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We unravel the stationary properties and the interaction quench dynamics oftwo bosons, confined in a two-dimensional anisotropic harmonic trap. Atranscendental equation is derived giving access to the energy spectrum andrevealing the dependence of the energy gaps on the anisotropy parameter. Therelation between the two and the one dimensional scattering lengths as well asthe Tan contacts is established. The contact, capturing the two-body shortrange correlations, shows an increasing tendency for a larger anisotropy.Subsequently, the interaction quench dynamics from attractive to repulsivevalues and vice versa is investigated for various anisotropies. A closedanalytical form of the expansion coefficients of the two-body wavefunction,during the time evolution is constructed. The response of the system is studiedby means of the time-averaged fidelity, the spectra of the spatial extent ofthe cloud in each direction and the one-body density. It is found that as theanisotropy increases, the system becomes less perturbed independently of theinteractions while for fixed anisotropy quenches towards the non-interactingregime perturb the system in the most efficient manner. Furthermore, weidentify that in the tightly confined direction more frequencies are involvedin the dynamics stemming from higher-lying excited states.

Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one