  Infrared heterodyne interferometry has been proposed as a practical
alternative for recombining a large number of telescopes over kilometric
baselines in the mid-infrared. However, the current limited correlation
capacities impose strong restrictions on the sensitivity of this appealing
technique. In this paper, we propose to address the problem of transport and
correlation of wide-bandwidth signals over kilometric distances by introducing
photonic processing in infrared heterodyne interferometry. We describe the
architecture of a photonic double-sideband correlator for two telescopes, along
with the experimental demonstration of this concept on a proof-of-principle
test bed. We demonstrate the \textit{a posteriori} correlation of two infrared
signals previously generated on a two-telescope simulator in a double-sideband
photonic correlator. A degradation of the signal-to-noise ratio of $13\%$,
equivalent to a noise factor $\text{NF}=1.15$, is obtained through the
correlator, and the temporal coherence properties of our input signals are
retrieved from these measurements. Our results demonstrate that photonic
processing can be used to correlate heterodyne signals with a potentially large
increase of detection bandwidth. These developments open the way to photonic
processing of wide bandwidth signals for mid-infrared heterodyne
interferometry, in particular for a large number of telescopes and for direct
imager recombiners.
