Dissipative quantum feedback in micro-cavity spectroscopy

Microcavities are used in a wide range of classical and quantum applications, from precision measurements, laser technologies, to control of mechanical motion. The dissipative photon loss via absorption, ubiquitous in any optical cavity, is known to introduce thermo-optical effects and impose fundamental limits on precision measurements. We reveal that such dissipative photon absorption can lead to a quantum feedback, via in-loop field detection of the absorbed optical field, whose field fluctuations can be squashed or anti-squashed. A closed-loop dissipative quantum feedback to the cavity field arises. This modifies the optical cavity susceptibility and causes excess noise and correlations when performing coherent response and quantum optomechanical measurements. We experimentally observe such unanticipated dissipative dynamics in optomechanical spectroscopy of sideband-cooled optomechanical crystals at cryogenic temperature ($\sim$ 8K) and ambient conditions. The dissipative feedback introduces effective modifications to the optical cavity linewidth and the optomechanical scattering rate, and gives rise to excess imprecision noise in the interferometric quantum measurement of mechanical motion. Such dissipative feedback differs fundamentally from a quantum non-demolition feedback, e.g. optical Kerr squeezing. The dissipative feedback itself always results in anti-squeezed out-of-loop optical field, while it can improve the coexisting Kerr squeezing under certain conditions. Our result applies to cavity spectroscopy in both optical and superconducting microwave cavities , and equally applies to any dissipative feedback mechanism of different bandwidth inside the cavity. It has wide-ranging implications for future dissipation engineering, such as dissipation enhanced sideband cooling and Kerr squeezing, quantum frequency conversion, and nonreciprocity in photonic systems.