from the EPSRC Established Career Fellowship. V.K., M.D., V.F.S. and A.K. acknowledge support from the Russian Ministry of Science and Education, contract (contract No. 11.G34.31.0067). P.G.S. acknowledges support from Greek GSRT program Aristeia (grant No. 1978). C.S., M. A. J.F., M.K and S.H. acknowledge support from the state of Bavaria.Light amplification by stimulated emission of radiation, well-known for revolutionising photonic science, has been realised primarily in fermionic systems including widely applied diode lasers. The prerequisite for fermionic lasing is the inversion of electronic population, which governs the lasing threshold. More recently, bosonic lasers have also been developed based on Bose-Einstein condensates of exciton-polaritons in semiconductor microcavities. These electrically neutral bosons coexist with charged electrons and holes. In the presence of magnetic fields, the charged particles are bound to their cyclotron orbits, while the neutral exciton-polaritons move freely. We demonstrate how magnetic fields affect dramatically the phase diagram of mixed Bose-Fermi systems, switching between fermionic lasing, incoherent emission and bosonic lasing regimes in planar and pillar microcavities with optical and electrical pumping. We collected and analyzed the data taken on pillar and planar microcavity structures at continuous wave and pulsed optical excitation as well as injecting electrons and holes electronically. Our results evidence the transition from a Bose gas to a Fermi liquid mediated by magnetic fields and light-matter coupling.Peer reviewe
Bright solitary waves and non-equilibrium dynamics in atomic Bose-Einstein condensates
No full textIn this thesis we investigate the static properties and non-equilibrium dynamics of bright solitary waves in atomic Bose-Einstein condensates in the zero-temperature limit, and we investigate the non-equilibrium dynamics of a driven atomic Bose-Einstein condensate at finite temperature.
Bright solitary waves in atomic Bose-Einstein condensates are non-dispersive and soliton-like matter-waves which could be used in future atom-interferometry experiments. Using the mean-field, Gross-Pitaevskii description, we propose an experimental scheme to generate pairs of bright solitary waves with controlled velocity and relative phase; this scheme could form an important part of a future atom interferometer, and we demonstrate that it can also be used to test the validity of the mean-field model of bright solitary waves. We also develop a method to quantitatively assess how soliton-like static, three-dimensional bright solitary waves are; this assessment is particularly relevant for the design of future experiments.
In reality, the non-zero temperatures and highly non-equilibrium dynamics occurring in a bright solitary wave interferometer are likely to necessitate a theoretical description which explicitly accounts for the non-condensate fraction. We show that a second-order, number-conserving description offers a minimal self-consistent treatment of the relevant condensate -- non-condensate interactions at low temperatures and for moderate non-condensate fractions. We develop a method to obtain a fully-dynamical numerical solution to the integro-differential equations of motion of this description, and solve these equations for a driven, quasi-one-dimensional test system. We show that rapid non-condensate growth predicted by lower-order descriptions, and associated with linear dynamical instabilities, can be damped by the self-consistent treatment of interactions included in the second-order description
Mapping of literature on Bose – Einstein condensation
No full textThis paper attempts to highlight quantitatively the growth and development of research work in this field on Bose-Einstein Condensation (BEC) in terms of publication output as per Science Citation Index (1982-2005). During 1982–2005 a total of 5258 papers were published by the scientists in this field. The average number of publications published per year were 219. The highest number of papers 814 were published in 2004. There were 77 countries involved in the research in this field. USA is the top producing country with 1632 publications (31%) followed by Germany with 620 publications (11.79%). Authorship and collaboration trend was towards multiauthored papers. Intensive collaboration was found during 1996-2005. One paper “Astrophysical Journal 543 (1), (2000), L39-L42” had 56 collaborators. There were 1635 international collaborative papers. Bilateral collaboration accounted for 24 percent of total collaborative papers. National Institute of Standards & Technology (USA) topped the list with 179 publications followed by University of Colorado (USA) with 160 publications. The most prolific authors were: W. Ketterle (USA) with 93 publications, K. Burnett (England) and M. Lewenstein (England) with 68 publications each and S. Stringari with 57 publications. The most preferred journals by the scientists were : Physical Review- A with 1504 papers, Physical Review Letters with 824 papers, Journal of Physics-B with 205 papers, Physical Review- B with 178 papers, Physics Letters-A with157 papers, Physical Review –E with 122 papers and Journal of Low Temperature Physics with 102 papers. The high frequency keywords were : Bose-Einstein Condensation (2012), Gases (1928), Atoms (860), and Dynamics (493)
Imprinting a topological interface using Zeeman shifts in an atomic spinor Bose–Einstein condensate
No full textWe propose to use spatial control of the Zeeman energy shifts in an ultracold atomic gas to engineer an interface between topologically distinct regions. This provides an experimentally accessible means for studying the interface physics of topological defects and textures. Using the spin-1 Bose–Einstein condensate as an example, we find spinor wave functions that represent defects and textures continuously connecting across the interface between polar and ferromagnetic regions induced by spatially varying Zeeman shifts. By numerical energy-minimization we characterize the defect core structures and determine the energetic stability. The techniques proposed could potentially be used in the laboratory to emulate complex interface physics arising, e.g., in cosmological and condensed-matter contexts in both uniform and lattice systems
Many body effects in one-dimensional attractive Bose gases
No full textIn this thesis we investigate the properties of ultra-cold quantum gases in reduced dimension and the effects of harmonic confinement on soliton-like properties. We study regimes of agreement between mean-field and many-body theories the generation of entanglement between initially independent finite sized atomic systems.
Classical solitons are non-dispersing waves which occur in integrable systems, such as atomic Bose-Einstein condensates in one dimension. Bright and dark solitons are possible, which exist as peaks or dips in density. Quantum solitons are the bound-state solutions to a system satisfying quantum integrability, given via the Bethe Ansatz. Such integrability is broken by the introduction of harmonic confinement. We investigate the equivalence of the classical field and many-body solutions in the limit of large numbers of atoms and derive numerical and variational approaches to examine the ground state energy in harmonic confinement and the fidelity between a Hartree-product solution and a quantum soliton solution.
Soliton collisions produce no entanglement between either state and result only in an asymptotic position and phase shift, however external potentials break integrability and thus give the possibility of entangling solitons. We investigate the dynamical entanglement generation between two atomic dimers in harmonic confinement via exact diagonalisation in a basis of Harmonic oscillator functions, making use of the separability of the centre-of-mass component of the Hamiltonian. We show repulsive states show complex dynamics, but with an overall tendency towards states of larger invariant correlation entropy, whereas attractive states resist entanglement unless a phase matching condition is satisfied. This phase matching condition could in theory be used to generate states with highly non-Poissonian number superpositions in atomic systems with controlled number
Tratamento microscópico do modo tesoura em condensado de Bose-Einstein confinado baseado em teorias de resposta linear
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Física.O modo tesoura foi objeto de estudo em vários sistemas de muitos corpos e recentemente em condensados de Bose-Einstein para demonstrar as propriedades de superfluido nesse sistema, devido às diferenças entre os casos de temperatura zero e finita
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