Standard quantum limits for broadband position measurement

I utilize the Caves-Milburn model for continuous position measurements to formulate a broadband version of the standard quantum limit (SQL) for monitoring the position of a free mass and illustrate the use of Kalman filtering to recover the SQL for estimating a weak classical force that acts on a quantum-mechanical test particle under continuous observation. These derivations are intended to clarify the interpretation of SQL’s in the context of broadband quantum measurement, with particular attention paid to the question of how it might be possible to verify that a given laboratory measurement does indeed achieve backaction-limited sensitivity. The method used to analyze force detection may be extended to the case of weak classical forces with arbitrary time dependence, including nonstationary and impulsive signals.