Universality of photon counting below a bifurcation threshold

TL;DR

This paper explores how quantum fluctuations enable photon emission below classical bifurcation thresholds and introduces a universal method to analyze photon counting statistics near such bifurcations, with an experimental proposal using Josephson junctions.

Contribution

It develops a universal approach to derive photon counting statistics near bifurcations based on the Martin-Siggia-Rose action, applicable to various bifurcation types.

Findings

Photon emission occurs below classical bifurcation thresholds due to quantum fluctuations.

A universal method for photon counting statistics near bifurcations is proposed.

Experimental setup with Josephson junctions demonstrates bifurcation behaviors.

Abstract

At a bifurcation point, a small change of a parameter causes a qualitative change in the system. Quantum fluctuations wash out this abrupt transition and enable the emission of quantized energy, which we term photons, below the classical bifurcation threshold. Close to the bifurcation point, the resulting photon counting statistics is determined by the instability. We propose a generic method to derive a characteristic function of photon counting close to a bifurcation threshold that only depends on the dynamics and the type of bifurcation, based on the universality of the Martin-Siggia-Rose action. We provide explicit expressions for the cusp catastrophe without conservation laws. Moreover, we propose an experimental setup using driven Josephson junctions that exhibits both a fold and a pitchfork bifurcation behavior close to a cusp catastrophe.