Static and Dynamic Study of Bose-Einstein Condensates

Abstract

The aim of the project is to study the formalism behind Bose-Einstein condensates. Using the imaginary time method, we obtain the ground state of the condensate solving the Gross-Pitaevskii equation with an ansatz wave function. Then, we study the two analytical limit cases: the Thomas-Fermi approximation and the non-interacting limit. After that, we perturb the condensate with the monopolar excitation operator and we observe the oscillations produced on the expectation value of ⟨r2⟩. We obtain the frequency of the oscillations of the condensate with a Fourier transform analysis. Finally, we expand our study considering a contribution beyond the mean-field theory in order to study the emergence of self-bound droplets. We compute the ground state for this system, following the same procedures as for the condensate