  We study the effect of the electromagnetic environment on the resonance
frequency of plasmonic excitations in dimers of interacting metallic
nanoparticles. The coupling between plasmons and vacuum electromagnetic
fluctuations induces a shift in the resonance frequencies (analogous to the
Lamb shift in atomic physics) which is usually not measurable in an isolated
nanoparticle. In contrast, we show that this shift leads to sizable corrections
to the level splitting induced by dipolar interactions in nanoparticle dimers.
For the system parameters which we consider in this work, the ratio between the
level splitting for the longitudinal and transverse hybridized modes takes a
universal form dependent only on the interparticle distance and thus is highly
insensitive to the precise fabrication details of the two nanoparticles. We
discuss the possibility to successfully perform the proposed measurement using
state-of-the-art nanoplasmonic architectures.
