  The properties of the pion quasiparticle in hot and dense isospin medium,
including the temperature and isospin chemical potential dependence of their
screening mass, pole mass and thermal width, as well as their relationships
with the pion superfluid phase transition, are investigated in the framework of
two-flavor ($N_{f}=2$) soft-wall AdS/QCD models. We extract the screening mass
of the pion from the pole of the spatial two-point Retarded correlation
function. We find that the screening masses of both neutral and charged pions
increase monotonously with the increasing of temperature. However, the isospin
chemical potential $\mu_{I}$ would depress the screening masses of the charged
pions, $m_{\pi^{\pm},\rm{scr}}$. With the increasing of $\mu_{I}$,
$m_{\pi^{\pm},\rm{scr}}$ monotonically decrease to zero on the boundary between
the normal phase and the pion superfluid phase, while the screening mass of the
neutral pion, $m_{\pi^0,\rm{scr}}$, remains almost unchanged. The pole mass
$m_{\rm{pole}}$ and thermal width $\Gamma$ of the pion are extracted from the
pole of temporal two-point Retarded correlation function, i.e., the
corresponding quasi-normal frequencies, $\omega=m_{\rm{pole}}-i\Gamma/2$. The
results show that the pole masses of the three modes ($\pi^0, \pi^+, \pi^-$)
are splitting at finite $\mu_{I}$. The thermal widths of the three modes
monotonically increase with temperature. Furthermore, the pole mass of $\pi^+$
decreases almost linearly with the increasing of $\mu_{I}$ and reaches zero at
$\mu_{I}=\mu_{I}^c$, It means that $\pi^+$ becomes a massless Goldstone boson
of the pion superfluid phase transition.
