PhD thesis in English

5. BEC excitation by modulation of scattering lengthThe main result obtained by using the Gaussian approximation is an analyticalestimate for the frequencies of the low-lying collective modes, expressed by Eqs. (5.5)and (5.6) [104, 105]. We emphasize that, although based on the Gaussian Ansatz,the variational approximation reproduces exactly the frequencies of collective modesnot only for the weakly interacting BEC, but also for the strongly interacting BECin the Thomas-Fermi regime [103, 104]. Therefore, it represents a solid analyticaldescription of BEC dynamics. Most importantly, a reasonable quantitative agreementwas obtained between the linear response theoretical results (5.5) and (5.6)and experimental results for BEC excited using the trap modulation. In general, adetailed experimental information on collective modes allows us to test our theoreticalunderstanding of the properties of an atomic BEC. The essential merit of testingtheoretical predictions using collective oscillation modes stems from the possibilityto measure frequencies of collective modes with a high accuracy on the order of lessthan 1% [100, 99, 101].We point out that the early theoretical studies of collective modes of BEC[102, 103, 104] focused on the exploration of dynamical properties in the linearregime of small amplitude oscillations. Certain nonlinear aspects of condensate dynamicsinduced by a trap modulation are given in Refs. [117, 118, 119], whereastwo-component BECs are dealt with in Refs. [120, 121]. In the next section we turnto the recent experimental study in which nonlinear effects arise from the modulationof the interaction strength and study how nonlinear dynamical features arereflected on the properties of the excitation spectrum.5.2 Harmonic modulation of the s-wave scattering length:experimentDetails of the Feshbach resonance of a 7 Li BEC were explored by the R. Hulet’sgroup from the Rice University in Ref. [122], and an extreme tunability of interactionswas experimentally demonstrated. In the mentioned experiment, atoms weretrapped by the optical trap, while the bias magnetic field was used for tuning thescattering length via the Feshbach resonance. For the range of values of magneticfield B, a ground-state condensate was produced and the corresponding densityprofiles were observed. By measuring the width of the condensate distribution andcomparing these values with the corresponding numerical data based on the GPequation (4.15), information on the scattering length spanning seven orders of mag-111