PhD thesis in English

More documents

Recommendations

Info

$Edge excitations of paired fractional quantum Hall states$

Abstract of the doctoral dissertationNumerical study of quantum gasesat low temperaturesThe concept of Bose-Einstein condensation was introduced in 1924, at the sametime as Bose-Einstein statistics, applicable to the integer-spin particles [1, 2]. Alreadyfirst theoretical quantum-mechanical considerations pointed to the existence ofthis phenomenon. It is well known that physical properties of atomic gases stronglydepend on the temperature. At room temperatures the properties of these systemscan be described by the classical statistical physics, and quantum features are negligible.However, as the temperature decreases, the wavelengths of the de Brogliemater waves increase, leading to the overlap of waves corresponding to different particles.In this case, quantum statistics plays a dominant role. According to the rulesof quantum statistics, integer-spin particles, bosons, are allowed to occupy the samesingle-particle quantum states. With the decrease in the temperature, the systemseeks the minimal-energy configuration, and for bosons this is a macroscopicallyoccupied single-particle ground state. Such a quantum state becomes dominant andthe occurrence is designated as a macroscopic quantum phenomenon. Accordingly,we distinguish a phase with a macroscopic occupation of the ground state (Bose-Einstein condensate) and a phase without this feature, which is called a normal gas.The phase transition between the two phases is Bose-Einstein condensation. In spiteof the firm theoretical foundation of the concept from the beginning, first direct experimentalobservation was achieved only in 1995, and the result was recognized bythe Nobel prize for physics in 2001.As briefly explained, the basic notion of Bose-Einstein condensation was introducedusing a model of noninteracting gas. Of course, in realistic gases, interactionscan not be neglected and only due to them the gas becomes liquid or solid at lowtemperatures. In order to remain close to the noninteracting gas description inexperiments, it is essential to use weakly interacting gases, such as dilute gases interactingvia short-range, van der Waals interaction. In this type of systems, withlong interparticle distances due to diluteness, the quantum phenomena become relevantonly at very low temperatures. Due to highly efficient cooling techniques,
the gases of alkali metals (Rb, Li, Na, ...) were selected as most suitable candidatesand Bose-Einstein condensation was observed for the first time [3, 4] in such systemswith the typical particle densities from 10 18 m −3 to 10 21 m −3 (six orders of magnitudelower than the density of air) and temperatures of the order of 100 nK. In order toreach this extreme low-temperature regime, it was necessary to develop many newcooling and trapping techniques: in experiments, atoms are confined using speciallydesigned configurations of external magnetic or electric fields. After many yearsof intensive experimental efforts, the achievement of Bose-Einstein condensation incold alkali vapors is nowadays a common technique in laboratories all over the world.The experiments make possible very detailed tests of fundamental theoreticalconcepts - collective excitations of a Bose-Einstein condensate, superfluidity (theappearance of vortices as a response to rotation), the properties of a phase diagram[5]. A very important and interesting feature of ultracold quantum gases is a possibilityto control relevant parameters of the system over many orders of magnitude.Basically, all parameters can be tuned: number of particles, density, temperature,dimensionality (by changing the shape of the external trap), and even the strengthof interactions between atoms using a technique called Feshbach resonance [6]. Bya simple modification of the external magnetic field, the effective interatomic interactioncan be tuned in the range of several orders of magnitude and this featuremakes cold atomic systems really unique. In more recent experiments, atoms aretrapped in periodic potentials, the so-called optical lattices [7]. In this way, it isnow possible to study, in a very clean setup, systems which are highly relevant incondensed matter physics, and which are not yet completely understood (with a notableexample of high-temperature superconductivity). For this reason, it is widelyaccepted that ultracold quantum gases represent Feynman’s quantum simulators [8].Intensive experimental progress and realization of the new ultracold phase of matterare strong stimuluses for further, interdisciplinary theoretical research.The main subject of this thesis is a thorough understanding of two interestingphysical scenarios for the manipulation of cold bosonic atoms, which were also thefocus of recent experimental studies. First, we have explored the phase diagram ofa rotating ideal bosonic gas in an anharmonic trap, while the second main topicdeals with nonlinear features of collective modes excited by harmonic modulation ofinteraction strength.On the way to accomplish this, after introductory Chapter 1, in Chapter 2 wehave first worked out details of an efficient numerical method capable of providing
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 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 62 and 63:
2. Diagonalization of Transition Am
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 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?