# Critical Response of a Quantum van der Pol Oscillator

## TL;DR

This paper investigates the quantum behavior of a driven van der Pol oscillator near critical points, revealing quantum-specific phenomena like negative susceptibilities and enhanced responses, with implications for quantum sensing.

## Contribution

It introduces a quantum model of the van der Pol oscillator and demonstrates quantum effects in its critical response, extending classical nonlinear sensing concepts to the quantum domain.

## Key findings

- Quantum response persists at single quantum level
- Negative and diverging susceptibilities observed at weak drives
- Strong incoherent pumping enhances linear response

## Abstract

Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.