  Non-Hermitian systems having parity-time ($\mathcal {PT}$) symmetry can
undergo a transition, spontaneously breaking the symmetry. Ultracold atomic
gases provide an ideal platform to study interaction effects on the transition.
We consider a model system of $N$ bosons of two components confined in a tight
trap. Radio frequency and laser fields are coupled to the bosons such that the
single particle Non-Hermitian Hamiltonian $h_{\mathcal PT}=-i
\Gamma\sigma_z+J\sigma_x$, which has $\mathcal {PT}$-symmetry, can be simulated
in a \emph{passive} way. We show that when interatomic interactions are tuned
to maintain the symmetry, the $\mathcal {PT}$-symmetry breaking transition is
affected only by the SU(2) variant part of the interactions parameterized by
$\delta g$. We find that the transition point $\Gamma_{\rm tr}$ decreases as
$|\delta g|$ or $N$ increases; in the large $|\delta g|$ limit, $\Gamma_{\rm
tr}$ scales as $\sim|\delta g|^{-(N-1)}$. We also give signatures of the
$\mathcal {PT}$-symmetric and the symmetry breaking phases for the interacting
bosons in experiment.
