PhD thesis in English

More documents

Recommendations

Info

$Edge excitations of paired fractional quantum Hall states$

5. BEC excitation by modulation of scattering lengthwhere P = √ 2/πNa av /l denotes the average interaction strength, Q = √ 2/πNδ a /lis a modulation amplitude, and Ω represents the modulation or driving frequency.The dimensionless experimental parameters from Ref. [15] have the valuesP = 15, Q = 10, λ z = 0.021 , (5.9)corresponding to the highly elongated trap with the modulated but always positive(repelling) interaction. In the experiment, the oscillations of the condensate sizewere observed by in-situ phase-contrast imaging, presented in Fig. 5.4.Figure 5.4: Oscillations of the BEC cloud, presented by a series of density profilestaken at equidistant time step of 15 ms. Results are taken from Ref. [15].The interpretation of the experimental data was based on the analytical resultsfor the frequencies of the low-lying collective modes obtained from the linearizedform of the Gaussian approximation. For experimental data, Eq. (5.5) yields thefollowing values for the frequencies of the quadrupole and the breathing mode:ω Q0 = 0.035375 , ω B0 = 2.00002 . (5.10)The external trap was stationary, thus preventing excitations of the dipole (Kohn)mode, corresponding to the center-of-mass motion. For the specific set of experimentalparameters basically only the quadrupole oscillation mode was excited in thisway and resonances located at the quadrupole frequency and its second harmonicwere observed.There are several advantages of such an experimental scheme: for instance, infuture experiments with multi-species BEC, a single component could be individuallyexcited in this way, while the excitation of other components would occur onlyindirectly.113
5. BEC excitation by modulation of scattering lengthHowever, due to the nonlinear form of the underlying GP equation, we expectnonlinearity-induced shifts in the frequencies of low-lying modes compared to thevalues obtained from Eq. (5.5), calculated using the linear stability analysis. Inparticular, in the case of a close matching of the driving frequency Ω and one ofthe BEC eigenmodes, we expect resonances, i.e. large amplitude oscillations of thecondensate size. When this happens, the role of the nonlinear terms becomes crucialand nonlinear phenomena become dominant. Furthermore, we emphasize thatoscillations with very small amplitudes, which occur in the linear regime, are experimentallyhard to observe. On the other hand, very large amplitude oscillationslead to a fragmentation of the condensate [15, 123]. Thus, the case in between is ofthe main experimental interest and represents our main objective, as we discuss inthe next section.5.3 Harmonic modulation of the s-wave scattering length:theoretical frameworkTo study nonlinear BEC dynamics, we use an approach that is complementary tothe recent theoretical considerations [113, 114, 115, 116] of a BEC with harmonicallymodulated interaction. In Ref. [114] the real-time dynamics of a sphericallysymmetric BEC was numerically studied and analytically explained using the resonantBogoliubov-Mitropolsky method [124]. On the other hand, in our approach inorder to discern induced dynamical features, we look directly at the excitation spectrumobtained from a Fourier transform of the time-dependent condensate width.From this type of numerical analysis we find characteristic nonlinear properties:higher harmonic generation, nonlinear mode coupling, and significant shifts in thefrequencies of collective modes with respect to their linear response counterparts.In addition, we work out an analytic perturbative theory with respect to the modulationamplitude, capable of capturing many of the mentioned nonlinear effectsobtained numerically.Nonlinearity-induced frequency shifts were considered previously in Ref. [117] forthe case of bosonic collective modes excited by modulation of the trapping potential,and also in Ref. [125] for the case of a superfluid Fermi gas in the BCS-BEC crossover.Our analytical approach is based on the Poincaré-Lindstedt method [126, 127, 128,124], in the same spirit as presented in Refs. [117, 125, 126]. However, the harmonicmodulation of the interaction strength introduces additional features that require a114
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 133: 5. BEC excitation by modulation of
Page 149 and 150: where n = 1, 2, 3, . . . is an inte
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

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

Delete template?

Save as template?