  In this paper we study a mixed system of bosons and fermions with up to six
particles in total. All particles are assumed to have the same mass. The
two-body interactions are repulsive and are assumed to have equal strength in
both the Bose-Bose and the Fermi-Boson channels. The particles are confined
externally by a harmonic oscillator one-body potential. For the case of four
particles, two identical fermions and two identical bosons, we focus on the
strongly interacting regime and analyze the system using both an analytical
approach and DMRG calculations using a discrete version of the underlying
continuum Hamiltonian. This provides us with insight into both the ground state
and the manifold of excited states that are almost degenerate for large
interaction strength. Our results show great variation in the density profiles
for bosons and fermions in different states for strongly interacting mixtures.
By moving to slightly larger systems, we find that the ground state of balanced
mixtures of four to six particles tends to separate bosons and fermions for
strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi
mixtures we find pronounced odd-even effects in systems of five particles.
These few-body results suggest that question of phase separation in
one-dimensional confined mixtures are very sensitive to system composition,
both for the ground state and the excited states.

Quantum Gases;Quantum Physics