A Generalized Schawlow-Townes Limit

TL;DR

This paper generalizes the Schawlow-Townes limit for feedback oscillators, showing how quantum mechanics and causality set fundamental spectral purity bounds, which can be surpassed through quantum engineering techniques.

Contribution

It introduces a generalized Schawlow-Townes limit applicable to a broad class of feedback oscillators, extending the standard quantum limit.

Findings

Realized bad-cavity oscillators can saturate the generalized limit.

Quantum engineering like spin squeezing can surpass this limit.

The spectral purity is fundamentally constrained by quantum mechanics and causality.

Abstract

We study a class of a feedback oscillators realized by a phase-insensitive amplifier in positive feedback, where either the amplifier or the feedback element may determine the oscillator's linewidth. The spectral purity of the output of such a device originates from basic demands of quantum mechanics and causality. The resulting expression generalizes the Schawlow-Townes limit, which is itself one component of a standard quantum limit for feedback oscillators. Recently realized bad-cavity oscillators such as super-radiant lasers and solid-state masers can saturate this generalized Schawlow-Townes limit. This limit can be surpassed through appropriate quantum engineering: for example by atomic spin squeezing in a super-radiant laser.