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arXiv:1405.4767 · Optica

Ultrasensitive measurement of microcantilever displacement below the shot-noise limit

Raphael C. Pooser, Benjamin J. Lawrie

Published Apr 21, 2015• 193 citations
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Abstract

The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate the first direct measurement of a MEMS cantilever displacement with a noise floor at 40% of the shot noise limit (SNL). By combining multi-spatial-mode quantum light sources with a simple differential measurement, we show that sub-SNL MEMS displacement sensitivity is highly accessible compared to previous efforts that measured the displacement of macroscopic mirrors with very distinct spatial structures crafted with multiple optical parametric amplifiers and locking loops. These results support a new class of quantum MEMS sensor with an ultimate signal to noise ratio determined by quantum correlations, enabling ultra-trace sensing, imaging, and microscopy applications in which signals were previously obscured by shot noise.

DOI
10.1364/optica.2.000393

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The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate the first direct measurement of a MEMS cantilever displacement with a noise floor at 40% of the shot noise limit (SNL). By combining multi-spatial-mode quantum light sources with a simple differential measurement, we show that sub-SNL MEMS displacement sensitivity is highly accessible compared to previous efforts that measured the displacement of macroscopic mirrors with very distinct spatial structures crafted with multiple optical parametric amplifiers and locking loops. These results support a new class of quantum MEMS sensor with an ultimate signal to noise ratio determined by quantum correlations, enabling ultra-trace sensing, imaging, and microscopy applications in which signals were previously obscured by shot noise.
Plasmonic sensors are important detectors of biochemical trace compounds, but those that utilize optical readout are approaching their absolute limits of detection as defined by the Heisenberg uncertainty principle in both differential intensity and phase readout. However, the use of more general minimum uncertainty states in the form of squeezed light can push the noise floor in these sensors below the shot noise limit (SNL) in one analysis variable at the expense of another. Here, we demonstrate a quantum plasmonic sensor whose noise floor is reduced below the SNL in order to perform index of refraction measurements with sensitivities unobtainable with classical plasmonic sensors. The increased signal-to-noise ratio can result in faster detection of analyte concentrations that were previously lost in the noise. These benefits are the hallmarks of a sensor exploiting quantum readout fields in order to manipulate the limits of the Heisenberg uncertainty principle.
We consider the quantum and classical noise limits to position measurement and force detection by an atomic force microscope (AFM) with an optical readout of cantilever position. We model this by treating the cantilever as a perfectly reflecting mirror for a highly damped optical cavity. There are three sources of noise: the shot noise in the output laser measurement, the thermal noise in the cantilever, and the measurement back-action noise. This last source of noise becomes large for good measurements, measurements for which there is a high correlation between the output phase of the light and the changing position of the cantilever. The back action simultaneously drives a diffusion process in momentum and diagonalizes the cantilever state in the position basis. This latter result is ``state reduction.'' Explicit expressions for the rate of the measurement back action in terms of the device parameters are given. We also calculate the signal-to-noise ratio in the limit of a bad cavity. A comparison to recent experiments suggests that current AFMs are not quantum limited.
The minimum resolvable signal in sensing and metrology platforms that rely on optical readout fields is increasingly constrained by the standard quantum limit, which is determined by the sum of photon shot noise and back-action noise. A combination of back-action and shot noise reduction techniques will be critical to the development of the next generation of sensors for applications ranging from high-energy physics to biochemistry and for novel microscopy platforms capable of resolving material properties that were previously obscured by quantum noise. This Perspective reviews the dramatic advances made in the use of squeezed light for sub-shot-noise quantum sensing in recent years and highlights emerging applications that enable new science based on signals that would otherwise be obscured by noise at the standard quantum limit.
Tracking small transverse displacements of an optical beam with ultra-high accuracy is a fundamental problem underlying numerous important applications ranging from pointing, acquisition and tracking for establishing a lasercom link, to atomic force microscopy for imaging with atomic-scale resolution. Determining what is the optimal quantum-optical probe and the best achievable sensitivity of measuring a small transverse optical beam displacement, is the fundamental question central to these sensing schemes. By mapping this problem to an array of nested Mach-Zehnder interferometers, we explicitly construct the optimal probe state. It is entangled across the spatial modes allowed within the Fresnel number product of the propagation geometry, and entangled across the temporal modes within the time-bandwidth product of the optical probe. We show that the optimal sensitivity of measuring the beam displacement achieves a Heisenberg limited scaling over both the number of temporal modes and the average number of photons transmitted per mode. Surprisingly, we discover a sub-Heisenberg limited scaling over the number of available spatial modes. To qualify the quantum enhancement, we also establish the optimal sensitivity of a classical-light probe, which gives shot-noise limit over both the number of temporal modes and the number of photons per mode, and Heisenberg limited scaling over the number of spatial modes. Finally, we construct an explicit design for quantum-enhanced beam tracking, which uses a Gaussian (multi-mode-entangled squeezed-state) probe and a Gaussian (multi-mode homodyne) receiver.