Optomechanical Magnetometry with a Macroscopic Resonator

We demonstrate a centimeter-scale optomechanical magnetometer based on a crystalline whispering-gallery-mode resonator. The large size of the resonator, with a magnetic-field integration volume of $0.45{\mathrm{cm}}^3$, allows high magnetic-field sensitivity to be achieved in the hertz-to-kilohertz frequency range. A peak sensitivity of $131\mathrm{pT}{\mathrm{Hz}}^{-1/2}$ is reported, in a magnetically unshielded noncryogenic environment using optical power levels beneath $100\mu \mathrm{W}$. Femtotesla-range sensitivity may be possible in future devices with the further optimization of laser noise and the physical structure of the resonator, allowing applications in high-performance magnetometry.

Figure 1

(a) The fabrication process. Black area, ceramic; yellow area, ${\mathrm{CaF}}_2$; gray area, Terfenol-D (Etrema products, Inc.). (b) Optical microscope images of the resonator.

Figure 2

Ringdown measurements. (a) Schematic of the apparatus used to perform the ringdown measurement of the optical-quality factor. FPC, fiber polarization controller; IM, intensity modulator (OC-192 Modulator JDS Uniphase); OSC, oscilloscope (Tektronix TDS 2024B), pulse generator (Stanford DG535), nanomax stage (Thorlabs MDT693A), prism (uncoated N-BK7 right-angle prism), and detector (New Focus Model-1811). (b) Plot of the relative detected optical intensity, with the electro-optic modulator (EOM) used to shutter the optical field at approximately 175 ns. The solid gray curve is an exponential fit to the data over the range 221–454 ns.

Figure 3

A schematic of the experimental setup used to perform magnetic-field sensing. Laser (Koheras Adjustik C15); ISO, isolator (Thorlabs-OFR); EOM, electro-optic modulator (Covega phase modulator); NA, network analyzer (Agilent E5061B); SA, spectrum analyzer (Agilent N9010A); PID, proportional integral derivative controller (New Focus LB1005); BT, bias tee (mini circuits 0.1–4200 MHz); HPF, high-pass filter (mini circuits 0.07–1000 MHz); LPF, low-pass filter (mini circuits dc-1.9 MHz); PS, power splitter (mini circuits 1–650 MHz); and A, amplifier (ZFL-500).

Figure 4

Experimental results. (a) Power spectral density $S(\omega )$ of the error signal at offset frequencies above the 13.6-MHz optical sideband frequency, showing the response an applied magnetic field at 200 kHz. The gray-shaded region indicates the shot noise floor. Inset: Response to the magnetic field as a function of the signal-field strength, with a 330-Hz spectrum analyzer resolution bandwidth. (b) System response $N(\omega )$ measured via network analysis as a function of the applied magnetic-field frequency. (c) Magnetic-field sensitivity $B_{\min }(\omega )$ as a function of frequency. (d) Finite element modeling of mechanical eigenmodes of the device. From left to right, the modes are the fundamental radial breathing mode at 69.8 kHz, a crown mode at 120.4 kHz, and the second-order radial breathing mode at 131.9 kHz. The vertical dashed lines in (a)–(c) show the frequencies of these three modes.