PhD thesis in English

More documents

Recommendations

Info

$Edge excitations of paired fractional quantum Hall states$

5. BEC excitation by modulation of scattering lengthcaptures most of the observed phenomena. The main results are analytic formulaedescribing the dependence of collective mode frequencies on the modulation amplitudeand on the external driving frequency for different trap geometries. Webelieve that the study presented in this Chapter is a step toward understandingresonant processes in a nonlinear system. To extend the applicability of our analyticalapproach, a perturbative expansion to higher order has to be performed, or anappropriate resummation of the perturbative series could be applied.The presented results could contribute to future experimental designs that mayinclude mixtures of cold gases and their dynamical response to harmonically modulatedinteractions, such as pattern formation induced by the modulation of differenttime dependence of the scattering length. In addition, our results could contributeto resolving beyond-mean-field effects in the collective mode frequencies, as proposedin Refs. [134, 135], and for dipolar BEC in [136]. Nonlinearity-induced shiftsof collective modes have to be properly taken into account to clearly delineate themfrom beyond-mean-field effects.133
Chapter 6SummarySince the first experimental observation of Bose-Einstein condensation in thedilute vapors of alkali atoms in 1995, the field of ultracold atoms constantly expands.The experimental advances in the manipulation of quantum gases pave a way to thedevelopment of new technologies, and allow exploration of the quantum world withpreviously unseen precision and flexibility, uncovering at the same time new varietyof far reaching physical phenomena. In this thesis we have studied two particularphenomena that give new insights into the properties of cold quantum gases andhave been recently addressed experimentally.To begin with, in Chapter 1 we have introduced the aspects of the research in thefield of ultracold atoms, main concepts, and its position within the wide forefrontof modern physics. In Chapter 2 we have developed an efficient numerical methodfor calculation of the eigenspectrum and eigenvectors of a system in an arbitrarytrapping potential. The devised approach is based on the exact diagonalizationof the time-evolution operator and can be applied for numerical studies of generalfew-body systems. We have carefully explored different types of systematic errorsthat arise in the process of the spatial discretization of the time-evolution operator.We have shown analytically and numerically that the discretization error vanishesas the exponential of 1/∆ 2 , where ∆ represents the discretization spacing. Thus,the method highly outperforms in efficiency the approaches based on the real- spacediscretization of the Hamiltonian, which exhibit polynomial error in ∆. For thehighly accurate calculation of matrix elements of the evolution operator, necessaryfor the application of the method, we use the short-time expansion of transitionamplitudes in the propagation time to high-orders. The chief ingredients of this partof the procedure are higher-order effective actions, that were derived previously. Wehave demonstrated the advantages of this method by calculating highly accurateenergy spectra in a numerically efficient way for several one- and two-dimensionalmodels.Motivated by experimental studies of rotating ultra-cold quantum gases, in Chap-134
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 38 and 39:
Having the efficient numerical meth
Page 40 and 41:
Chapter 2Properties of quantum syst
Page 42 and 43:
2. Diagonalization of Transition Am
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
||2. Diagonalization of Transition
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74:
Page 77 and 78:
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 125 and 126: Chapter 5Nonlinear BEC dynamics by
Page 127 and 128: 5. BEC excitation by modulation of
Page 149 and 150: where n = 1, 2, 3, . . . is an inte
Page 153: 5. BEC excitation by modulation of
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?