Quantum limits on the time-bandwidth product of an optical resonator

TL;DR

This paper investigates the quantum limits of the time-bandwidth product in optical resonators, demonstrating that quantum mechanics and thermodynamics impose fundamental constraints, countering previous claims of surpassing these limits with nonreciprocal optics.

Contribution

It quantizes a proposed nonreciprocal resonator model and shows quantum and thermodynamic principles impose fundamental limits, requiring additional noise or dissipation.

Findings

Quantum mechanics enforces a limit on the time-bandwidth product.

Extra noise or dissipation is necessary in nonreciprocal resonators.

Previous claims of breaking the limit are challenged by quantum and thermodynamic constraints.

Abstract

A thought-provoking proposal by Tsakmakidis et al. [Science 356, 1260 (2017)] suggests that nonreciprocal optics can break a time-bandwidth limit to passive resonators. Here I quantize their resonator model and show that quantum mechanics does impose a limit, or requires extra noise to be added in the same fashion as amplified spontaneous emission in an active resonator. I also use thermodynamics to argue that extra dissipation or noise must be present in their proposed device.