Self-similar Expansion of the Density Profile in a Turbulent Bose-Einstein Condensate

In a recent study we demonstrated the emergence of turbulence in a trapped Bose-Einstein condensate of Rb-87 atoms. An intriguing observation in such a system is the behavior of the turbulent cloud during free expansion. The aspect ratio of the cloud size does not change in the way one would expect for an ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous expansion can be understood, at least qualitatively, in terms of the presence of vorticity distributed throughout the cloud, effectively counteracting the usual reversal of the aspect ratio seen in free time-of-flight expansion of non-rotating condensates.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Analysis of dynamical tunneling experiments with a Bose-Einstein condensate

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures in direct analogy to the position and momentum correlations originally considered by EPR.

Matter-wave amplification and phase conjugation via stimulated dissociation of a molecular Bose-Einstein condensate

We propose a scheme for parametric amplification and phase conjugation of an atomic Bose-Einstein condensate (BEC) via stimulated dissociation of a BEC of molecular dimers consisting of bosonic atoms. This can potentially be realized via coherent Raman transitions or using a magnetic Feshbach resonance. We show that the interaction of a small incoming atomic BEC with a (stationary) molecular BEC can produce two counterpropagating atomic beams - an amplified atomic BEC and its phase-conjugate or "time-reversed" replica. The two beams can possess strong quantum correlation in the relative particle number, with squeezed number-difference fluctuations.

Foil-based atom chip for Bose-Einstein condensates

We describe a novel method of fabricating atom chips that are well suited to the production and manipulation of atomic Bose–Einstein condensates. Our chip was created using a silver foil and simple micro-cutting techniques without the need for photolithography. It can sustain larger currents than conventional chips, and is compatible with the patterning of complex trapping potentials. A near pure Bose–Einstein condensate of 4 × 104 87Rb atoms has been created in a magnetic microtrap formed by currents through wires on the chip. We have observed the fragmentation of atom clouds in close proximity to the silver conductors. The fragmentation has different characteristic features to those seen with copper conductors.

Complex solitons in Bose-Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

Finite-temperature dynamics of vortices in Bose-Einstein condensates

We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

Anisotropic merging and splitting of dipolar Bose-Einstein condensates

We study the merging and splitting of quasi-two-dimensional Bose-Einstein condensates with strong dipolar interactions. We observe that if the dipoles have a non-zero component in the plane of the condensate, the dynamics of merging or splitting along two orthogonal directions, parallel and perpendicular to the projection of dipoles on the plane of the condensate, are different. The anisotropic merging and splitting of the condensate is a manifestation of the anisotropy of the roton-like mode in the dipolar system. The difference in dynamics disappears if the dipoles are oriented at right angles to the plane of the condensate as in this case the Bogoliubov dispersion, despite having roton-like features, is isotropic.

Stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates: Feedback laser-detuning control and suppression of dynamical instability

We present a feedback control scheme that designs time-dependent laser-detuning frequency to suppress possible dynamical instability in coupled free-quasibound-bound atom-molecule condensate systems. The proposed adaptive frequency chirp with feedback is shown to be highly robust and very efficient in the passage from an atomic to a stable molecular Bose-Einstein condensate.

Coherent scattering of light by Bose-Einstein condensation in a tight confinement

We have observed strong scattering of a probe light by dilute Bose-Einstein condensate (BEC) Rb-87 gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.

Dinâmica da condensação de Bose-Einstein em gases fracamente interagentes

A presente dissertação estuda com detalhes a evolução temporal fora do equilíbrio de um condensado de Bose-Einstein homogêneo diluído imerso em um reservatório térmico. Nós modelamos o sistema através de um campo de Bose escalar complexo. É apropriado descrever o comportamento microscópico desse sistema por meio da teoria quântica de campos através do formalismo de Schwinger-Keldysh. Usando esse formalismo, de tempo real a dinâmica do condensado é solucionada por um grupo de equações integro-diferencial auto consistente, essas são solucionadas numericamente. Estudamos também o cenário quench, e como a densidade do gás e as interações entre as flutuações tem o efeito de provocar as instabilidades nesse sistema. Aplicamos esse desenvolvimento para estudar o comportamento de duas espécies homogêneas de um gás de Bose diluído imerso em um reservatório térmico.

Tópicos de teoria de campos com aplicações a condensados de Bose-Einstein

A tese de doutorado apresenta uma aplicação de técnicas de teoria de campos em um sistema da matéria condensada. Motivados por experimentos em gases atômicos, apresentamos um estudo sobre misturas binárias de gases atômicos na presença de uma interação do tipo Josephson. O foco principal é o estudo de um modelo de dois campos complexos não-relativisticos com simetria O(2). Esta simetria é quebrada por interações que produzem um desbalanço nas populações das duas espécies bosônicas. Estudamos o modelo na aproximação de campo médio mais flutuações gaussianas, usando o formalismo de teoria de campos a temperatura finita em tempo imaginário. Os resultados mostram que, num certo intervalo de temperaturas, as duas espécies bosônicas condensam à mesma temperatura crítica e a fase relativa do condensado é fixa, determinada pela fase do campo externo aplicado.