Beyond the Petermann limit: can exceptional points increase sensor precision?

Abstract

Experiments near the lock-in region in maximally dissipative non-Hermitian systems, e.g., conventional laser gyroscopes near the deadband, have run up against the Petermann limit, where excess noise exactly cancels any scale-factor enhancement resulting in no overall enhancement in precision. As a result, one might be tempted to conclude that exceptional points (EPs) generally cannot be used to increase the precision of laser sensors. Indeed, using a linear eigenmode analysis we show that the Petermann limit applies not just to maximally dissipative systems, but for any type of EP, owing to the fact that EPs are rotationally invariant. It turns out, however, that this restriction comes from the assumption of linearity. We find that nonlinearity breaks the rotation symmetry such that the different types of EPs are no longer equivalent above threshold. In particular, for sufficiently high measurement frequencies, EPs in conservatively coupled systems having a saturation imbalance can lead to an increase in the fundamental precision beyond the Petermann limit. Importantly, we find that only one mode lases under these conditions. We show that the beat note can be recovered by interference with an auxiliary mode, but that this has consequences for the quantum and classical noise that depend on the recovery scheme. Thus, it remains to be seen whether practical experiments can be designed that can take advantage of this enhancement.

References in corpus (16)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetric laser-absorber
• Enhanced sensitivity operation of an optical gyroscope near an exceptional point
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Topologically protected midgap states in complex photonic lattices
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Quantum Noise Theory of Exceptional Point Sensors
• No exceptional precision of exceptional point sensors
• Petermann-factor limited sensing near an exceptional point
• Optical realization of relativistic non-Hermitian quantum mechanics
• Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators
• Impact of giant resonant dispersion on the response of intracavity phase interferometry and laser gyros
• Quantum-Noise-Limited Sensitivity-Enhancement of a Passive Optical Cavity by a Fast-Light Medium
• Dispersion enhanced tunability of laser-frequency response to its cavity-length change