Quantum Fluctuations in the Equilibrium State of a Thin Superconducting Loop

TL;DR

This paper investigates how quantum fluctuations influence the supercurrent oscillations in a superconducting loop with a Josephson junction, revealing suppression and smearing effects that depend on loop size and fluctuation strength.

Contribution

It provides a detailed analysis of quantum fluctuation effects on supercurrent oscillations, including amplitude suppression and shape changes, in superconducting loops of various sizes.

Findings

Quantum fluctuations suppress supercurrent oscillation amplitude.

Smearing of saw-tooth dependence due to fluctuations.

Power-law relation between current amplitude and junction conductance.

Abstract

We study the oscillatory flux dependence of the supercurrent in a thin superconducting loop, closed by a Josephson junction. Quantum fluctuations of the order parameter in the loop affect the shape and renormalize the amplitude of the supercurrent oscillations. In a short loop, the amplitude of the sinusoidal flux dependence is suppressed. In a large loop, the supercurrent shows a saw-tooth dependence on flux in the classical limit. Quantum fluctuations not only suppress the amplitude of the oscillations, but also smear the cusps of the saw-tooth dependence. The oscillations approach a sinusoidal form with increasing fluctuation strength. At any finite length of the loop, the renormalized current amplitude is finite. This amplitude shows a power-law dependence on the junction conductance, with an exponent depending on the low-frequency impedance of the loop.