Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential

We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in absence of BEC but with the Rabi frequencies of fermionic excited states explicitly depending on the number of bosons and on the boson-fermion interaction strength. From this, the possibility to control quantum fermionic dynamics by means of Feshbach resonances is suggested.