  Sensitive microwave detectors are critical instruments in radioastronomy,
dark matter axion searches, and superconducting quantum information science.
The conventional strategy towards higher-sensitivity bolometry is to
nanofabricate an ever-smaller device to augment the thermal response. However,
this direction is increasingly more difficult to obtain efficient photon
coupling and maintain the material properties in a device with a large
surface-to-volume ratio. Here we advance this concept to an ultimately thin
bolometric sensor based on monolayer graphene. To utilize its minute electronic
specific heat and thermal conductivity, we develop a
superconductor-graphene-superconductor (SGS) Josephson junction bolometer
embedded in a microwave resonator of resonant frequency 7.9 GHz with over 99\%
coupling efficiency. From the dependence of the Josephson switching current on
the operating temperature, charge density, input power, and frequency, we
demonstrate a noise equivalent power (NEP) of 7 $\times 10^{-19}$ W/Hz$^{1/2}$,
corresponding to an energy resolution of one single photon at 32 GHz and
reaching the fundamental limit imposed by intrinsic thermal fluctuation at 0.19
K.
