PhD thesis in English

More documents

Recommendations

Info

$Edge excitations of paired fractional quantum Hall states$

Having the efficient numerical method at our disposal, in Chapter 3 we studyproperties of a rotating ideal gas. The introduction of the angular momentum intothe system is one way of reaching the highly correlated regime in the cold atomsetup. As will be explained, beside other effects, a rotation effectively introduces adeconfining component into the trap potential. Particularly, in the regime of a fastrotation, the gas may experience the complete deconfinement. Hence an additionalquartic potential was used for the trapping in the experiments from Ref. [12], butthe interesting regime of fast rotation has not been completely understood. Usingthe exact diagonalization of a time evolution operator, we study numerically Bose-Einstein condensation in the modified external potential which is a combination ofthe harmonic and quartic component. The shape of the potential changes fromconvex with a single minimum to the Mexican hat shape, depending on the rotationfrequency. We explore how the change of the trapping potential influences the phasediagram properties. We also calculate the density profiles of the gas and time-offlightpictures in different regimes and find that typical time-scales for free expansionare increased by an order of magnitude in the delicate regime of fast rotation.In Chapter 4, we continue and expand a brief exposition of subsection 1.2.3, anddiscuss several different mean-field frameworks for the description of properties of aweakly interacting BECs. First we present the zero temperature mean-field description.We neglect quantum fluctuations and assume that all atoms are condensed atT = 0. In that case, we show that BEC properties are captured by the effectivenonlinear equation, the famous Gross-Pitaevskii equation [34, 19, 13, 14]. Then wemove to the study of finite-temperature mean-field models of BEC. The relevanceof this aspect is two-fold: on one hand, mean-field models are widely used for theinterpretation of experimental data, and on the other hand, from the conceptualpoint of view, it turns out that different models suffer from different unphysicaldrawbacks. We review and compare the existing models by calculating density profileswithin different approximations. To illustrate the influence of weak interactionson the Bose-Einstein condensation, we re-derive the mean-field interaction-inducedshift of the condensation temperature.Chapter 5 deals with the collective excitations of BEC in the nonlinear regime.Characteristics of a BEC can be probed by monitoring its dynamical response tothe external perturbation. Usually, the ground-state BEC is produced and thenit is perturbed by a modulation of the external trap potential. A specific featureof the recent experiment [15] is the harmonic modulation of the s-wave scattering17
length via a Feshbach resonance, yielding a time-dependent interaction strengthg = g(t). An external driving frequency Ω is used for the modulation, and dependingon its closeness to some of the condensate eigenfrequencies, either a resonant ornon-resonant behavior can be observed. This is a new venue for studying nonlineardynamical regime, since the equation governing the condensate dynamics on themean-field level is nonlinear, and large amplitude oscillations are readily producedin the resonant regime. By combining different analytical and numerical methods weanalyze how nonlinear effects influence the properties of the excited collective modes,with implications on the interpretation of the actual experimental data. Prominentnonlinear features, such as: mode coupling, higher harmonics generation, and significantshifts in the frequencies of collective modes are found and quantitativelyexplained using an analytic perturbative approach.At the end of each chapter, we present possible future directions for extending thestudy of research topics of this thesis. Finally, we summarize all results in Chapter6. Additional material and derivations are organized in Appendices.18
Page 1 and 2: UNIVERSITY OF BELGRADEFACULTY OF PH
Page 3 and 4: Thesis advisor, Committee member:Dr
Page 6 and 7: lence for Computer Modeling of Comp
Page 8 and 9: dobijanje kondenzata odabrani su at
Page 10 and 11: Uticaj slabih interakcija na fenome
Page 12 and 13: Abstract of the doctoral dissertati
Page 14 and 15: highly accurate information on ener
Page 16 and 17: Keywords: cold quantum gases, Bose-
Page 18 and 19: CONTENTS3.4.2 Time-of-flight graphs
Page 20 and 21: NomenclatureRoman Symbolsagk BLMNn(
Page 22 and 23: Chapter 1Introduction1.1 ForewordTh
Page 24 and 25: ently explored to illustrate the ve
Page 26 and 27: Summations in the last expression c
Page 28 and 29: Figure 1.1: The hallmark of the Bos
Page 30 and 31: we discuss in some detail the exper
Page 32 and 33: In the first papers [3, 4], the TOF
Page 34 and 35: where a BG is the off-resonant scat
Page 36 and 37: system given by( ) ǫ Bog ⃗k =
Page 40 and 41: Chapter 2Properties of quantum syst
Page 42 and 43: 2. Diagonalization of Transition Am
Page 66 and 67: ||2. Diagonalization of Transition
Page 74: 2. Diagonalization of Transition Am
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
Page 85 and 86: 3. Rotating ideal BEC350300SC appro
Page 87 and 88: 3. Rotating ideal BEC3.2 Finite num
Page 89 and 90:
3. Rotating ideal BECN - N 03.0·10
Page 91 and 92:
3. Rotating ideal BEC3.3 Global pro
Page 93 and 94:
3. Rotating ideal BECever, it does
Page 95 and 96:
3. Rotating ideal BECT c [nK]120110
Page 97 and 98:
3. Rotating ideal BEC3.533210 3 κ
Page 99 and 100:
3. Rotating ideal BECn(x, y)10·10
Page 101 and 102:
3. Rotating ideal BECpancy numbers
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
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Chapter 5Nonlinear BEC dynamics by
Page 127 and 128:
5. BEC excitation by modulation of
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
where n = 1, 2, 3, . . . is an inte
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Chapter 6SummarySince the first exp
Page 157 and 158:
short-range interactions.The excita
Page 159 and 160:
of the ground state. Imaginary-time
Page 161 and 162:
(A.13). With another boundary condi
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
Page 175 and 176:
REFERENCES[94] M.-O. Mewes, M. R. A
Page 177 and 178:
REFERENCES[116] K. Staliunas, S. Lo
Page 179 and 180:
CURRICULUM VITAE - Ivana Vidanović
show all

PhD thesis in English

Create successful ePaper yourself

Delete template?

Save as template?