PhD thesis in English

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$Edge excitations of paired fractional quantum Hall states$

approximations become a demand.4. Mean-field description of an interacting BEC103
Chapter 5Nonlinear BEC dynamics by harmonicmodulation of s-wave scattering lengthA thorough knowledge of the excitation spectra of a quantum system is quiteimportant since the properties of its excitations characterize the phase of the matterin a very precise way. The excitation spectra capture information on the system’scorrelations and define the response of the system to external perturbations. Experimentally,they are determined by exposing the system to a weak perturbationand by measuring the induced dynamics. Thus, the dynamics of the system and itsexcitation spectra are closely related concepts.First microscopic derivation of the excitation spectrum of a superfluid, given byEq. (1.28), was published in the seminal paper of Bogoliubov in 1947 [30]. The obtainedspectrum contains a collective phonon mode in the limit of a vanishing wavenumber, and single-particle excitations in the limit of a large wave number. Theoriginal aim of Bogoliubov was the explanation of the superfluidity in 4 He and thecollective motion of bosonic particles was identified as the underlying mechanismthat leads to the phenomenon. Yet, the Bogoliubov approach assumes weak interactions,while 4 He is a strongly interacting system and the agreement between thetheoretical and experimental results is only qualitative. The dilute vapors of alkaliatoms were the first proper experimental realization of a weakly interacting bosonicsystem that allowed quantitative tests of the theoretical concepts introduced in theearly papers of Landau [96] and Bogoliubov [30]. For this reason, the experimentsstudying the collective bosonic modes were initiated soon after the first achievementof an atomic BEC.A basic underlying idea of the early experiments was a clear demonstrationof the distinction between the collective response of the condensed cloud and theresponse of thermal atoms to external perturbations. A common scenario in themajority of experiments is to start with the ground-state condensate at very lowtemperature, where the condensate depletion is negligible, and to induce collectiveoscillation modes by a temporary modulation of the external trapping potential104
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UNIVERSITY OF BELGRADEFACULTY OF PH
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Thesis advisor, Committee member:Dr
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lence for Computer Modeling of Comp
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dobijanje kondenzata odabrani su at
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Uticaj slabih interakcija na fenome
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Abstract of the doctoral dissertati
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highly accurate information on ener
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Keywords: cold quantum gases, Bose-
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CONTENTS3.4.2 Time-of-flight graphs
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NomenclatureRoman Symbolsagk BLMNn(
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Chapter 1Introduction1.1 ForewordTh
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ently explored to illustrate the ve
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Summations in the last expression c
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Figure 1.1: The hallmark of the Bos
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we discuss in some detail the exper
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In the first papers [3, 4], the TOF
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where a BG is the off-resonant scat
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system given by( ) ǫ Bog ⃗k =
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Having the efficient numerical meth
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Chapter 2Properties of quantum syst
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2. Diagonalization of Transition Am
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||2. Diagonalization of Transition
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Page 74: 2. Diagonalization of Transition Am
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Page 79 and 80: magnetic field ⃗ B = 2M ⃗ Ω.3.
Page 81 and 82: 3. Rotating ideal BECof the rotatio
Page 83 and 84: 3. Rotating ideal BEC3.1 Numerical
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Page 99 and 100: 3. Rotating ideal BECn(x, y)10·10
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Page 103 and 104: 3. Rotating ideal BEC6·10 4 0 0.02
Page 105 and 106: Chapter 4Mean-field description of
Page 107 and 108: 4. Mean-field description of an int
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Page 127 and 128: 5. BEC excitation by modulation of
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Page 155 and 156: Chapter 6SummarySince the first exp
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Page 163 and 164: Appendix B Time-dependent variation
Page 165 and 166: List of papers by Ivana VidanovićT
Page 167 and 168: References[1] S. N. Bose, Plancks g
Page 169 and 170: REFERENCES[21] W. Ketterle, D. S. D
Page 171 and 172: REFERENCES[45] A. Bogojević, A. Ba
Page 173 and 174: REFERENCES[70] M. R. Matthews, B. P
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REFERENCES[94] M.-O. Mewes, M. R. A
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REFERENCES[116] K. Staliunas, S. Lo
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CURRICULUM VITAE - Ivana Vidanović
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PhD thesis in English

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