  One-dimensional spinor gases with strong delta interaction fermionize and
form a spin chain. The spatial degrees of freedom of this atom chain can be
described by a mapping to spinless noninteracting fermions and the spin degrees
of freedom are described by a spin-chain model with nearest-neighbor
interactions. Here, we compute momentum and occupation-number distributions of
up to 16 strongly interacting spinor fermions and bosons as a function of their
spin imbalance, the strength of an externally applied magnetic field gradient,
the length of their spin, and for different excited states of the multiplet. We
show that the ground-state momentum distributions resemble those of the
corresponding noninteracting systems, apart from flat background distributions,
which extend to high momenta. Moreover, we show that the spin order of the spin
chain---in particular antiferromagnetic spin order---may be deduced from the
momentum and occupation-number distributions of the system. Finally, we present
efficient numerical methods for the calculation of the single-particle
densities and one-body density matrix elements and of the local exchange
coefficients of the spin chain for large systems containing more than 20
strongly interacting particles in arbitrary confining potentials.

Quantum Gases