  Bulk FeSe is superconducting with a critical temperature $T_c$ $\cong$ 8 K
and SrTiO$_3$ is insulating in nature, yet high-temperature superconductivity
has been reported at the interface between a single-layer FeSe and SrTiO$_3$.
Angle resolved photoemission spectroscopy and scanning tunneling microscopy
measurements observe a gap opening at the Fermi surface below $\approx$ 60 K.
Elucidating the microscopic properties and understanding the pairing mechanism
of single-layer FeSe is of utmost importance as it is a basic building block of
iron-based superconductors. Here, we use the low-energy muon spin
rotation/relaxation technique (LE-$\mu$SR) to detect and quantify the
supercarrier density and determine the gap symmetry in FeSe grown on SrTiO$_3$
(100). Measurements in applied field show a temperature dependent broadening of
the field distribution below $\sim$ 60 K, reflecting the superconducting
transition and formation of a vortex state. Zero field measurements rule out
the presence of magnetism of static or fluctuating origin. From the
inhomogeneous field distribution, we determine an effective sheet supercarrier
density $n_s^{2D} \simeq 6 \times 10^{14}$ cm$^{-2}$ at $T \rightarrow 0$ K,
which is a factor of 4 larger than expected from ARPES measurements of the
excess electron count per Fe of 1 monolayer (ML) FeSe. The temperature
dependence of the superfluid density $n_s(T)$ can be well described down to
$\sim$ 10 K by simple s-wave BCS, indicating a rather clean superconducting
phase with a gap of 10.2(1.1) meV. The result is a clear indication of the
gradual formation of a two dimensional vortex lattice existing over the entire
large FeSe/STO interface and provides unambiguous evidence for robust
superconductivity below 60 K in ultrathin FeSe.
