Soft-photon emission from electron-pair tunneling in small Josephson junctions

Handel introduced the notion that ultralow-frequency noise for normal electrons (in Brownian motion) arises from Bloch-Nordsieck soft-photon emission. Using instantons, previously shown to arise in the quantum sine-Gordon field theory of an extended Josephson junction capacitor, we show here that copious soft-photon emission exists at the one-loop level of quantum electro-dynamics. This gives rise to noise of the form ${\left(\frac{1}{\omega }\right)}^{(1-\beta )}$ in small Josephson junctions.