Fig. 2: Observation of a resonator steady-state response suggesting nonlinear damping.
From: Apparent nonlinear damping triggered by quantum fluctuations
a Measured transmission magnitude ∣S21∣ (dots) for different drive powers. While the shift in resonance frequency is expected from a classical analysis of the damped driven Kerr oscillator using Eq. (2), Min∣S21∣ is expected to remain constant (dashed line). b Measured Min∣S21∣ (dots) as a function of drive power. Eq. (2) yields Min∣S21∣ = ∣1 − κext/(κint + κext)∣, suggesting a damping rate which increases with power \({\kappa }_{{{{{{{{\rm{int}}}}}}}}}\to {\kappa }_{{{{{{{{\rm{int}}}}}}}}}^{{{{{{{{\rm{nl}}}}}}}}}(| a| )\) from \({\kappa }_{{{{{{{{\rm{int}}}}}}}}}^{{{{{{{{\rm{nl}}}}}}}}}=2\pi \times 193\) kHz to \({\kappa }_{{{{{{{{\rm{int}}}}}}}}}^{{{{{{{{\rm{nl}}}}}}}}}=2\pi \times 255\) kHz. Indeed, adding nonlinear damping \({\kappa }_{{{{{{{{\rm{int}}}}}}}}}^{{{{{{{{\rm{nl}}}}}}}}}(| a| )\) to Eq. (2) leads to theoretical predictions (solid lines in a) in good agreement with the data. At the three highlighted points, the expectation values of photon number ∣a∣2 (where the minimum of ∣S21∣ is achieved) are 1.1, 6.8 and 13.2.
