Thermodynamic sensing of quantum nonlinear noise correlations

We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity (WC) or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the WC of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields.