  The upcoming launch of the James Webb Space Telescope (JWST) means that we
will soon have the capability to characterize the atmospheres of rocky
exoplanets. However, it is still unknown whether such planets orbiting close to
M dwarf stars can retain their atmospheres, or whether high-energy irradiation
from the star will strip the gaseous envelopes from these objects. We present a
new method to detect an atmosphere on a synchronously rotating rocky exoplanet
around a K/M dwarf, by using thermal emission during secondary eclipse to infer
a high dayside albedo that could only be explained by bright clouds. Based on
calculations for plausible surface conditions, we conclude that a high albedo
could be unambiguously interpreted as a signal of an atmosphere for planets
with substellar temperatures of $T_{sub}=$ 410-1250 K. This range corresponds
to equilibrium temperatures of $T_{eq}=$ 300-880 K. We compare the inferred
albedos of eight possible planet surface compositions to cloud albedo
calculations. We determine that a layer of clouds with optical depths greater
than $\tau=0.5$-$7$, would have high enough albedos to be distinguishable from
a bare rock surface. This method of detecting an atmosphere on a rocky planet
is complementary to existing methods for detecting atmospheres, because it
provides a way to detect atmospheres with pressures below 1 bar (e.g. Mars),
which are too tenuous to transport significant heat but thick enough to host
high-albedo clouds.
