Black-body radiation shift: Δν_BBR ∝ −⟨α⟩·T⁴ (Stark from thermal photons)

At non-zero ambient temperature, thermal black-body photons exert an AC Stark shift on the atomic clock transition, Δν_BBR = −Δα·⟨E²⟩_BBR/(2h), where Δα is the differential polarisability between clock levels and ⟨E²⟩_BBR ∝ T⁴ from…