Methods of Enhancing the Stability of Quantum Noise Limited Feedback Oscillators

A feedback oscillator, with an amplifier whose output is partially fed back to its input, provides a stable reference for standardization and synchronization. The laser is a feedback oscillator whose performance can be limited by quantum fluctuations. The resulting frequency instability, quantified by the Schawlow-Townes formula, sets a limit to laser linewidth. Here, we show that the Schawlow-Townes formula applies to feedback oscillators beyond lasers. This is because it arises from quantum noise added by the amplifier and an out-coupler in the feedback loop. Tracing the origin of quantum noise in an oscillator informs techniques to systematically evade it: squeezing and entanglement can enable sub-Schawlow-Townes linewidth feedback oscillators. We clarify the quantum limits to the stability of feedback oscillators, derive a standard quantum limit (SQL) for feedback oscillators, and disclose quantum strategies for realizing sub-SQL-feedback oscillators.