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In this study, we conducted a detailed investigation into the time evolutionof the probability density within a 1D double-well potential hosting aBose-Fermi mixture. This system comprised spinless bosons and spin one-halffermions with weak repulsive contact interactions. Notably, even at very loweffective coupling constants, periodic probabilities were observed, indicatingcorrelated tunneling of both bosons and fermions, leading to completemiscibility, which disappears when an external electric field is turned on. Theelectric field accentuated fermion-fermion interactions due to the Pauliexclusion principle, altering both boson density and interactions and leadingto spatial redistribution of particles. These findings underscore the complexinterplay between interactions, external fields, and spatial distributionswithin confined quantum systems.  Our exploration of higher interaction strengths revealed conditions underwhich probability density functions are decoupled. Furthermore, we observedthat increased fermion interaction, driven by the electric field, led to highertunneling frequencies for both species because of the repulsive nature of theboson-fermion interaction. Conversely, increased boson-boson interactionresulted in complete tunneling of both species, especially when boson densitywas high, leading to effective fermion repulsion. Expanding our analysis toscenarios involving four bosons demonstrated that higher interaction valuescorresponded to increased oscillation frequencies in tunneling probabilities.Finally, by manipulating interaction parameters and activating the electricfield, we achieved complete tunneling of both species, further increasingoscillation frequencies and resulting in intervals characterized by overlappingprobability functions.

Influence of a static electric field on a one-dimensional Bose-Fermi mixture confined in a double potential welll