PhD thesis in English

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$Edge excitations of paired fractional quantum Hall states$

3. Rotating ideal BEC500040003000n(x, y)TOF = 0 ms50002500500040003000n(x, y)TOF = 8 ms500025002000020000100010000-15-10-5x051015-10-15-5051510y0-15-10-5x051015-10-15-5051510y500040003000n(x, y)TOF = 16 ms50002500500040003000n(x, y)TOF = 24 ms500025002000020000100010000-15-10-5x051015-10-15-5051510y0-15-10-5x051015-10-15-5051510y500040003000n(x, y)TOF = 40 ms50002500500040003000n(x, y)TOF = 60 ms500025002000020000100010000-15-10-5x051015-10-15-5051510y0-15-10-5x051015-10-15-5051510yFigure 3.12: Time-of-flight absorption density profiles in xy-plane for an overcriticallyrotating (η = 1.04) condensate of N = 3 · 10 5 atoms of 87 Rb with theanharmonicity κ = κ BEC at T = 30 nK. The flight time, is given at each plot. Thedimensionless unit length on all graphs corresponds to 1.34 µm and the linear sizeof profiles is approximately 53.6 µm. The discretization parameters are given inTable 3.3.the TOF absorption imaging sequence in the xy-plane for an overcritically (η = 1.04)rotating Bose-Einstein condensate with the anharmonicity κ = κ BEC and the particlenumber N = 3 · 10 5 at T = 30 nK, exhibiting an interesting behavior. The initialdensity profile has a minimum at the origin, due to the shape of the anharmonicpotential. The free expansion of the condensate leads to an increase in the particledensity at the origin, and only afterwards the condensate density profile expandsmonotonically. Fig. 3.13 presents the time dependence of the particle density at81
3. Rotating ideal BEC6·10 4 0 0.02 0.04 0.06 0.08 0.112·10 3 0 0.02 0.04 0.06 0.08 0.1n(0, 0)5·10 44·10 43·10 42·10 41·10 4010·10 38·10 36·10 34·10 32·10 30η=0.80η=1.00η=1.04TOF [ms]Figure 3.13: Condensate density at the origin of x − y plane as a function of thetime of flight (TOF) for the condensate of N = 3 · 10 5 atoms of 87 Rb at T = 30 nKfor several rotation frequencies Ω in units of η = Ω/ω. The quartic anharmonicityis κ = κ BEC and the discretization parameters are given in Table 3.3.the origin for varying rotation frequencies, parameterized by the ratio η = Ω/ω.We read off that approaching the critical rotation slows down the expansion ofthe condensate. For overcritical rotation this is even more pronounced, due to theappearance of the peak in the particle density for the expansion time t > 0. Thisleads to an expansion that is typically an order of magnitude slower for the rotationwith η > 1.3.5 Conclusions and outlookIn this Chapter the exact diagonalization of a time evolution operator is appliedto the study of ideal Bose gases in the anharmonic trap. Earlier derived higherordereffective actions are used for an efficient numerical calculation of both globaland local properties of fast-rotating Bose-Einstein condensates. To this end we havecalculated large numbers of single-particle eigenvalues and eigenstates and using thisinformation, we have obtained the condensation temperature and the ground-stateoccupancy of the condensate, as well as density profiles and TOF absorption graphs.We have have focused on a critical and an overcritical rotation and have found asubstantial increase in the time scale for the expansion of the condensate after the82
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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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Page 52 and 53: 2. Diagonalization of Transition Am
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Page 105 and 106: Chapter 4Mean-field description of
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Page 125 and 126: Chapter 5Nonlinear BEC dynamics by
Page 127 and 128: 5. BEC excitation by modulation of
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5. BEC excitation by modulation of
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Chapter 6SummarySince the first exp
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short-range interactions.The excita
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of the ground state. Imaginary-time
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(A.13). With another boundary condi
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Appendix B Time-dependent variation
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List of papers by Ivana VidanovićT
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References[1] S. N. Bose, Plancks g
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REFERENCES[21] W. Ketterle, D. S. D
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REFERENCES[45] A. Bogojević, A. Ba
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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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