Tunneling Dynamics Of A Bose-fermi Mixture In A Double Well Coupled With An Optical Microcavity

This paper mainly studies the effect of tunneling dynamics on a Bose-Fermi mixture coupled with a single-mode optical microcavity field in a double well. The main contents of the research include two aspects. Firstly, a few bosons (about10) and a single fermion in a double well coupled with an optical cavity were explored, and then we discussed the influence of optical microcavity on particals tunneling preferentially. Secondly, the number of bosons and fermions in atomic systems are104～106, then the tunneling dynamics of a Bose-Fermi mixture in a double well coupled with an optical microcavity were explored.In the beginning we make a brief introduction to the general knowledge and basic models used in this paper, such as Bose distribution, Jaynes-Cummings model, two-mode approximation, mean-field theroy and Bose-Hubbard model.In the first work, we investigate the tunneling dynamics of a Bose-Josephson junction with a single fermion impurity coupled with a optical cavity using the two-mode approximation. Tilting the double-well potential, the boson and fermion should tunnel from one well to the other. The question is which particle will tunnel first. We find that it depends on the interaction between these particles when there is no coupling between Bose-Josephson junction and the cavity. Coupling with the optical cavity, which particle will tunnel first is not only related to the interaction between the particles, but also related to the interaction between the optical cavity and particles. It is shown that the optical cavity can help particles to tunnel from one well to the other, which particle can be helped depends on the value of the coupling. The optical cavity coupling can effect the expected value of the relative number difference. Comparing to bosons, the fermion was affected more observably.In the second work, beginning with the Schrodinger equations of the Bose-Fermi mixture in a double well coupled with a cavity, we deduce the time evolution expression for the particle and the photon operator. Then an effective classical Hamiltonian for this system is derived, and its dynamics is investigated from the perspective of the phase portrait. It is shown that the strong condensate-cavity interplay does alter the dynamics of the system drastically. We find that the evolution of the relative number difference can be controlled by the interaction between fermions and the ones between bosons and fermions, respectively; The coupling with the cavity adds more stable points to the system. The motional mode increases and the chaos can be enhanced accordingly.