Tunneling Dynamics And Phase Transition Of A Bose-fermi Mixture In A Double Well

The coherent nonlinear tunneling dynamics of ultracold boson-fermion mixture in asymmetric double-well potential is studied in this paper. Four types of phase are foundfor the mixture. The first one is two species localizing in diferent potential wells. Thesecond one is two species coexisting in the same well. The third one is two species equallypopulated in two wells. The fourth one is one species equally populated in two wellswhile the other species is in one well. The phase transitions among these four states havebeen investigated. The interspecies and intraspecies interactions as well as bosonic andfermionic numbers can dramatically afect these phase transitions.In addition, loading a boson-fermion mixture in a double-well potential, due to theinterspecies interaction, will provide us with a system for investigating the dynamic be-havior of two coupled nonlinear oscillators. we study the collective dynamics of boson-fermion mixture in a symmetric double-well potential and find measure synchronization(MS), phase synchronization (PS), local measure synchronization (LMS), nonlocal mea-sure synchronization (NLMS) and complete synchronization (CS). The transitions be-tween diferent synchronizations depend largely on the interspecies interaction strengthswhich are experimentally adjustable. Dependence of the two diferent critical value ofcoupling strength Ubfon intraspecies interaction strengths Uband Ufis found clearly asoccurence of diferent synchronizations.