  Recently, the concept of strong light-matter coupling has been demonstrated
in semiconductor structures, and it is poised to revolutionize the design and
implementation of components, including solid state lasers and detectors. We
demonstrate an original nanospectroscopy technique that permits to study the
light-matter interaction in single subwavelength-sized nano-cavities where
far-field spectroscopy is not possible using conventional techniques. We
inserted a thin ($\approx$ 150 nm) polymer layer with negligible absorption in
the mid-IR (5 $\mu$m < $\lambda$ < 12 $\mu$m) inside a metal-insulator-metal
resonant cavity, where a photonic mode and the intersubband transition of a
semiconductor quantum well are strongly coupled. The intersubband transition
peaks at $\lambda$ = 8.3 $\mu$m, and the nano-cavity is overall 270 nm thick.
Acting as a non-perturbative transducer, the polymer layer introduces only a
limited alteration of the optical response while allowing to reveal the optical
power absorbed inside the concealed cavity. Spectroscopy of the cavity losses
is enabled by the polymer thermal expansion due to heat dissipation in the
active part of the cavity, and performed using an atomic force microscope
(AFM). This innovative approach allows the typical anticrossing characteristic
of the polaritonic dispersion to be identified in the cavity loss spectra at
the single nano-resonator level. Results also suggest that near-field coupling
of the external drive field to the top metal patch mediated by a metal-coated
AFM probe tip is possible, and it enables the near-field mapping of the cavity
mode symmetry including in the presence of strong light-matter interaction.
