Continuous force and displacement measurement below the standard quantum limit

Abstract

Quantum mechanics dictates that the precision of physical measurements must always comply with certain noise constraints. In the case of interferometric displacement measurements, these restrictions impose a standard quantum limit (SQL), which optimally balances the precision of a measurement with its unwanted backaction¹. To go beyond this limit, one must devise more sophisticated measurement techniques, which either ‘evade’ the backaction of the measurement² or achieve clever cancellation of the unwanted noise at the detector^3,4. In the half-century since the SQL was established, systems ranging from LIGO⁵ to ultracold atoms⁶ and nanomechanical devices^7,8 have pushed displacement measurements towards this limit, and a variety of sub-SQL techniques have been tested in proof-of-principle experiments^{9,10,11,12,13}. However, so far, no experimental system has successfully demonstrated an interferometric displacement measurement with sensitivity (including all relevant noise sources—thermal, backaction and imprecision) below the SQL. Here, we exploit strong quantum correlations in an ultracoherent optomechanical system to demonstrate off-resonant force and displacement sensitivity reaching 1.5 dB below the SQL. This achieves an outstanding goal in mechanical quantum sensing and further enhances the prospects of using such devices for state-of-the-art force sensing applications.