PhD thesis in English

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