PhD thesis in English

Chapter 5Nonlinear BEC dynamics by harmonicmodulation of s-wave scattering lengthA thorough knowledge of the excitation spectra of a quantum system is quiteimportant since the properties of its excitations characterize the phase of the matterin a very precise way. The excitation spectra capture information on the system’scorrelations and define the response of the system to external perturbations. Experimentally,they are determined by exposing the system to a weak perturbationand by measuring the induced dynamics. Thus, the dynamics of the system and itsexcitation spectra are closely related concepts.First microscopic derivation of the excitation spectrum of a superfluid, given byEq. (1.28), was published in the seminal paper of Bogoliubov in 1947 [30]. The obtainedspectrum contains a collective phonon mode in the limit of a vanishing wavenumber, and single-particle excitations in the limit of a large wave number. Theoriginal aim of Bogoliubov was the explanation of the superfluidity in 4 He and thecollective motion of bosonic particles was identified as the underlying mechanismthat leads to the phenomenon. Yet, the Bogoliubov approach assumes weak interactions,while 4 He is a strongly interacting system and the agreement between thetheoretical and experimental results is only qualitative. The dilute vapors of alkaliatoms were the first proper experimental realization of a weakly interacting bosonicsystem that allowed quantitative tests of the theoretical concepts introduced in theearly papers of Landau [96] and Bogoliubov [30]. For this reason, the experimentsstudying the collective bosonic modes were initiated soon after the first achievementof an atomic BEC.A basic underlying idea of the early experiments was a clear demonstrationof the distinction between the collective response of the condensed cloud and theresponse of thermal atoms to external perturbations. A common scenario in themajority of experiments is to start with the ground-state condensate at very lowtemperature, where the condensate depletion is negligible, and to induce collectiveoscillation modes by a temporary modulation of the external trapping potential104