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We study a mixture of $N_{b}$ bosons with point hard-core boson-bosoninteractions and $N_{f}$ noninteracting spinless fermions with point hard-coreboson-fermion interactions in 1D optical lattice with external harmonic confinepotential. Using an extended Jordan-Winger transformation (JWT) which maps thehard-core Bose-Fermi mixture into two component noninteracting spinlessfermions with hard-core interactions between them, we get the ground states ofthe system. Then we determine in details the one particle density matrix,density profile, momentum distribution, the natural orbitals and theiroccupations based on the constructed ground state wavefunctions. We alsodiscuss the ground state properties of the system with large but finiteinteractions which lead to the lift of ground degeneracy. Our results showthat, although the total density profile is almost not affected, thedistributions for bosons and fermions strongly depend on the relativestrengthes of boson-boson interactions and boson-fermion interactions.

Bose-Fermi mixture in one-dimensional optical lattices with hard-core interactions