Mean-field model of jet formation in a collapsing Bose-Einstein condensate

We perform a systematic numerical study, based on the time-dependent Gross-Pitaevskii equation, of jet formation in collapsing and exploding Bose-Einstein condensates as in the experiment by Donley et al (2001 Nature 412 295). In the actual experiment, via a Feshbach resonance, the scattering length of atomic interaction was suddenly changed from positive to negative on a pre-formed condensate. Consequently, the condensate collapsed and ejected atoms via explosion. On disruption of the collapse by suddenly changing the scattering length to zero, a radial jet of atoms was formed in the experiment. We present a satisfactory account of jet formation under the experimental conditions and also make predictions beyond experimental conditions which can be verified in future experiments.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Estabilidade de sistemas condensados com interação atrativa ou repulsiva

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Oscilações não-lineares em condensados de Bose-Einstein

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamics of the corotating vortices in dipolar Bose-Einstein condensates in the presence of dissipation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bright dipolar Bose-Einstein-condensate soliton mobile in a direction perpendicular to polarization

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonlinear optical lattices, are investigated. In particular, with a starting optical lattice (OL) configuration such that it is linear in the x-direction and nonlinear in the y-direction, we consider the z-direction either unconstrained (quasi-2D OL case) or with another linear OL (full 3D case). We perform this study both analytically and numerically: analytically by a variational approach based on a Gaussian ansatz for the soliton wavefunction and numerically by relaxation methods and direct integrations of the corresponding Gross-Pitaevskii equation. We conclude that, while 3D solitons in the quasi-2D OL case are always unstable, the addition of another linear OL in the z-direction allows us to stabilize 3D solitons both for attractive and repulsive mean interactions. From our results, we suggest the possible use of spatial modulations of the nonlinearity in one of the directions as a tool for the management of stable 3D solitons.

Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

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.

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T-c of a harmonically confined Bose gas as reported in Gerbier , Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

Bose-Einstein condensate in a quartic potential:static and dynamic properties

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

Image acquisition and manipulation protocols for CT-PET fusion to improve the accuracy of gross tumour volume localisation for 3D conformal radiotherapy for lung cancer

Aims: To develop clinical protocols for acquiring PET images, performing CT-PET registration and tumour volume definition based on the PET image data, for radiotherapy for lung cancer patients and then to test these protocols with respect to levels of accuracy and reproducibility. Method: A phantom-based quality assurance study of the processes associated with using registered CT and PET scans for tumour volume definition was conducted to: (1) investigate image acquisition and manipulation techniques for registering and contouring CT and PET images in a radiotherapy treatment planning system, and (2) determine technology-based errors in the registration and contouring processes. The outcomes of the phantom image based quality assurance study were used to determine clinical protocols. Protocols were developed for (1) acquiring patient PET image data for incorporation into the 3DCRT process, particularly for ensuring that the patient is positioned in their treatment position; (2) CT-PET image registration techniques and (3) GTV definition using the PET image data. The developed clinical protocols were tested using retrospective clinical trials to assess levels of inter-user variability which may be attributed to the use of these protocols. A Siemens Somatom Open Sensation 20 slice CT scanner and a Philips Allegro stand-alone PET scanner were used to acquire the images for this research. The Philips Pinnacle3 treatment planning system was used to perform the image registration and contouring of the CT and PET images. Results: Both the attenuation-corrected and transmission images obtained from standard whole-body PET staging clinical scanning protocols were acquired and imported into the treatment planning system for the phantom-based quality assurance study. Protocols for manipulating the PET images in the treatment planning system, particularly for quantifying uptake in volumes of interest and window levels for accurate geometric visualisation were determined. The automatic registration algorithms were found to have sub-voxel levels of accuracy, with transmission scan-based CT-PET registration more accurate than emission scan-based registration of the phantom images. Respiration induced image artifacts were not found to influence registration accuracy while inadequate pre-registration over-lap of the CT and PET images was found to result in large registration errors. A threshold value based on a percentage of the maximum uptake within a volume of interest was found to accurately contour the different features of the phantom despite the lower spatial resolution of the PET images. Appropriate selection of the threshold value is dependant on target-to-background ratios and the presence of respiratory motion. The results from the phantom-based study were used to design, implement and test clinical CT-PET fusion protocols. The patient PET image acquisition protocols enabled patients to be successfully identified and positioned in their radiotherapy treatment position during the acquisition of their whole-body PET staging scan. While automatic registration techniques were found to reduce inter-user variation compared to manual techniques, there was no significant difference in the registration outcomes for transmission or emission scan-based registration of the patient images, using the protocol. Tumour volumes contoured on registered patient CT-PET images using the tested threshold values and viewing windows determined from the phantom study, demonstrated less inter-user variation for the primary tumour volume contours than those contoured using only the patient’s planning CT scans. Conclusions: The developed clinical protocols allow a patient’s whole-body PET staging scan to be incorporated, manipulated and quantified in the treatment planning process to improve the accuracy of gross tumour volume localisation in 3D conformal radiotherapy for lung cancer. Image registration protocols which factor in potential software-based errors combined with adequate user training are recommended to increase the accuracy and reproducibility of registration outcomes. A semi-automated adaptive threshold contouring technique incorporating a PET windowing protocol, accurately defines the geometric edge of a tumour volume using PET image data from a stand alone PET scanner, including 4D target volumes.