Hard-core Bose-Fermi Mixtures In One-Dimensional Split Wells

In recent years in the field of condensed matter physics of cold atoms, one-dimensional strongly interacting ultra-cold atom systems have attracted extensive research interests both in theories and experiments. In the many-body quantum system, the strong interaction between particles and low-dimensional system with geometric symmetry amplify the quantum fluctuation and correlation of the system. Experimentally, one-dimensional system can be achieved by using two perpendicular laser beams and the Feshbach resonance technique is adopted to adjust the effective interaction between atoms.In physics, a Tonks-Girardeau gas is a Bose-Einstein Condensate in which the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to lower the energy the system would have to avoid overlap in space, showing features characteristics of fermions. The system wave function, due to the exchange in coordinate space between bosons satisfying the symmetry while the exchange between fermions satisfying anti-symmetry, is linked through the unit anti-commutation operator. This is the so-called Bose-Fermi mapping.In this paper, the density profiles and momentum distributions of the Bose-Fermi mixture, confined in one-dimensional infinite square potential well and the harmonic oscillator potential well both with a tunable intermediate 8 potential barrier, are discussed. Through the Bose-Fermi mapping and numerical calculation, we find that the reduced single-particle density, momentum distribution and natural orbital of the system are related to the 8 barrier strength and the total particle number. The emergence of second peaks in momentum distribution shows a remarkable correlation between particles on both side of the split.