Continuous force and displacement measurement below the standard quantum limit

Abstract

Quantum mechanics dictates that the precision of physical measurements must be subject to certain constraints. In the case of inteferometric displacement measurements, these restrictions impose a 'standard quantum limit' (SQL), which optimally balances the precision of a measurement with its unwanted backaction 1 . To go beyond this limit, one must devise more sophisticated measurement techniques, which either 'evade' the backaction of the measurement 2 , 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 LIGO 5 to ultracold atoms 6 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 9-13 . However, to-date, 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 1.5dB 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.

Quantum Acoustomechanics with a Micromagnet

“…According to the results in Fig. 4, this lies well within the sensitivity range of most state-of-the-art ultra-sensitive micromechanical sensors [32,[42][43][44][45][46], which can even resolve motion on the quantum level [31,47,48]. Thus, the acoustic-induced mode splitting is experimentally measurable.…”

“…It is convenient to define mechanical and acoustic quality factors as Q x ≡ ω x /γ x and Q p ≡ ω p /γ p , respectively. Experimental values for Q x exceed Q x 10 8 both in nanofabricated resonators [28][29][30][31] and levitated systems [32,33]. Regarding Q p , unusually high values (Q p ≈ 10 5 − 10 7 ) have been reported in millimeter-sized Yttrim-Iron-Garnet (YIG) spheres [18,34], but no measurements have been performed for isolated micromagnets of the sizes considered in this article.…”

Nonclassical states of levitated macroscopic objects beyond the ground state

“…Detection of the mechanical squeezing requires a detection of mechanical displacement with sub-shot-noise precision. This can be done by different means, e.g., either by a back-action-evading operation [52], a squeezingenhanced [53] or a variational [54] measurement, or by swapping the mechanical state with the state of a reddetuned pulse [8,11,55] and subsequent optical tomography. Evaluation of this task however goes beyond the scope of the current manuscript.…”

Quantum sensing with nanoparticles for gravimetry: when bigger is better

“…The sensing sensitivity is now set by the SQL where back-action noise caused by photon momentum kicks, and imprecision noise caused by phase fluctuations contribute equally, yielding a displacement readout sensitivity of 2 × σ zpf . However, the SQL does not correspond to a fundamental quantum limit [62]. Methods to read out the mechanical motion whilst minimizing or evading the effects of back-action are known as quantum nondemolition measurements.…”