  We propose and theoretically analyze an experiment where displacement sensing
of an optically levitated nanoparticle in front of a surface can be used to
measure the induced dipole-dipole interaction between the nanoparticle and its
thermal image. This is achieved by using a surface that is transparent to the
trapping light but reflective to infrared radiation, with a reflectivity that
can be time modulated. This dipole-dipole interaction relies on the thermal
radiation emitted by a silica nanoparticle having sufficient temporal coherence
to correlate the reflected radiation with the thermal fluctuations of the
dipole. The resulting force is orders of magnitude stronger than the thermal
gradient force and it strongly depends on the internal temperature of the
nanoparticle for a particle-to-surface distance greater than two micrometers.
We argue that it is experimentally feasible to use displacement sensing of a
levitated nanoparticle in front of a surface as an internal thermometer.
Experimental access to the internal physics of a levitated nanoparticle in
vacuum is crucial to understand the limitations that decoherence poses to
current efforts devoted to prepare a nanoparticle in a macroscopic quantum
superposition state.
