Dissipative and Dispersive Optomechanics in a Nanocavity Torque Sensor

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Dissipative and Dispersive Optomechanics in a Nanocavity Torque Sensor

Marcelo Wu, Aaron C. Hryciw, Chris Healey, David P. Lake, Harishankar Jayakumar, Mark R. Freeman, John P. Davis, and Paul E. Barclay

Phys. Rev. X 4, 021052 – Published 19 June 2014

Abstract

Dissipative and dispersive optomechanical couplings are experimentally observed in a photonic crystal split-beam nanocavity optimized for detecting nanoscale sources of torque. Dissipative coupling of up to approximately 500 MHz/nm and dispersive coupling of 2 GHz/nm enable measurements of sub-pg torsional and cantileverlike mechanical resonances with a thermally limited torque detection sensitivity of $1.2 \times 1 0^{- 20} Nm / \sqrt{Hz}$ in ambient conditions and $1.3 \times 1 0^{- 21} Nm / \sqrt{Hz}$ in low vacuum. Interference between optomechanical coupling mechanisms is observed to enhance detection sensitivity and generate a mechanical-mode-dependent optomechanical wavelength response.

Received 25 March 2014

DOI:https://doi.org/10.1103/PhysRevX.4.021052

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Marcelo Wu^1,2, Aaron C. Hryciw², Chris Healey^1,2, David P. Lake¹, Harishankar Jayakumar¹, Mark R. Freeman^2,3, John P. Davis³, and Paul E. Barclay^1,2,*

¹Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta T2N 1N4, Canada
²National Institute for Nanotechnology, Edmonton, Alberta T6G 2M9, Canada
³Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E9, Canada

^*pbarclay@ucalgary.ca

Popular Summary

In recent years, optical cavities—wherein light follows a closed path—have proven to be remarkable tools for nanoscale experiments. Cavity optomechanics uses light to measure and control the motion of optical resonators. By amplifying the interaction between light and mechanical vibrations, cavity-optomechanical sensors have recently enabled unprecedented sensitivity in measuring minute displacements of on-chip devices. These sensors can be used for detecting environmental stimuli such as acceleration, measuring small fields, and sensing particles, which have applications in diverse areas of physics and engineering. We describe the fabrication and optimization of an optomechanical sensor for detecting small amounts of torque using dissipative coupling, a new effect that has been discussed theoretically but has not—before now—been used for torque sensing.

Optomechanical sensors generally rely on dispersive coupling, in which the displacement of the mechanical device changes the wavelength of its optical resonance. This signal is amplified by the cavity before being transmitted to the output. In our case, we use an optical fiber to both input light into the device and collect the signal at the output. We use two nanomechanical resonators, which serve as optical mirrors that can move independently. Our device also allows its displacement to affect the length of time that light stays inside the cavity. Furthermore, the proximity of the optical fiber to the cavity plays a role by influencing how the light is transmitted. Both of these effects, collectively referred to as dissipative coupling, are imprinted on the output as an enhancement in the original signal. Using both dispersive and dissipative coupling effects, we have achieved an order-of-magnitude improvement in torque sensitivity in ambient conditions and in vacuum.

The record torque sensitivity exhibited by this device will be useful for studying magnetic materials and sensing magnetic fields. Furthermore, moving to the low-temperature regime will further increase the sensitivity of the nanocavity.

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Vol. 4, Iss. 2 — April - June 2014

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Figure 1
(a) Scanning electron micrograph of a split-beam nanocavity. Top left inset: Top view of the nanocavity overlaid with the field distribution ( $E_{y}$ ) of the optical mode. Left inset: 60-nm-wide nanocavity central gap. Right inset: Gap separating the suspended nanobeam from the device layer. Inset scale bars: 500 nm. (b) Displacement fields of split-beam nanocavitymechanical modes of interest. Dotted arrows indicate the position and direction of torque for efficient actuation.
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Figure 2
Illustration of the effect of mechanical displacement on the optical response of a cavity with (left) dispersive, (center) dissipative intrinsic, and (right) dissipative external optomechanical coupling. (a) Change in the resonance line shape. (b) Amplitude of the optomechanically actuated signal.
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Figure 3
(a) ${\bar{S}}_{VV} (λ, ω)$ in ambient conditions, with the fiber taper hovering approximately 300 nm above the nanocavity; $T (λ)$ is superimposed in white. Right side in white: ${\bar{S}}_{VV} (λ_{b}, ω)$ at $λ_{b}$ indicated by the blue line. (b) Blue (green) data: Calibrated displacement spectrum $S_{x x}^{1 / 2}$ of $T_{y}$ ( $T_{z}$ ), when the fiber taper is touching the anchored mirror, with $λ$ set at the blue (green) line in (a). Dotted lines indicate the noise floor. Red data: Uncalibrated displacement spectrum of $C$ with the taper touching the suspended mirror. Black data: Vacuum measurement of the displacement spectrum, uncalibrated. Left inset: Highlight of $T_{y}$ ( $Q_{m} = 1800$ ) in vacuum. Top right inset: $T (λ)$ with a fiber-touching device.
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Figure 4
(a) ${\bar{S}}_{VV}^{1 / 2} (λ, ω = ω_{m})$ of the $C$ and $T_{y, z}$ modes. The grey line is scaled as $d T (λ) / d λ$ . (b)–(d) Fit (black line) of the optomechanical coupling model to the ${\bar{S}}_{VV}^{1 / 2} (λ, ω = ω_{m})$ of the (b) $T_{y}$ , (c) $T_{z}$ , and (d) $C$ modes. The dashed colored lines indicate relative contributions from dispersive, external dissipative, and intrinsic dissipative couplings. (e)–(g) Comparison between fit values (black points) and numerically simulated values (shaded regions) of $g_{OM}$ , $g_{i}$ , and $g_{e}$ . The widths of the colored boxes represent numerically simulated ranges due to fabrication imperfections.
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Figure 5
Change in optical transmission due to (a) dispersive, (b) intrinsic dissipative, and (c) external dissipative optomechanical couplings, respectively. (d) Relative strength of the three contributions: $\partial T / \partial Δ$ , $\partial T / \partial γ_{i}$ , and $\partial T / \partial γ_{e}$ . (e) Comparative strength when contributions are brought to similar amplitudes. The Fano modification is omitted for display purposes.
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Figure 6
Numerical simulation of the coefficients $g_{OM}$ and $g_{i}$ from finite-element simulations (comsol). The dashed line $g_{OM}$ data are calculated directly from $ω (x)$ . $g_{i}$ is calculated from $γ_{i} (x)$ . All other data points are calculated perturbatively. (a) Dependence of $g_{OM}$ (left axis) and $g_{i}$ (right axis) of the torsional mode $T_{z}$ on the variation in the gap size $d$ . The shaded area corresponds to uncertainty in the gap ( $\pm 5 nm$ ) due to fabrication tolerances and scanning electron micrograph image resolution. (b) Fiber-induced dispersive optomechanical coupling coefficient $g_{OM}$ of the out-of-plane modes $T_{y}$ and $C$ . The shaded area indicates the uncertainty of the fiber height $h$ . Larger $g_{OM}$ values at higher $h$ are due to limited finite-element resolution. (c) Dependence of $g_{OM}$ (left axis) and $g_{i}$ (right axis) for out-of-plane modes on the vertical offset of the suspended mirror. The shaded area corresponds to a region of uncertainty ( $\pm 25 nm$ ) in the vertical position of the suspended mirror due to postfabrication stresses and substrate effects.
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