Blackbody-radiation-noise broadening of quantum systems

Precision measurements of quantum systems often seek to probe or must account for the interaction with blackbody radiation. Over the past several decades, much attention has been given to AC Stark shifts and stimulated state transfer. For a blackbody in thermodynamic equilibrium, these two effects are determined by the expectation value of photon number in each mode of the Planck spectrum. Here, we explore how the photon number variance of an equilibrium blackbody generally leads to a parametric broadening of the energy levels of quantum systems that is inversely proportional to the square-root of the blackbody volume. We consider the the effect in two cases which are potentially highly sensitive to this broadening: Rydberg atoms and atomic clocks. We find that even in blackbody volumes as small as 1\,cm$^3$, this effect is unlikely to contribute meaningfully to transition linewidths.