  We report systematic measurements of ac-susceptibility,
nuclear-quadrupole-resonance spectrum, and nuclear-spin-lattice-relaxation time
($T_1$) on the pressure ($P$)- induced heavy-fermion (HF) superconductor
CeRhIn$_5$. The temperature ($T$) dependence of $1/T_1$ at $P$ = 1.6 GPa has
revealed that antiferromagnetism (AFM) and superconductivity (SC) coexist
microscopically, exhibiting the respective transition at $T_N = 2.8$ K and
$T^{MF}_c$ = 0.9 K. It is demonstrated that SC does not yield any trace of gap
opening in low-lying excitations below $T_c^{onset} = 2$ K, but $T_c^{MF} =
0.9$ K, followed by a $T_1T$ = const law. These results point to the
unconventional characteristics of SC coexisting with AFM. We highlight that
both of the results deserve theoretical work on the gapless nature in low-lying
excitation spectrum due to the coexistence of AFM and SC and the lack of the
mean-field regime below $T_c^{onset} = 2$ K.
