Extended Data Fig. 6: Cavity control of sample dissipations.

a. Schematic representation of the thermal loads on the sample determined by its coupling with the cold finger through the cavity-independent factor \({K}_{\mathrm{ext}-\mathrm{int}}\) and with the photon thermal bath through the cavity-dependent factor \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\). b. Density of states of the solid (peaked at the mode frequency \(\Omega \)) and of the cavity (peaked at multiples of the fundamental mode \({\omega }_{c}\)). The cavity density of states is multiplied by the Boltzmann distribution at the temperature of the photon bath \({{\rm{T}}}_{{\rm{ph}}}\) = 300 K. c. Dependence of the temperature ratio \({{T}_{\mathrm{int}}\left({\omega }_{c},Q\right)/T}_{\mathrm{ext}}\) as a function of the cavity frequency for different temperatures of the cold finger \({{\rm{T}}}_{{\rm{ext}}}\). The absolute temperature renormalization scales with \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\). d. Evolution of the temperature ratio \({{T}_{\mathrm{int}}\left({\omega }_{c},Q\right)/T}_{\mathrm{ext}}\) upon tuning the cavity frequency for different values of the cavity-independent coupling constant \({K}_{\mathrm{ext}-\mathrm{int}}\) at a fixed cold finger temperature \({{\rm{T}}}_{{\rm{ext}}}\) = 80 K. The values of the cavity-independent constant \({K}_{\mathrm{ext}-\mathrm{int}}\) indicated in the legend have been normalized by \({K}_{\mathrm{ph}-\mathrm{int}}({\omega }_{c},Q)\) evaluated at \({\omega }_{c}=\Omega \).