Comment on “Absence of a Dissipative Quantum Phase Transition in Josephson Junctions”

Authors: Pertti J. Hakonen and Edouard B. Sonin

Physical Review X 11, 018001 (2021)

Abstract: Recently, Murani et al. [1] questioned the existence of the dissipative quantum phase transition (DQPT) in a single Josephson junction (JJ) predicted nearly 40 years ago [2,3]. This conclusion is based on misperception of the principles underlying the DQPT theory.

First, we recall in a nutshell the basics of the DQPT theory. The DQPT is a joint effect of Coulomb interaction, dissipation, and quantum mechanics. The Coulomb blockade makes the JJ an insulator at small bias. However, it is effective only if the Coulomb energy $E_C\sim e^2/C$ exceeds the quantum-mechanical uncertainty $\hslash /\tau$, where $\tau =R_{s}C$ is the time of the charge relaxation in the circuit. Here, $C$ is the capacitance of the JJ, and $R_s$ is the shunt resistance. The condition $E_C\sim \hslash /\tau$ agrees with the condition $R_s=R_q$, where the DQPT was predicted [2,3] (the dashed line in Fig. 1). Here, $R_q=h/4e^2$ is the quantum resistance. The existence of the DQPT has been supported by experimental work [4–9], and possible applications for qubits have been discussed [10].

DOI: https://doi.org/10.1103/PhysRevX.11.018001