Tunable Amplification and Cooling of a Diamond Resonator with a Microscope

Harishankar Jayakumar, Behzad Khanaliloo, David P. Lake, and Paul E. Barclay

Phys. Rev. Applied 16, 014063 – Published 27 July 2021

Abstract

Control of the dynamics of mechanical resonators is central to quantum science and metrology applications. Optomechanical control of diamond resonators is attractive owing to the excellent physical properties of diamond and its ability to host electronic spins that can be coherently coupled to mechanical motion. Using a confocal microscope, we demonstrate tunable amplification and damping of the motion of a diamond nanomechanical resonator. Observation of both normal-mode cooling from room temperature to 80 K and amplification into self-oscillations with $60 μ W$ of optical power is observed via waveguide optomechanical readout. This system is promising for quantum spin optomechanics, as it is predicted to enable optical control of stress-spin coupling with rates of approximately $1$ MHz (100 THz) to ground (excited) states of diamond nitrogen-vacancy centers.

Received 20 February 2021
Accepted 10 March 2021

DOI:https://doi.org/10.1103/PhysRevApplied.16.014063

Physics Subject Headings (PhySH)

Color centers Light-matter interaction Nanophotonics Optomechanics Quantum information with hybrid systems

Micromechanical & nanomechanical oscillators Nanomechanical devices Nitrogen vacancy centers in diamond

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

Harishankar Jayakumar^*,†,‡, Behzad Khanaliloo^†,§, David P. Lake ^¶, and Paul E. Barclay^∥

Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta T2N 1N4, Canada

^*harish@umn.edu
^†These authors contributed equally.
^‡Current address: University of Minnesota, 321 Church Street SE, Minneapolis, Minnesota 55455, USA.
^§Current address: Rockley Photonics Inc.
^¶Current address: California Institute of Technology, 1200 E California Boulevard, Pasadena, California 91125, USA.
^∥pbarclay@ucalgary.ca

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Vol. 16, Iss. 1 — July 2021

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Images

Figure 1
(a) A schematic of the optomechanical system and apparatus. A microscope objective mounted on a piezo stage focuses a green laser onto the sample. The sample and fiber taper are located in a cryostat on nanopositioners. The SEM image shows a diamond nanobeam similar to that used in the experiment, with an illustration of the dimpled optical fiber taper drawn in yellow, in approximately the position used for evanescent coupling to the nanobeam. Also visible are the diamond supports used to stabilize the fiber taper during the measurements. (b) The power spectral density of the fiber-taper transmission near the $v_{1}$ nanobeam mode frequency at room and low temperature. (c) A schematic of the geometry of the optomechanical system.
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Figure 2
(a) A spectrograph showing the power spectral density of the $v_{1}$ nanobeam mode as a function of the microscope focus height, for varying green laser power. The sample is at room temperature. A negative $z_{f}$ indicates that the focal position is below the nanobeam. (b) Optomechanical damping of $v_{1}$ , normalized by its intrinsic dissipation rate, as a function of the focal height and varying power. The fits are from the model in Eq. (1), input with a normalized $I (z_{f})$ profile derived from $Δ f_{m}$ . Contributions from the etalon and microscope gradient terms in Eq. (2) are shown. The shaded regions indicate where optomechanical damping will cause self-oscillation.
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Figure 3
The amplitude (left axis) and maximum internal dynamic stress (right axis) of the $v_{1}$ mode at room temperature as a function of the microscope focal plane height for 2-mW and 3-mW microscope power. The sample is at room temperature. When the nanobeam self-oscillates, a maximum stress just below approximately $100$ MPa near the nanobeam clamping points can be realized. The inset shows the effective normal-mode temperature for 3-mW microscope power as a function of the microscope height, scanning through the regime of maximum damping.
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Figure 4
The nanobeam-microscope optomechanics at cryogenic temperature $T_{s} = 5 K$ : (a) a spectrograph and (b) the oscillation amplitude of the $v_{1}$ nanobeam-mode motion for varying focal plane height, detected via fiber-taper transmission. (c) The power spectral density of the $v_{1}$ -mode motion detected by fiber-taper transmission with the microscope off ( $P_{m} = 0$ mW) and on ( $P_{m} = 3$ mW), with $z_{f}$ optimized to maximize $Δ Γ_{m}$ .
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Figure 5
Exciting in-plane motion: a spectrograph of the fundamental in-plane $h_{1}$ nanobeam-mode motion for a varying lateral focal spot position, detected via fiber-taper transmission. $P_{m} = 420 μ W$ and $T_{s} = 5 K$ .
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Figure 6
Competition between optomechanical back action and thermomechanical line-width broadening. (a) The area under the $h_{1}$ nanobeam-mode spectrum for a varying lateral focal spot position. (b) The corresponding line width extracted by fits to the mode spectrum. Measurements at $P_{m} = 200 μ W$ and $T_{s} = 5 K$ .
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