Many-body excitations and de-excitations in trapped ultracold bosonic clouds

We employ the MultiConfiguraional Time-Dependent Hartree for Bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, a static and a dynamic one, have been studied and contrasted. In static simulations the low-lying excitations have been computed by utilizing the LR-MCTDHB method - a linear response theory constructed on-top of a static MCTDHB solution. Complimentary, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave-function. In particular, we investigate dipole-like oscillations induced by shifting the origin of the confining potential and breathing-like excitations by quenching frequency of a parabolic part of the trap. To contrast static predictions and dynamic results we have computed time-evolutions and their Fourier transforms of several local and non-local observables. Namely, we study evolution of the $\left< x(t) \right>$, its variance $\operatorname{Var}(x(t))$, and of a local density computed at a selected position. We found out that the variance is the most sensitive and informative quantity - along with excitations it contains information about the de-excitations even in a linear regime of the induced dynamics. The dynamic protocols are found to access the many-body excitations predicted by the static LR-MCTDHB approach.