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Työväentutkimus Vuosikirja

Dynamics and excitations of Bose-Einstein condensates

J.-P. Martikainen

Published Dec 1, 2001• 3 citations
OpenAlex

Abstract

iii List of publications iv Summary of the original publications v Contribution by the author vi

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Ultracold gases are of great interest in modern physics. The main reason is that in the systems of ultracold gases the parameters can be easily tuned, thus they can be used as a testing ground for various quantum many-body theories. Interesting macroscopic quantum effects have been observed in the ultracold gas systems, for instance Bose-Einstein condensation. In this thesis, theoretical knowledge of ultracold gases is extended. A summary of the methods used in this thesis is given, including a detailed description of the density response theory and the time-evolving block decimation (TEBD) algorithm. Collective excitations of an ultracold gas in a three-dimensional (3D) spherically symmetric trap are studied in detail in publications II and III. As a result, several collective modes are discovered such as a low energy Higgs-type mode, a second sound-like mode, and a strong mode resembling the Leggett mode. Using the TEBD algorithm, physics of a polaron in a one-dimensional (1D) lattice, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in 1D are studied in publications IV and I, respectively. In publication I a method to detect the FFLO phase is suggested, namely by the observation of the change in the double occupancy after a lattice depth modulation. Publication IV compares a variational ansatz and the TEBD simulations and finds an excellent agreement, indicating that the variational ansatz can be used to describe the system for a certain range of interactions.
This 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).
We have analytically explored the phenomenon of quantum scattering for unfixed quantum scatterers. We have considered short ranged (Fermi-Huang δp3\delta_p^3δp3​ [1]) interaction between the incident `particle' and the scatterer with no interactions among the scatterers, and the scatterers as (i) particle(s) in a 1-D box, (ii) particle(s) in a 1-D double box, (iii) particle(s) in a 1-D grating, (iv) particle(s) in a 2-D rectangular box, (v) particle(s) in a 3-D harmonic trap, (vi) Bose-Einstein condensates in a double well, (vii) Bose-Einstein condensates in an optical lattice, etc. Coherent scattering from all possible positions of the quantum scatterers in the finite geometry gives rise to rich physics. We have predicted differential scattering cross-section for `particle' scattering, not only for the above cases, but also for 3-D harmonically trapped Bose and Fermi gases in thermodynamic equilibrium. Our predictions can be tested within the present day experimental setups.