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Quantum optical sensors are ubiquitous in various fields of research, frombiological or medical sensors to large-scale experiments searching for darkmatter or gravitational waves. Gravitational-wave detectors have been verysuccessful in implementing cavities and quantum squeezed light for enhancingsensitivity to signals from black hole or neutron star mergers. However, thesensitivity to weak forces is limited by available energy and opticaldecoherence in the system. Here, we derive the fundamental sensitivity limit ofcavity and squeezed-light enhanced interferometers with optical loss.This limitis attained by the optimal use of an additional internal squeeze operation,which allows to mitigate readout loss. We demonstrate the application ofinternal squeezing to various scenarios and confirm that it indeed allows toreach the best sensitivity in cavity and squeezed-light enhanced linear forcesensors. Our work establishes the groundwork for the future development ofoptimal sensors in real-world scenarios where, up until now, the application ofsqueezed light was curtailed by various sources of decoherence.

Fundamental sensitivity limit of lossy cavity-enhanced interferometers with external and internal squeezing