Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the number of atoms in the condensate is increased, with $T$ held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.Comment: 4 pages LaTeX, 3 eps figures. To appear as a letter in J. Phys.

Long-range sound-mediated dark soliton interactions in trapped atomic condensates

A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An idealized double well geometry is shown to yield perfect energy transfer and complete periodic identity reversal of the two solitons. Two experimentally relevant geometries are analyzed which should enable the observation of this long-range interaction

Speech production in children with Down's syndrome: The effects of reading, naming and imitation

People with DS are known to have difficulties with expressive language, and often have difficulties with intelligibility. They often have stronger visual than verbal short-term memory skills and, therefore, reading has often been suggested as an intervention for speech and language in this population. However, there is as yet no firm evidence that reading can improve speech outcomes. This study aimed to compare reading, picture naming and repetition for the same 10 words, to identify if the speech of eight children with DS (aged 11-14 years) was more accurate, consistent and intelligible when reading. Results show that children were slightly, yet significantly, more accurate and intelligible when they read words compared with when they produced those words in naming or imitation conditions although the reduction in inconsistency was non-significant. The results of this small-scale study provide tentative support for previous claims about the benefits of reading for children with DS. The mechanisms behind a facilitatory effect of reading are considered, and directions are identified for future research

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP

We investigate the dynamics of a Bose--Einstein condensate (BEC) in a triple-well trap in a three-level approximation. The inter-atomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. New eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three level Landau-Zener model and the STIRAP scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.Comment: RevTex4, 7 pages, 11 figures, content extended and title/abstract change

Slow 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ in the light of recent experiments. Extending our previous results to later times, we argue that short wavelength thermal fluctuations make vortices poorly defined until after the transition has occurred. Further, if and when vortices appear, it is plausible that that they will decay faster than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title, this paper differs from its predecessor by including temperature, as well as pressure, quenche

Coherent control of stimulated Raman scattering using chirped laser pulses

A novel method for the control of stimulated Raman scattering and hot electron production in short-pulse laser-plasma interactions is proposed. It relies on the use of a linear frequency chirp in nonbandwidth limited pulses. Theoretical calculations show that a 12% bandwidth will eliminate Raman forward scattering for a plasma density that is 1% of the critical density. The predicted changes to the growth rate are confirmed in two-dimensional particle-in-cell simulations. Relevance to areas of current research is also discussed. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70620/2/PHPAEN-8-8-3531-1.pd

Gapless finite-TT theory of collective modes of a trapped gas

We present predictions for the frequencies of collective modes of trapped Bose-condensed $^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.Comment: 4 pages Latex and 2 postscript figure

A Gapless Theory of Bose-Einstein Condensation in Dilute Gases at Finite Temperature

In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with higher order cubic and quartic terms. The quadratic part is diagonalized exactly by transforming to a quasiparticle basis, while the non-quadratic terms are dealt with using first and second order perturbation theory. The conventional treatment of these terms, based on factorization approximations, is shown to be inconsistent. Infra-red divergences can appear in individual terms of the perturbation expansion, but we show analytically that the total contribution beyond quadratic order is finite. The resulting excitation spectrum is gapless and the energy shifts are small for a dilute gas away from the critical region, justifying the use of perturbation theory. Ultra-violet divergences can appear if a contact potential is used to describe particle interactions. We show that the use of this potential as an approximation to the two-body T-matrix leads naturally to a high-energy renormalization. The theory developed in this paper is therefore well-defined at both low and high energy and provides a systematic description of Bose-Einstein condensation in dilute gases. It can therefore be used to calculate the energies and decay rates of the excitations of the system at temperatures approaching the phase transition.Comment: 39 pages of Revtex. 1 figur