Quantum limits for stationary force sensing

State-of-the-art sensors of force, motion and magnetic fields have reached the sensitivity where quantum noise meter is significant or even dominant. In particular, best optomechanical devices has Standard Quantum Limit (SQL), which directly follows from Heisenberg uncertainty relation corresponds to balancing measurement imprecision perturbation probe by back action meter. The SQL not truly fundamental several methods for its overcoming been proposed demonstrated. At same time, two constraints are more known. first limit arises finiteness probing strength (in case optical interferometers - circulating power) known as Energetic or, in a general context, Cram\'{e}r-Rao Bound (QCRB). second dissipative dynamics probe, prevents full efficacy evasion techniques developed SQL. No particular name assigned this limit; we propose term Dissipative (DQL) it. Here develop unified theory these limits deriving constraint they follow cases. Our analysis reveals phase transition occurring at boundary between QCRB-dominated DQL regimes, manifested discontinuous derivatives optimal spectral densities field noise. This leads counter-intuitive (but favorable) finding that quantum-limited can be achieved with certain lossy systems. Finally, show originates non-autocommutativity internal thermal it overcome non-stationary measurements.